mechanika 2006

Mechanical Engineering Students’ AssociationDepartment of Mechanical Engineering

Mechanical Engineering Annual Magazine

Vol. I March 2006

[email protected]/mesa

EditorsRahul SwarnkarDeepak Kumar

Mechanika

Indian Institute of Technology GuwahatiMechanical Engineering Students’ AssociationDepartment of Mechanical Engineering

Mechanical Engineering Students’ Association Indian Institute of Technology Guwahati

MECHANIKA The Mechanical Engineering Magazine

INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI

www.iitg.ernet.in/mesa

FROM THE DESK OF HEAD OF DEPARTMENT

March 30, 2006 IITG Campus

It’s a matter of great pleasure that Mechanical Engineering Students’ Association in our department is publishing the First Edition of its annual magazine. The magazine shares the knowledge of the different conventional & emerging fields of mechanical engineering through its technical articles alongwith general articles which serve as a basis for career of the students. I congratulate the entire working body of MESA, especially the publication committee for this grand success. I am also thankful to the faculty members of the department for their motivation and cooperation. I am confident that MESA, with this pace and desire, will always achieve its goals. I wish all the best to MESA in its future endeavours.

Dr P S Robi

HOD, ME

MESSAGE FROM THE FACULTY ADVISOR, MESA


It is a matter of great pleasure to me that Mechanical Engineering Students' Association (MESA); IIT-Guwahati is going to publish the 1st edition of its annual magazine. At this stage, I would rather recall George Bernard Shaw’s statement, “If you have an idea, and I have an idea, and we exchange these ideas, then each of us will have two ideas”. The articles presented in this magazine has drawn upon a diverge range of skills and experiences from faculties and students of Mechanical Engineering (ME) Department. In this way, it is an endeavor to share the knowledge about the updates in various fields of engineering and technology through meaningful articles. It also covers the research contributions from the students of ME-Department at UG and PG levels. I express my sincere thanks to Dr. P. S. Robi (HOD) and my colleagues of department for their valuable suggestions and financial support for the magazine. I congratulate all the members of MESA, especially the publication committee for this great success. Suggestions for improvement of this magazine are most welcome and would be incorporated in the next edition with a view to make this magazine more useful.

Dr.Niranjan Sahoo Faculty Advisor, MESA

MESSAGE FROM THE PRESIDENT, MESA

March 30, 2006

IITG Campus Welcome, MESA, a spirit embarked few years ago, with the aim to strengthen the integrity among future mechanical engineers, is now turning into a big success. With all the enthusiasm and hard work delivered by its members, MESA has a very bright future for sure. Considering our active involvement in spreading technical knowledge & personality development of students, the department has given us official status of Students’ Association at the beginning of current academic year (2005-06). Adding another feather in our hat, I am pleased that the first edition of MESA’s annual magazine “Mechanika” is out in IITG Campus. Right from 2nd year students to faculty members, various authors have contributed a wide spectrum of articles in this magazine. The magazine provides an overview to different fields of mechanical engineering through its meaningful articles alongwith technical papers based on the current research work going on at IIT Guwahati. I congratulate all members of MESA, especially the publication committee for this great success. My message is to work even harder in the future and not to stop at such laurels. I would like to thank our faculty advisor, Dr Niranjan Sahoo for his valuable advice. Further, with due regards to all faculty members for their kind support, faculty involvement in the activities of MESA has been our greatest achievement so far. I cannot skip thanking our Vice-President, Mr. Deepak Kumar, who has been on his toes to make this magazine happen. MESA is acting as a bridge between official academic curriculum and practical world.

Rahul Swarnkar President, MESA

MESSAGE FROM THE VICE PRESIDENT, MESA


Few years back some of our seniors dreamt of an association to provide a platform for mechanical engineering students to exchange their ideas and knowledge. This dream has now turned into Mechanical Engineering Students’ Association (MESA), which is now the biggest students’ association at IIT Guwahati in terms of number of members and activities. I am glad to say that MESA is publishing the first edition of its annual magazine. This magazine, Mechanika, is the biggest achievement of this academic year for our association. Students from B.Tech and M.Tech as well as some faculty members have contributed articles for this magazine. I take the pleasure to congratulate all the members of MESA for this initiation and achievement. Also, I am cordially thankful to Dr. Niranjan Sahoo, the faculty advisor of MESA, and other faculty members of the department for their cooperation. In addition, I would like to thank and appreciate the persistent efforts of our President, Mr. Rahul Swarnkar, who has been involved in this publication right from article collection to editing and the final design of the magazine. I hope this magazine will be a source of inspiration for the coming working body of MESA. Finally, I wish MESA all the best for its success in future. I hope this reincarnate association will soon realize its entire goals.

Deepak Kumar

Vice President, MESA

Index Latest Trends in Computational Fluid Dynamics and Heat Transfer, A look at the Lattice-Boltzmann Method : Tanuj kush ………………………………………………………………..……………………

(1)

It is raining cats and dogs!!: G. V. Anoop………………………………..………………………………………… (3) Aerospace Vehicles- A brief Introduction: Dr. Niranjan sahoo …………………………………………… (6) Logistics and Supply Chain Management – New Opportunities for Technically Qualified Professionals: Prof. Narayan Rangaraj………………………………………………………………..……………

(9)

International Heat and Mass Transfer Conference: Alok Verma…………………………………………. (11) Artificial Neural Networks and their Applications: Dr. U S Dixit …………….………………………… (13) Numerical Solution of Sod’s Shock Tube Problem by Van Leer Method: Deepak Kumar, Vivek Kumar………………………………………………………………………………………………….………………

(17)

Buoyancy Assisting Mixed Convection in Two-Dimensional Laminar Plane Wall Jet Flow: K Kumar Raja……………………………………………………………………………………………………………………

(22)

Higher Order Solution of the Euler Equations on Unstructured Meshes using Polynomial Reconstruction : Mohamed Yousuf A .U. , Gundeti Lavan Kumar ………………………………………

(29)

Microfluidics-An Introduction: Punit Chhabra…………………………………………………………………. (33) Placement Details….…………….………………………………………………………………………………………… (35) B.Tech Projects ……………………………………………………………………………………………………………… (36) M.Tech Projects ……………………………………………………………………………………………..……………… (38) Publication by Students………………………………………………………………….………….…………………… (40) Seventh Convocation……………………………………………………………………………………………………… (41) Activities of MESA………………………………………………………….……………………………………………… (43) Working Members………………………………………………………………………………….……………………… (44)

Mechanika, Mechanical Engineering Students’ Association, Indian Institute of Technology Guwahati

MARCH 2006. MECHANIKA 1

LATEST TRENDS IN COMPUTATIONAL FLUID DYNAMICS AND HEAT TRANSFER

A LOOK AT THE LATTICE-BOLTZMANN METHOD

Tanuj Kush Final year, B.Tech 2006 Batch, Dept. of Mechanical Engineering

Indian Institute of Technology Guwahati

One of the newest methods to have caused a stir in the scientific community is the lattice – Boltzmann method (LBM) which is gaining a wide acceptance throughout the world as a computationally cheaper alternative to its elder cousin, the Finite Volume Method (FVM). For the neophyte, the FVM is a well-established method to model as well as simulate flow fields. These flow fields may range from something as simple as the flow of water through a pipe to something as complex as the flow past a high performance aircraft at large Mach numbers. As the name suggests, this method also employs a lattice, which can be thought of to be analogous to the control volume employed in the FVM. The method involves, in brief, a set of discrete directions in which the microscopic particles (which may be thought of as analogous to macro-molecules) are allowed to propagate and carry with them heat flux, momentum and the like. In propagating, they are also allowed to collide with one another thereby transferring momentum and bringing about pressure gradients. The rules governing these propagation and collision steps are designed such that the time average motion is consistent with the Navier Stokes equations. Indeed, researchers have shown that these microscopic equations can be modified to yield the Navier Stokes Equations in a macroscopic scale. This method gains its fundamentals from the Boltzmann equation which is inherently microscopic in nature. This equation has been used in many forms with different names, with the most common being the one which uses a uniform grid, unit time step and a relaxation model,

( ) ( ) iiii trfe

ttrf

Ω=∇⋅+∂

∂,

, r

where if is the particle distribution function (PDF) similar to a probability distribution parameter. The parameter ier is the velocity in the ith discrete direction along which the PDFs are allowed to propagate and collide. The term

iΩ signifies the relaxation model used. The relaxation can be physically interpreted as the time that the particle is given to transfer its flux to its neighboring particle and come to an equilibrium state. This is further exemplified by the commonly used BGK model wherein, a single relaxation time τ is used,

( ) ( )[ ]trftrf iii ,,1 )0(−−=Ωτ

with the zero superscript representing the equilibrium PDFs. The solution algorithm offers no extra complexities as one may expect. This then, further adds to the usability of the LBM. The algorithm simply consists of repeatedly colliding and then streaming the PDFs as per the computational domain and the boundary conditions. A simple two step solution algorithm is thus applied which is the crux of the lattice-Boltzmann method.

As the latest PDFs are obtained, the corresponding physical quantities like flow velocities, pressure, temperature etc. as per the demands of the flow problem can be calculated.

Initial conditions

Collision step

Propagation step

Update PDFs

Run till timeachieved



The method involves more of statistical physics than fluid mechanics, as all investigations are done at the micro level. However, when it was noticed that the results could be obtained at the macroscopic level, researchers began spending more time to develop this technique. The LBM however, has seen significant growth only in the last couple of decades where it was applied to all sorts of fluid flow problems including compressible flow, turbulence modeling, two phase flow, particle laden flow and even some bio-medical flow like flow of blood through a stenotic artery. The LBM is not just limited to modeling fluid flows. It has also been demonstrated to be highly useful while modeling heat transfer applications, typically ones that involve a fair level of complexity like multiphase flow, conjugate heat transfer etc. The application of the LBM to heat transfer though, has not picked up the same momentum yet. With only patches of researchers all over the world working on this, development of the LBM for heat transfer applications can best be described as embryonic. As a matter of fact, a good amount of pioneering work in the same is being conducted here, at the IIT Guwahati. This work includes, in brief, application to conjugate heat transfer, two phase flow, flow with varying thermo-physical properties etc. One of the recent applications of the LBM here at the IIT Guwahati has been in solving the basic parabolic heat conduction equations in one, two and three dimensions with a range of boundary conditions, to show the applicability and versatility of the LBM. This work illustrated that the LBM produces second order accurate results with considerably less CPU clock times, lesser number of iterations and a solution procedure far simpler than the FDM/FVM approach. Some of the rather attractive advantages that the LBM has to offer are that it easily accommodates a variety of boundary conditions that have always befuddled scientists. Some of these include an accurate representation of wall fluxes with steep gradients, inflow and outflow conditions and the like. Lesser convergence times, lesser computational resources and effective parallelization all bolster the case at hand. The LBM is favored for use on parallel computers because it only requires the

information of its immediately adjacent neighbours for every computation. Also, like conventional FVM techniques, this method can also be implemented on complex grids to handle complex geometries. Some of these include computations on non-uniform unstructured grids with triangular or quadrilateral grid lattices. To sum up, this method has, in the past decades, shown true promise and potential and will soon be a major competitor to the conventional FVM platform. However, this will require a lot of research and development on the part of its patrons. (The author is involved in application and validation of this method to unstructured grids by solving the conjugate heat transfer problem in two dimensions. For any queries, please contact the author at [email protected]) REFERENCES: 1. D. A. Wolf-Gladrow, Lattice-Gas Cellular

Automata and Lattice Boltzmann Models: An Introduction, Springer-Verlag, Berlin-Heidelberg, 2000.

2. S. Succi, The Lattice Boltzmann Method for Fluid Dynamics and Beyond, Oxford University Press, 2001.

3. S. C. Mishra, A. Lankadasu and K. Beronov, Application of the lattice Boltzmann method for solving the energy equation of a 2-D transient conduction-radiation problem, Int. J. Heat Mass Transfer, (in press) 2005

WEB LITERATURES: 4. http://www.lstm.uni-

erlangen.de/~thzeiser/lb_e.html 5. http://www.phys.jyu.fi/research/dismat/Flui

d/Lattice.html 6. http://research.nianet.org/~luo/HPCC-

LBE_1999.html



IT IS RAINING CATS AND DOGS!!

G. V. Anoop

The author is a final year Computer Science student. He topped CAT-2005 and has calls from all IIMs

Mr. A seemed a very very strong force for CAT-2005. He had the golden work experience, did very well in all his mock tests - was always among the top 30 in the country – and was dominating competition in a very competitive zone of the country, Delhi. Come D-day with the number of questions reducing to double-digits for the first time ever, Mr. A was unnerved. Within a couple of hours, all his dreams had turned to ashes and he merged into the hordes of unsuccessful aspirants.

CAT – A Changing Aptitude Test. To quote the oft-quoted statement “The only thing permanent about CAT is change”. So what does one do in a constantly unpredictable environment? One, have a strong attack on all fronts. Two, have no fixed mindset. CAT generally tends to be more a battle of the human psychology. Half the battle is won in your mind. Every mock test is a potential enemy, sowing doubts about your ability to perform; like a virus, that doubt is very quick to spread its effects once it settles.

So, all you CATters out there, the first thing to do is to sincerely believe that you can crack CAT. Come on people, you are all truly the best brains of the country. It is no fluke that you are all here. Each one of you has the aptitude for two people to share and simultaneously crack CAT. So, first get that killer punch inside your head.

What CAT does require however is discipline and analysis. It does require a significant amount of analysis after each test to examine your problem areas; examine previous trends and then sit down and iron out your flaws. I shall proceed to give an overview of the general preparation graph of a typical aspirant. THE PRELIMINARY STAGE– PREPARATION This involves going through the nitty-gritty of things and familiarizing yourself and the general

questions that are asked in the test. It would involve getting back in touch with all those old formulae and the grammar rules. Maths and DI should prove fairly straightforward in this stage. The material of the coaching institutes contains tips for faster solving of problems and also a collection of all the formulae that you would need for the test. Go through these diligently and work out these problems to increase your comfort level. More important, solve the exercises within the time limits given. Also, go through each topic and do not leave out any topic. The English section is different in its approach. Primary in everyone’s mind here are the dreaded Wordlists. A good vocabulary is needed in CAT – no second thoughts about it. The process unfortunately involves broadening your range of words. Wordlists provide the readymade solution – boring yes; but also effective. If you can find anything else that will provide the same effect of broadening your word base, please by all means, go ahead. Wordlists are just that – a readymade convenient way of solving the problem at hand. They are in no way a compulsion for preparation. The other aspects of the English section are once again handled by the material of the institutes. They provide ample practice and are effective. Reading Comprehension (RC) is a different story altogether. Please again do remember that on the average, one has to attempt at least 3 RC’s in the exam to have a chance of a decent relative score. Develop the habit of reading various kinds of articles to prepare yourself for the fast skimming that is required for a RC. Also keep in mind that the English section is the best scoring section for many people around the country and you will have to score higher than normal to keep your hopes afloat.



PART TWO – MOCK TESTS They represent the bulk of the preparation for CAT. They hold tremendous information on your strengths and weaknesses in a particular area. Properly analyzed and corrections made, there is no one to stop you on your way. A serious CAT aspirant generally takes plenty of tests, around 25 in general, to continually fine-tune his strategy and also to develop new ways of solving problems effectively. They give feedback on the ideal time division for the three sections – varies from each candidate-to-candidate. People generally adopt a 40-40-40 minute approach for all three sections. Differ from this if you are certain of your strength in any section. It is imperative to remember that there cannot be any ego clashes or weak decision making here i.e. let’s assume you have completed your 40 minutes of Verbal and are a minute into a RC. You cannot convince yourself into completing that RC and thus cutting back on any other section. Do this only if you are extremely sure of your ability to score in the other sections in spite of the reduced time. For the record, my strategy was a 35-45-40 corresponding to the order English-Math’s-DI. In the actual exam, it changed to a 37-45-38 strategy. Try the strategy of browsing through the paper when it is given to you initially for the first 2 to 3 minutes. The objective of this is to just get an intuitive feel of the relative strengths of the sections. You could draft up your strategy here with some flexibility to absorb unexpected shocks. Of course, you must have the ability to sum up the level of the paper just at first glance. For this, you need practice and a comfort level with the general type of questions. After the test, analyze your tests. I keep repeating this point in the hope that its importance gets across. Look at the classification of problems – the coaching institutes classify the problems as ‘Easy’, ‘Moderate’, and ‘Speed breaker’. Analyze your problem selection and the areas where you got stuck. Look at previous trends in that area – Were you always weak in this area? Are the scores improving? By area, I mean every sub-

division i.e. Geometry, Graphs, Paragraph Rearrangement etc. MISCELLANEOUS TIPS There is no end to the number of tips that a candidate can receive. CAT solving is composed of a number of self-made rules to identify easy scoring questions. It is needless to say that these rules depend entirely and vary for each candidate. Nevertheless, there are some general tips, which by and large apply to the candidates – those that I have been fortunate enough to learn from my experiences this year. Foremost among these is the necessity to read the maximum number of questions – in other words, attempt to minimize the number of questions that you are unable to even read in the two hours. There have been infinite instances of “Ooh, Aah, This was so easy and I didn’t even read it!!” In the general scenario of a cutoff of 9-10 marks, and you unable to read two three easy questions, the resulting feeling is one of inexpressible pain. Trust me, it is not pleasant and it hurts a lot. Two, develop the ability to detach yourself from a problem which you cannot solve at that time – do this irrespective of the time that you had already spent on the problem. Have no regrets and memories – forget it once you move away. That problem is history. The Math’s section is generally the section with absolute-easy questions hidden in a maze of complex questions. Search out these questions. For all the candidates, attempting DI in the end, you might want to consider attempting Data Sufficiency questions at the end, since they are simple in nature and less taxing on the brain rather than a complete DI set taking 5-6 minutes. CONCLUSION As I stated earlier, there is no dearth of small microscopic tips that you could receive which would hopefully enable you to gain that extra mark. It is analogous to gaining that extra few tenths of a second in a race. Do actively re-examine your strategies and your problem selections. There are always patterns that you



can discern which will enable you to inch ahead. And finally, do remember to keep your belief in yourself. 70% of candidates accept defeat in their minds by October. Do not join this group; keep chipping away. These all sound like quotes being mouthed by your grandmother but I cannot emphasize their importance. All that I have said above has been experienced personally. So dispel the doubt from your minds, replenish your self-confidence and march ahead. Success is just around the corner. All the very best!!



AEROSPACE VEHICLES: A BRIEF INTRODUCTION

Dr. Niranjan Sahoo

Assistant Professor, Department of Mechanical Engineering Indian Institute of Technology Guwahati

The beauty and regularity of heavenly bodies have fascinated people from time immemorial. In the heaven, the earth sparkles like lovely blue and green jewel in the velvety darkness of space with countless stars shining all around. Since the beginning of the history, man has yearned to reach for the heaven. Long before flight was thought possible; man’s thirst for flight was motivated by the ‘wings of eagles and birds flying in the sky’. Man’s dream of breaking the barriers of earth and soaring to heaven was fulfilled when Wright brothers proved “man could fly”. The revolutionary inventions of first airplane flight by Wright brothers on the eventful day of December 17, 1903 has motivated the man to conquer formidable challenges relating to the mystery of flying. Since then, many advances in air travel have evolved with small steps forward rather than giant leaps. In many instances, predictions for future start with projecting what evolutionary improvements will develop from what is flying in the sky today. There is a saying by aviation experts: ‘Requirements push and Technology pulls’. The requirements of new missions drive the engineers and scientists to work on the leading edge technology to find solutions to the problems posed by even more demanding requirements through invention. The technology pulls forward ‘break through’ to develop new aircraft around the globe. The past four decades have seen major flights cruising from subsonic to hypersonic speeds. The most routine flights made possible when American Jet Transport started its first flight (Boeing-707) on October 26, 1958 cruising at Mach 0.7. Traveling at speeds faster than sound speed and thus breaking ‘Sound Barrier’ became reality with the taste of supersonic travel from London to Bahrain in the aircraft ‘Concorde’ commenced by British airways on January 21, 1976. On November 22, 1977, the first ever-fastest commercial passenger aircraft ‘Concorde’ with its cruising altitude 60,000ft at Mach 2 crossed Atlantic Ocean from London to

New York little less than 3.5 hours as opposed to about eight hours for a subsonic flight. Now the age of ‘hypersonic flight’ is about to dawn airliners and re-entry vehicles. The first such major landmark has been achieved after the launch of USSR satellite SPUTNIK-II on November 3, 1957. It was the first man-made earth satellite that carried living organism (a dog named LAIKA) into the space and remained in orbit till April 13, 1958. In the bumper year of 1961, Yuri Gagarin (USSR) became the first man in the history to fly in space with an orbital space craft VOSTAK-I that entered the earth atmosphere at Mach 25 on April 12. His safe return from the space has inspired the future objectives of hypersonic flight. In the same year i.e. on June 23, U.S. air force test pilot Major R. White accomplished the concept of ‘miles per second’ flight in an X-15 airplane by flying at Mach 5.3. White again extended this record with same X-15 flight at Mach 6. Since 1961, major space programs carried out by U.S. space agency NASA and Indian Space Research Organization (ISRO) have achieved milestones in the development of satellites and aero-assisted space transfer vehicles. Some of the developmental activities are listed in Table 1 and 2. In addition to the above activities, there are independent and separate research programs by each country in the areas of missile technology and satellite launch vehicles that are invariably linked to the hypersonic flow regime. On hypersonic vehicle design and research Townend (1991) lists three recurrent themes:

• Replacement of ballistic space launchers with reusable aerospace planes.

• Hypersonic airliners • Transatmospheric orbital transfer

vehicles. These can be attributed to many space programs like British HOTOL-single stage to orbit studies, German SANGER-two stage aerospace plane



and Japanese HOPE. In the Indian scenario of missile technology, the concept of hypersonic reusable plane AVTAR has shown renewed interest because it is capable of performing as missile and satellite launcher for manned and unmanned vehicle in the range of Mach 4 to 8. The first ever prototype hypersonic commercial aircraft that can circumnavigate the globe in less than four hours is yet to come in reality. NASA in collaboration with Boeing (the world’s largest aircraft builder) has designed the future generation Hyper-X experimental plane (X-43A) to fly as fast as Mach 10 using scramjet engines (Graham 2002). The pace with which X-programs are launched has picked up in recent years with an emphasis on demonstrating technology for unmanned air vehicles and reusable launch vehicles (Wilson 1999). Another new hypersonic vehicle concept (Gene et al. 1987) is the aero-assisted orbital transfer vehicle (AOTV) flying at Mach 30 at an altitude of 76 km. It is designed to transport material and people between the space shuttle in low earth

orbit (about 300 km above the surface of earth) and satellites in geo-synchronous orbit (about 35,000 km above the earth). When AOTV leaves geo-synchronous orbit and returns to low earth orbit, it dips into the earth atmosphere and uses aerodynamic drag to reduce its velocity, thus enabling rendezvous with space shuttle. References

• Graham W (2002) X-planes advance. Flight International, 6-12 August: 31-35.

• Gene PM, Kelvin GB, John FW, Carol BD (1987) Aerothermodynamic heating and performance analysis of a high-lift aeromaneuvering AOTV concept. AIAA Journal of Spacecraft and Rockets 24 (3): 198-204.

• Wilson JR (1999) X-33 and RLV take parallel paths. Aerospace America, February: 38-42.

• Internet sites: http://www.nasa.gov, http://www.isro.org

Table 1: NASA’s manned space program

Space crafts/ Orbiter fleet

Year of launch

No. of flights/mission Mission objectives

1. Mercury* 1961-1963 6 To orbit a manned spacecraft around earth and to investigate man’s ability to function in space.

2. Gemini* 1965-1966 10 To perform earth’s reentry and landing at pre-selected point on the land.

3. Apollo* 1968-1972 11 Scientific exploration of moon and man’s capability to work in lunar environment.

4.Skylab Programs

1973-1974 3 First experimental space station to perform medical experiments on human adaptability on zero gravity.

5. Space Shuttles 1981-Till date 113 (a) Columbia

1981-2003

29 Orbital flight test programs and manned space missions dedicated to medical research.

(b) Challenger 1983-1985 9 Reusable winged space ship mission.

(c) Discovery 1984-2002 30 Deployment of communication satellite.

(d) Atlantis 1985-2002 26

Launching of Galileo inter-planetary probe to Jupiter.

(e) Endeavour 1992-2002 19 Reusable winged space ship mission.

* Spacecrafts Courtesy: http://www.nasa.gov



Table 2: Indian Space Programs

* Satellites Courtesy: http://www.isro.org

Satellites/ Launch Vehicles

Year of launch

No. of flights/mission Mission objectives

1. Aryabhata* 1975

1 First Indian satellite providing technological experience in building and operating satellite system.

2. Bhaskara* 1979-1981 2 Experimental remote sensing satellite. 3. APPLE*

1981 1 First experimental geo-stationary communication satellite.

4. Rohini* 1979-1983

4 Measuring in-flight performance of launch vehicle.

5. SROSS* 1987-1994 4 Performance monitoring of launch vehicles.

6. IRS* 1988-2000 8 Operational remote sensing satellites.

7. INSAT* 1982-2002 7 Operational communication satellites.

8. Launch vehicles

(a) SLV 1979-1983 4 Orbited ‘Rohini’ satellites in space.

(b) ASLV 1987-1994 4 Orbited ‘SROSS’ satellites in space.

(c) PSLV 1993-1999 5 Orbited ‘IRS’, Korean satellite ‘KITSAT’ & German satellite ‘TUBSAT’ into space.

(d) GSLV-D1

2001

1 Orbited experimental communication satellite GSAT-1 in geo-synchronous orbit.

(e) GSLV-D2 2003 1 Orbited experimental communication satellite GSAT-2 in geo-synchronous orbit.



LOGISTICS AND SUPPLY CHAIN MANAGEMENT – NEW OPPORTUNITIES FOR

TECHNICALLY QUALIFIED PROFESSIONALS

Narayan Rangaraj Visiting Professor, Department of Mechanical Engineering, IIT Guwahati Professor, Industrial Engineering and Operations Research, IIT Bombay

Young minds are attracted to the logic and sometimes the rigour of scientific training and those with a ‘practical’ bent of mind are attracted to technology and its possibilities. With further opening of one’s world-view, management as a career also becomes an attractive option. But apart from a generic qualification, the type of training and outlook that one sees in a good engineering or science curriculum does not seem to have anything to do with what management is all about (managing people, resources, organizations, finance etc.) This article is an attempt to point out some technically challenging areas, which definitely qualify under the term ‘management’, but which have a strong role and space for analysis, and in some cases, fairly rigorous methods and application of scientific principles, together with the mature view of business and society that a manager should have. In the world of manufactured products, it is now seen that product design should meet the functional requirements of intended customers from the design stage itself (not just at the time of marketing a product). This has led to techniques such as quality function deployment, where the voice of customer preferences is formally brought in at an early stage. It has also now been acknowledged that for cost effectiveness, manufacturing processes need to be considered at the time of design, and that has led to paradigms of design for manufacture, concurrent engineering, and collaborative design and manufacture (when multiple high quality suppliers are involved). We take this a step further to highlight that design of products and analysis of manufacturing processes need to be accompanied by a design of the procurement, production and distribution system that is demanded of the product by the market. An early term for the study of this system, under the manufacturing umbrella, was that of Industrial Engineering. This term, although now

not so fashionable, is actually increasingly relevant in the world of management and system design. Its quantitative counterpart Operations Research (or Operational Research in British terminology) is undergoing a renaissance and rediscovery. If one begins to list the issues that must be addressed for a (well)-engineered product to be manufactured and meet the customer’s requirement at a competitive cost, it would be a long list indeed. [Try it!]. A basic one is that of deciding on what to manufacture and what to procure, and therefore, where to manufacture and where to procure from. Does a cycle manufacturer in the south who plans to supply to northern markets do so with an existing plant in the south, or open a new one in the north? Even if there are scale economies of pure manufacture (say, assembly), does it make logistical sense to procure components from the north, assemble in the south and sell in the north? For example, Japan imports iron ore from India, transports it to Japan, manufactures high quality steel, and sells it all over the world. This must make logistical sense for the strategy to succeed. If this tricky question is settled in the medium run, how is the chain of activities and firms managed in the short run? What is a strategy of how much to procure for several locations from several sources? Consider a manufacturer of consumer goods, where there are multiple sources (subcontractors) with various costs of production, costs of transport (which include fixed as well as variable costs), capacities of production and other factors such as reliability of production and transport. These problems, especially if addressed formally in modern information-technology based management systems, are highly technical in their content. Even if there is a human judgmental element in the final decision, the basic analysis is non-trivial and requires modeling, computation, analysis and of course, a fit with the management processes of the organization.



There are techniques of optimization, probabilistic analysis and sometimes simulation and scenario analysis, which address these. In the shorter run, there are a number of problems of inventory management, with various decisions to do with frequency of ordering, quantities of order, well-thought-out provision of stocks at various locations to take care of uncertainties and market opportunities. Supporting these decisions are forecasting, inventory theory, and statistical analysis of data related to sales, lost demand, unsold stocks, leakages and anomalies and other sources of profits or costs. Similar issues arise in the service industry, whether it is to do with call center staffing models, health care system design or travel and transport planning. For example, consider an owner of a fleet of trucks, who receives a request for supplying trucks at some location at a certain cost. Should she accept the bid? Not easy to answer, if the assets (trucks) are multipurpose and need to be available at the right place and right time to take advantage of alternate opportunities. A live, recent example of the issues in logistics and supply chain management is the supply of food grain and agricultural supplies in the North East, during the Bihu festival period of high demand. Traders speculate on demands and prices that they can command. The railways, as a carrier, are wittingly or unwittingly used in this speculation, and their wagons are not unloaded in normal time as part of the strategy of hoarding (in commodities other than food grains, this would be a perfectly valid scheme of supply demand imbalance and ‘discovering’ true prices in the market). As a response (and also to answer warranted and sometimes unwarranted criticism from the government and the public), the railways temporarily raised the demurrage rates (penalty for holding on to these rates and their adjustment over time are highly specialized tasks, requiring probabilistic analysis of medium and long horizon costs of operating a contract between shippers and carriers. So a contract, from being a legal document to facilitate trade, has become a strategic management wagons beyond a specified allowance), to disincentivize

traders who for speculative reasons were causing delays in unloading. The setting of tool, with implications on the costs of operations, market success and business decisions, overall. India is undergoing a revolution in retailing, global participation in many supply chain categories, some aspects of infrastructure (Roads, for example) and management thinking. There would be good opportunities for engineers, scientists and others to play a role in this. The Inland Container Depot at Amingaon, the railway siding at Changsari and perhaps the customs point at the Bangladesh border at Dhubri are likely to be places of exciting developments in the days to come, so keep your eyes open and ears peeled! In short, in the area of logistics and supply chain management, there are a number of technical opportunities for professionals, which benefit from a scientific view of a system, with an engineering feel for practical business processes. This has to be tempered with some view of economics, a clear grasp of the potential of information technology and other disciplines. All this makes it challenging, but over a period of time, the firms (and governments) who address these challenges and decisions will succeed.



18th NATIONAL & 7th ISHMT-ASME

HEAT AND MASS TRANSFER CONFERENCE 4-6 Jan, 2006

Alok Verma,, B.Tech 2nd Year, Department of Mechanical Engineering


In January this year IITG organized the 18th National and 7th ISHMT-ASME Heat and Mass Transfer Conference. The conference was jointly organized under the auspices of The Indian Society for Heat and Mass Transfer (ISHMT) and American Society of Mechanical Engineers (ASME). The conference was organized with an aim of bringing together a number of leading experts of the world on a common platform to speak and outline their vision on the frontier research activities in this area. The conference had been a phenomenal success. In terms of magnitude, the numbers of papers and participants, this conference was almost double than the previous heat and mass transfer conferences. According to the statistics, a total of 365 research papers, including 2 plenary and 17 keynote papers were presented and more than 400 leading researchers from academia, R&D organizations from 20 different countries participated in this mega heat and mass transfer event. Not lagging behind were the industries which in order to complement with the research and development taking place in academic institutions and R&D laboratories, showed an equal enthusiasm to participate in the proceedings of the conference. This gala began on 4th January, in the newly built indoor stadium, with the invocation and lighting of the inaugural lamp by the Chief Guest (Prof. R. Natarajan) and other members. This was followed by welcome address by the organizing secretary Prof. S.C Mishra. Later Prof. G Barua (Director IITG) and Shri A. K. Saikia (Chairman, BOG, IITG) expressed their excitements on IITG organizing this huge conference and wished for its success. Following this Prof. S. V. Garimella (ASME representative) and Prof S.P.Venkateshan

(Chairman of the conference) addressed the participants. The inaugural ceremony ended with an inspiring speech by the chief guest Prof. R. Natarajan.

The proceedings of the conference began with a plenary lecture on A thermal engineering approach to low temperature biology and medicine by Boris Rubinsky, University of California Berkeley, USA; followed by Plenary cum endowment lecture on Experiments in desalination by A.E. Muthunayagam, Kerala State Council for Science, Technology and Environment, India. The post lunch session of the day one saw many eminent scientists delivering keynote lectures on various issues of concern in the field of heat and mass transfer. These included Thermal challenges in the semiconductor industry by Ravi Mahajan, Intel Corporation, USA; New understanding of convective heat transfer enhancement and its engineering applications by W.Q. Tao, Xi'an Jiaotong University, CHINA; Recent advances in transcritical CO2 cycle technology by Eckhard Groll, Purdue University, USA; Advances in fuel cell research by Rowland P. Travis, Imperial College London, UK and many more. After tea there was paper presentation in the form of posters. On day 1 about 135 papers were presented in H1 and H2.



After this busy and hectic day of lectures, presentations, etc, the participants welcomed the little break they got in the evening, they were seen roaming around in the NAC, library building, get into small chit chat with fellow students and appreciating the beauty of the campus. In night they were entertained with a Cultural Program by Dr. Vidyadhar Prasad Mishra, Allahabad University and Bihu Dance (Assamese Special) by a famous group in the indoor stadium. The audience were taken by the breathtaking intricate moves by the dancers. The guests were later treated with delicious delicacies in dinner at the IIT Guesthouse.

Day 2 began with the keynote lectures on Spectral remote sensing for furnaces and flames by Tae-Ho Song, Korea Advanced Institute of Science and Technology, KOREA; Advances in heat flux and high temperature instrumentation by S.V. Subba Rao, VSSC, Trivandrum, INDIA; Air cooling in electronic systems: Have fundamental limits finally been reached? by Alfonso Ortega, University of Arizona, USA.

In the afternoon there was an industrial session which included the active participation by some giant organizations in public and private sector like Aditya Birla group, BHEL, Ansys, Fluent, Subros Ltd. Following this was ISHMT General Body Meeting in Senate Hall. Later in the evening, there was presentation of 110 research papers in poster form in H1 and H2 (NAC). In the night the participants were entertained by the world famous Ranganiketan - Manipuri Cultural Arts Troupe. The group has over the years performed over 200 shows in more than 20 countries around the globe. A whopping crowd of 2500 (members of IITG

community and guests) watched the show. It left everyone there mesmerized and left a long lasting impression of the rich culture that the northeast region has.

The last day of this grand gala began with keynote lecture on Radiative heat transfer in nano to mega-scale systems by Shigenao Maruyama, Tohoku University, Japan. It was followed by more lectures on Impingement cooling with free-surface liquid jets by John H. Lienhard, Massachusetts Institute of Technology, USA; Heat transfer from rotating systems by B.V.S.S.S. Prasad, IIT Madras, India; Gas-liquid two-phase flow in micro channels: the effects of gas-liquid injection methods by Masahiro Kawaji, University of Toronto, CANADA; Heat transfer and fluid flow issues in the Indian nuclear reactors of the next decade by S. K. Gupta, Atomic Energy Regulatory Board, Mumbai. Following tea there was presentation of 101 papers in poster form in H1&H2 (NAC). The conference came to an end with a Valedictory Function in senate hall followed by a lunch at IIT Guesthouse.

On the financial side, the conference had been supported by many government agencies and private organization. Aditya Birla Group, Mumbai; North Eastern Council, Shillong; All India Council for Technical Education, New Delhi are some of the major sponsors. Some other sponsors are Atomic Energy Regulatory Board, Mumbai; L&T Ltd, Mumbai; NPC, Mumbai; CSIR, New Delhi; National Science Foundation, USA; Fluent India Pvt. Ltd; BHEL, Tiruchirapalli; Department of Science & Technology, New Delhi. In this field of sponsorship academic institutions were not lagging behind, some of institutions that provided supports were VIT, Vellore; IIT Kharagpur; IIT Delhi; IIT Kanpur; IIT Madras. IITG had a plan to hold this conference earlier in 2001. Since the development of infrastructure took its own time, it was in 2006 that IITG managed to hold this Conference. The painstaking efforts of the entire IITG community made the 18th NATIONAL & 7th ISHMT-ASME Heat and Mass Transfer Conference a phenomenal success.



ARTIFICAL NEURAL NETWORKS AND THEIR APPLICATIONS

Dr. U.S. Dixit

Associate Professor, Department of Mechanical Engineering Indian Institute of Technology Guwahati

Artificial Neural Networks have been applied in a number of areas of engineering, medicine and social science. These networks have been developed in an effort to emulate the capabilities of human brain. The popular applications of neural networks include pattern recognition and predicting the outcome of physical processes. Neural networks are often considered as an alternative to physical modeling tools like Finite Element Methods etc. In this article, apart from describing some of the popular applications, the directions have been provided for using neural networks in conjunction with various computational techniques. In this form, the neural networks complement the physics based numerical methods rather than competing with them. 1. INTRODUCTION Artificial neural networks can be defined as a model of reasoning based on the human brain [1]. They can also be understood as networks for finding out an approximate function relating input and output. They are composed of a number of connected processing units, called neurons. Each neuron can receive some data and generates output data according to its processing function. For the sake of brevity, in this article, the term neural network has been used to mean artificial neural network.

Fig.1. A typical neural network architecture

A typical neural network is shown in Fig.1. In this figure, there are total 7 neurons. These neurons are arranged according to functions, which they perform. Three neurons are put in the first layer from the left, which is known as input layer. Neurons in this layer are receiving input data, each neuron receiving one component of the input vector. For example, here the neurons are receiving x, y and z

components. To give an example from the physical word, x may represent temperature, y the pressure and z the relative humidity in an aircraft cabin. Next, there are 3 neurons in the middle layer, which is called the hidden layer. They may not represent a physically known parameter. The number of neurons in the hidden layer can be anything from 0 to a very large quantity, say 50. Finding out the optimum number of neurons in the hidden layer has been widely investigated and is still a hot research area. These neurons may receive the weighted input from the neurons in the input layer and provide an output depending on their processing function. The processing function is usually a non-linear function. There can be more than one hidden layers in a network. The weighted output from various neurons goes into the neurons (only one shown in Fig.1) of output layer and is again processed to give an output. To be consistent with our example, here the output may represent the comfort index of the passengers in the aircraft cabin. So, how dose a neural network approximates the functional relation? If we know the processing function of the neurons and the weights of each connection, we can predict comfort o depending on the value of x, y and z in a very short time. One may take the advantage of parallel computation too! Question is how do we find the parameters of the neural network i.e. weights connecting the neurons etc.? For that purpose, the network has to be trained by supplying a number of exemplars. That means we have to

y

z

x

o

Input layer

Hidden layer

Output layer



provide the network with some examples, each of the sort: When pressure was a, temperature b and humidity c, the comfort was d. We expect from the trained network to do two things:

1. It must give the correct answer for the examples for which it has been trained. This is called recall or memory capability.

2. It must also give the correct answer for the examples for which it has not been trained. This is called generalization capability.

In order to ensure that the network has a good generalization capability, we have to test the trained network with some independent data. The training data is used to decide the network architecture including the estimation of weights etc. A well-trained network gives a very less amount of error between the actual (called target) and network predicted value. One can find out the network parameters by minimizing an error function. Then, it has to be ensured that fitted network provides correct prediction for testing data as well. The big question is how many training and testing data are required and how they should be chosen. We should be able to design a good neural network with minimum training and testing data. This is also an important research area. The training time of a network should be less. This is especially desirable when training is to be carried out online. A number of techniques have been developed to make the training process faster. Radial basis function (RBF) neural network is faster, but requires more training data in comparison to more common multi-layer perceptron (MLP) network. Neural network can be used not only for providing one estimate based on the input data, but also a lower and an upper estimate along with the most likely estimate. The author has published some papers regarding the application of neural networks in this manner [2-4]. Having a network with the capability to predict the three estimates of a quantity makes a better decision-

support system in comparison to a network, which gives just one estimate. The training and testing data supplied should be free of noise. Invariably, there are few wrong data present due to human error or other factor. It is a good idea to put a data filtration module before sending the data for designing of the network. 2. POPULAR APPLICATION OF NEURAL NETWORKS The neural networks have been applied in a number of areas. Following subsections provide only a glimpse of their applications. There are a number of books and papers describing the content of this section in detail. 2.1 Optical character recognition Machine classifiers for recognizing the hand written characters have been developed. One application is sorting of the letters by postal codes. This application has been presented by Le Cun et al. [5]. In a typical system, an image of a digit (in PIN or ZIP code) is acquired by camera or scanner. The input to a neural network is then provided in the form of black and white pixels representing the digit. The output has only 10 categories (digits 0-9). The requirement was to associate the image presented with one of the ten classes with high classification accuracy. A neural network having one input layer, 3 hidden layers and one output layer was used. There were a total of 990 neurons in the hidden units. The network was trained with 7291 training data. The training time was equal to 3 days of CPU time on a Sun Sparc Station 1 machine. After the training, the network was presented 2007 unseen data and it recognized them 95% of the time. More research in the field of optical character recognition will help in developing reading machines for the blind persons. It will also help in digitizing the handwritten as well as printed documents. In banking sector, signatures can be verified using this technology.

2.2 Biometrics Biometrics is the science of using biological properties for identifying the individuals.



Biometrics systems can be of two types- one depending on the physical properties like fingerprints and other depending on the behavior of user like signature recognition. Neural networks can be used to identify faces, fingerprints and speech [6]. There have been some attempts to use neural networks in capturing the behavior of keystroke pattern of the user [7]. Such a system will provide more security to user in banking sector, as the behavior is difficult to copy. Moreover the hardware requirement is only a keyboard. 2.3 Diagnosis of disease The neural networks have been used for the diagnosis of disease. For example, Abbass [8] has presented a neural network based approach for breast cancer diagnosis. Both supervised and unsupervised networks are used in the field of disease diagnosis. Supervised networks require target data, whereas the unsupervised networks are self-learning networks and can extract the features. 2.4 Military applications Neural networks can be used for identifying the military targets based on the satellite photographs. Rogers et al. [9] has reviewed the application of neural networks for automatic target recognition (ATR). Usually, a number of sensors are used for the target recognition and the neural network is used to assist the decision making process for ATR. 2.5 Process modeling The modeling of a process is carried out based on the physics of the process. However, the process can also be modeled if lots of examples of input and output parameters are provided [2-4]. The network then can find out the relation between the output and input parameters. This is called modeling the data. There are thousands of the papers showing the application in various areas. However, there are a number of researchers who criticize modeling using neural networks, because it takes away from the physics of the process. Some other researchers combine the physical modeling with the powers of neural networks.

3. NEURAL NETWORKS AS A FRIEND OF OTHER NUMERICAL TECHNIQUES It is not necessary that neural networks should always be used as an alternative to other physics based numerical methods. They can also be used in conjunction with the techniques like finite element method (FEM), finite difference method (FDM), finite volume method (FVM) etc. The following subsections suggest some of the possible applications for future research. 3.1 Neural network module as a post-processor with FEM Finite element method gives the values of primary variables at the nodes. The values at the nodes can be taken as inputs for training a network. It will then be possible to predict the primary variable at any point in the domain. Moreover, the derivatives can also be estimated at any point. The values of primary variable and derivatives are expected to be uniformly accurate at all points. The neural network module can also be used for error analysis purpose. As the network provides the global approximation of the function, it can be put in the governing differential equation and boundary conditions to find out the error in the equations as well as boundary conditions. The error information may be used for refinement purpose. The use of neural networks also reduces the memory requirement. Instead of storing the data for each node, a very less number of network parameters need to be stored. Nodal values can be constructed when required.

3.2 Parametric study The neural networks can be used for parametric studies. Many programs require very high execution time. These programs can be used for generating the training and testing data. The program may be based on FEM, CFD or any other package. The network can be designed based on training and testing data. This network can be used for generating the results for a number of cases.



3.3 Neural network as a suitable guess

provider

In this application, neural networks can be used for providing the initial guesses. Refined solution can be obtained with CFD/FEM codes taking the initial guess as basis. This will reduce the total time for the analysis. 3.4 Neural networks for optimization Neural networks can also be used for solving the inverse problems. This capability can be used for solving optimization problems, particularly in the problems where the goal value is known and the design variables have to be found. Alternatively, neural network module can be used as a function and any optimization technique can be employed. The optimization solution obtained by neural networks can be further refined by searching in a very small domain around the estimate obtained from neural networks. This time the values can be obtained by running the parent code. 4. CONCLUSIONS In this article, a brief introduction of neural networks has been provided. There are a myriad number of applications of neural networks, out of which a few have been discussed here. Most of the time, a neural network is used as an alternative to physics based models. However, it is possible to use in conjunction with physics based methods as discussed in Section 3. Moreover, recently there have been some applications to use the neural networks for solving the partial differential equations [10]. Presently, they take more time than other techniques. However, with the development of computational machine working with parallel processors, computational time will be drastically reduced.

5. REFERENCES [1] Negnevitsky, M. (2002), Artificial Intelligence: A Guide to Intelligent Systems, Pearson Education, Singapore. [2] Dixit, U.S. and Chandra, S. (2003), A neural network based methodology for the prediction of roll force and roll torque in fuzzy form for cold flat rolling process, Int. J. Adv. Manuf. Tech., Vol. 22, no. 11-12, pp. 883-889. [3] Kohli, A. and Dixit, U.S. (2004), A neural network based methodology for prediction of surface roughness in turning process, Int. J. Adv. Manuf. Tech., Vol. 25, no. 1-2, pp. 118-129. [4] Ojha, D.K. and Dixit, U.S. (2005), An economic and reliable tool life estimation procedure for turning, Int. J. Adv. Manuf. Tech., Vol. 26, no. 7-8, pp. 726-732. [5] Le Cun, Y., Boser, B., Denker, J.S., Henderson, D., Howard, R.E., Hubbard, W. and Jackel, L.D. (1989), Backpropagation applied to handwritten ZIP code recognition, Neural computation, Vol. 1, No. 4, pp. 541-551. [6] Hassoun, M.H. (1999), Fundamentals of Artificial Neural Networks, Prentice-Hall of India, New Delhi. [7] Alexandre, T.J. (1997), Biometrics on smart cards: An approach to keyboard behavioral signature, Future Generations Computer Systems, Vol. 13, pp.19-26. [8] Abbas H.A.(2002), An evolutionary artificial neural networks approach for breast cancer diagnosis, Artificial Intelligence in Medicines, Vol. 25, No.3, pp. 265-281 [9] Rogers S.K., Colombi, J.M., Martin, C.E., Gainey, J.C., Fielding, K.H., Burns, T.J., Ruck, D.W., Kabrisky, M. and Oxley, M. (1995), Neural networks for automatic target recognition, Vol. 8, No. 7/8, pp. 1153-1184. [10] Lagaris, I.E., Likas, A. and Fotiadis, D.I. (1998), Artificial neural networks for solving ordinary and partial differential equations, IEEE Trans. Neural Networks, Vol. 9, pp. 987-1000.



NUMERICAL SOLUTION OF SOD’S SHOCK TUBE PROBLEM

BY VAN LEER METHOD

Deepak Kumar 1, Vivek Kumar 2

1 B.Tech 3rd Year (2003-2007 Batch), Department of Mechanical Engineering 2 B.Tech 3rd Year (2003-2007 Batch), Department of Mechanical Engineering


For solving Shock Tube problem 1-D Euler equation has been used. The Euler equations comprise of

inviscid compressible continuity, momentum and energy equations. With finite difference approach

using Van Leer’s flux vector splitting scheme [1] a C++ code generated the numerical solution to the

problem and then comparison with the exact solution was made. The problem has been solved for two

set of initial conditions as proposed by Sod (1978) [2] and the results have been plotted at t=6.3 ms for

the first set of initial conditions and another at t=3.9 ms for another set of initial conditions. Then

comparisons of both the results are made by plotting the graphs.

1. INTRODUCTION The shock Tube Problem presents an exact solution to the full system of one-dimensional Euler equations containing simultaneously a shock wave, a contact discontinuity and an expansion fan. This problem, also called Riemann problem, is of practical and theoretical interest. It can be realized experimentally by sudden breakdown of a diaphragm in a long one dimensional tube separating two initial gas states at different pressures and densities. The initial conditions are following:

0

0

; ; 0; ; 0

L L L

R R R

u u p p x x tu u p p x x t= = ρ = ρ < == = ρ = ρ > =

with pR<pL and the diaphragm is located at x=xo. We assume that the two regions contain the same gas. If we neglect the viscous effects along the tube walls and assuming the tube to be infinitely long avoiding reflections at the tube ends, the exact solution of the Euler equations can easily be obtained on the basis of simple waves separating regions of uniform conditions. Important informations about this problem can be obtained from references [3, 4, 5]. At the bursting of the diaphragm, at t=0, a shock wave propagates to the right in the low pressure gas and simultaneously an expansion fan

propagates to the left in the high pressure gas. In addition, a contact discontinuity separating the two gas regions propagates to the right in the tube. Since the shock and the contact discontinuity move in regions of uniform conditions, they will have a constant velocity and the expansion is centered at the diaphragm position xo at t=0. Following regions (Fig. 1) are generated during the process: region R contains the undisturbed gas at low pressure PR. It is separated by a shock wave 1 from region 2, which represents the disturbed low-pressure gas. The contact discontinuity 3 separates region 2 from disturbed high-pressure gas region 4, which in turn has been influenced by the expansion fan 5 propagating to the left into the undisturbed high pressure region L.

Fig 1: Characteristics and discontinuities originating at

the interface between two gas states- the Riemann problem



The diaphragm is located at x = 5 m. It breaks at t = 0. Before it breaks it separates the gas with different conditions. The states of the gas on the left are indicated by uL, pL, ρL and that on the right side by uR, pR, ρR. In the present case, consider air for which γ=1.4. Once the diaphragm breaks at t=0, the resultant flow is governed by the 1-D Euler equation. The flow is complex with an expansion wave moving to the left and a shock wave & a contact surface moving to the right.

Fig 2: Schematic representation of shock Tube

Here Van Leer’s flux vector splitting method has been used to capture the solution numerically at t=6.3 ms and 3.9 ms respectively for the following two initial conditions (test data applied by Sod, 1978) :- (i) pL=100 KPa, ρL=1 kg/m3 pR=10 KPa, ρR=0.125 kg/m3, uL=uR=0 m/s (1st Set of Data) (ii) pL=100 KPa, ρL=1 kg/m3, pR=1 KPa, ρR=0.01 kg/m3, uL=uR=0 m/s (2nd Set of Data) 2. GOVERNING EQUATION The Navier-Stokes equation reduces to the Euler equation if the coefficient of viscosity is set to zero. Since the shock tube problem involves high velocity so for solving this problem 1D Euler equation has been used. The form of the equation is

+ = 0t xU F

( )21

2

U uP u

1

ρρ

ργ

⎛ ⎞⎜ ⎟= ⎜ ⎟⎜ ⎟

+⎜ ⎟−⎝ ⎠

( )

2

312

uF P u

Pu u1

ρ

ργ ργ

⎛ ⎞⎜ ⎟

= +⎜ ⎟⎜ ⎟

+⎜ ⎟⎜ ⎟−⎝ ⎠

where

ρ = density of the gas,

u = velocity of the gas

P = pressure of the gas γ = specific gas ratio

Boundary Condition

LU(0, t) U= and RU(L, t) U=

3. SOLUTION METHODOLOGY The Van Leer’s Flux Vector spitting method has been used for solving the above problem. The split fluxes are given by:

( )[ ]2

2VL

2

2

2u

1u

f4c

1c

cu cρ+

+( −1)

⎛ ⎞⎜ ⎟( −1) +⎜ ⎟

= + ⎜ ⎟⎜ ⎟γ⎜ ⎟⎝ ⎠2( − )γ

γγ

( )[ ]2

2VL

2

2

2

1

f4c

1

u

uc

cu cρ−

− ( −1)

⎛ ⎞⎜ ⎟( −1) −⎜ ⎟

= − − ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠2( − )

γ

γ

γ

γ

Where C is the propagation speed of sound. Now we can write the Euler equation in the split form as

U f f 0t x x

+ −∂ ∂ ∂+ + =

∂ ∂ ∂

Here f+ is discretised with a backward difference and f- is discretised with forward difference. Thus we finally get the Euler equation in descretised form as

This scheme is first-order accurate in space and time. 4. NUMERICAL RESULTS A uniformly spaced grid with 1000 points is used. 4.1. For t=6.3 ms we have the following results

and



Fig 3(a): Density vs Tube Length at t=6.3 ms

Fig 3(b): Velocity vs Tube Length at t=6.3 ms

Fig 3(c): Pressure vs Tube Length at t=6.3 ms

Fig 3(d): Mach Number vs Tube Length at t=6.3 ms

Fig 3(e): Mass Flux vs Tube Length at t=6.3 ms

Fig 3(f): Entropy vs Tube Length at t=6.3 ms



4.2. For t=3.9 ms we have the following results:

Fig 3(g): Density vs Tube Length at t=3.9 ms

Fig 3(h): Velocity vs Tube Length at t=3.9 ms

Fig 3(i): Pressure vs Tube Length at t=3.9 ms

Fig 3(j): Mach Number vs Tube Length at t=3.9 ms

Fig 3(k): Mass Flux vs Tube Length at t=3.9 ms

Fig 3(l): Entropy vs Tube Length at t=3.9 ms



5. CONCLUSION The numerical solution of the Sod’s Shock Tube Problem or Riemann Problem is very close to the exact solution in the entire domain of the problem with the small deviations only in certain regions. This shows the effectiveness and robustness of the Van Leer scheme. 6. ACKNOWLEDGEMENT We would like to thank our supervisor Dr. A. K. Dass for his guidance and constant encouragement throughout the progress of the work.

7. REFERENCES [1] Van Leer, B. (1979). ‘Towards the ultimate conservative difference scheme. V: A second order sequel to Godunov’s method.’ Journal of Computational Physics, 32, 101-136. [2] Sod, G.A. (1978). ‘A Survey of several finite difference methods for systems of non linear hyperbolic conservation laws.’ Journal Computational Physics, 27, 1-31. [3] Charles Hirsch, Numerical Computation of INTERNAL AND EXTERNAL FLOWS, Vol I and II, John Wiley & Sons. [4] Riemann Solvers and Numerical Methods for Fluid Dynamics, 2nd Edition, Springer. [5] T.J. Chung, Computational Fluid Dynamics, Cambridge University Press, 2002.



BUOYANCY ASSISTING MIXED CONVECTION IN TWO-DIMENSIONAL LAMINAR PLANE WALL JET FLOW

K. Kumar Raja

M. Tech 2004 Batch, Dept. of Mechanical Engineering Indian Institute of Technology Guwahati

Mixed convection flow is encountered in many industrial situations. Flow and heat transfer characteristics studies are carried out for buoyancy assisting two-dimensional laminar incompressible plane wall jet flow in detail. This situation is common in electronics cooling, defroster system, paper industry fluid injection systems, heat exchangers, cooling of combustion chamber wall in a gas turbine, automobile demister and others. Stream function vorticity formulation of governing equation is solved by ADI method. Clustered Cartesian grids are used for the computations. Results presented for similarity profile, isotherm contour, local Nusselt number for different Re, Pr and Gr. Keywords: buoyant wall jet, clustered grids, similarity profile, entrainment, Nusselt number.

INTRODUCTION Mixed convection flow is encountered in many industrial situations. Flow and heat transfer characteristics studies are carried out for buoyancy assisting two-dimensional laminar incompressible plane wall jet flow in detail. This situation is common in electronics cooling, defroster system, paper industry fluid injection systems, heat exchangers, cooling of combustion chamber wall in a gas turbine, automobile demister and others. Buoyancy induced heat transfer is attracted by many researchers. The study is carried out for many practical situations. Moallemi-and Jang [1] studied Prandtl number (Pr) effect on lid driven cavity flow problem. They presented results for Reynolds number ranging from 100 to 2200 and different Pr and Richardson number Ri. They have reported closed-form empirical co-relation for average Nusselt number as function of Re, Pr and Ri. This relation is valid for laminar range only. Hong et al. [2] reported the effect of inclination angle and Pr in laminar mixed convection in a duct with a backward facing step. Their study covered both buoyancy assisting and opposing flow conditions. They found that the reattachment length is increased when inclination angle is increased from 0 to 180 degree but it will reduce the wall friction coefficient and Nusselt number (Nu). Low Prandtl number fluid approaches fully developed condition at shorter distance and vice versa. Downstream location velocity profiles are given for the comparison of forced and mixed convection cases to understand the effect of buoyancy. Close form relations are given for

primary and secondary vortex reattachment length, location of the peak Nusselt number and maximum Nusselt number. Buoyancy opposing laminar mixed convection plane wall jet flow is reported by Higuera [3]. The flow detachment due to adverse pressure gradient in [3]. The flow detachment due to adverse pressure gradient in downstream direction is studied analytically and numerically by considering two different cases viz (a) ambient fluid passing over cold plate and (b) cold fluid passing over adiabatic plate. Marzouk et al [4] studied numerically a heated pulsed asymmetric jet in laminar region. They solved the governing equation by finite difference method. They noticed that the pulsation accelerates the initial development of the jet and improves in diffusing the entrainment of the ambient fluid near the nozzle. Rao et al. [5] presented the results for laminar mixed convection with surface radiation from a vertical plate with a heat source as conjugate case. Angirasa [6] has studied laminar buoyant wall jet and reported the effect of velocity and the width of the jet during convective heat transfer from the vertical surface. Quintana et al. [7] experimentally investigated the mean and fluctuating characteristics of a plane unsteady laminar wall jet for constant wall temperature. Recently, Bhattacharjee and Loth [8] simulated laminar and transitional cold wall jets. They investigated the significance of three different inlet profiles viz. parabolic, uniform and ramp. They presented the detailed results of time-averaged wall jet thickness and temperature distribution with RANS approach for higher Reynolds number and DNS approach for three-



dimensional wall jet. Kanna and Das [9] studied the conjugate laminar plane wall jet and reported closed form solution for interface temperature, local Nusselt number and average Nusselt number. The conjugate heat transfer of a laminar offset jet is reported by Kanna and Das [10]. The governing equation is solved by ADI method and clustered cartesian grids are used for the computations. They found that the local Nusselt number increases to a peak value and further it is decreased in the downstream direction, However lot of study is carried out on laminar plane wall jet flow, buoyancy assisted laminar plane wall jet is not presented by anybody which motivates the present study. The present study is motivated by the cooling of heated slabs due to laminar plane wall jet flow. These types of flow situations occur in electronics cooling, refrigerated air curtain, paper industry, electrical motor cooling etc. Nomenclature Gr Grashof number h inlet slot height, m n normal direction Nu local Nusselt number Nu average Nusselt number Pr Prandtl number, ν α Re Reynolds number for the fluid T∞ constant ambient temperature, 0C t nondimensional time

,u v dimensional velocity components along (x, y) axes, m/s u, v dimensionless velocity components along (x, y) axes U Inlet mean velocity, m/s

,x y Dimensional Cartesian co-ordinates along and normal to the plate, m x, y dimensionless Cartesian co-ordinates along and normal to the plate Greek symbols ε convergence criterion θ dimensionless temperature κ clustering parameter ψ dimensionless stream function ω dimensionless vorticity Subscripts

f fluid max maximum w wall ∞ ambient condition FORMULATION Two-dimensional (2D), incompressible, laminar mixed convection in a laminar plane wall jet flow is considered for the study. The governing equation for a constant property fluid with the Boussinesq approximation is available in many references e.g. [11]. The physical problem configuration and the coordinate system of the problem under consideration are shown in Fig 1. A horizontal surface of length 30 times the height of the slot in streamwise direction is maintained at a temperature Tw, which is higher than the ambient temperatureT∞ . A parabolic velocity jet is located at the leading edge of the horizontal surface and discharges the jet tangentially to the horizontal surface, thereby washing the hot wall. The velocity distribution in the jet is taken as parabolic and its temperature is the same as the ambient temperature. The width of the jet is h (0.05) which equal to the slot height. A vertical adiabatic wall is assumed to be present at the top of the jet, as shown in Fig. 1 (a).

u(y)x

y

g

wT

T

Toc

oc

Figure1. (a) Schematic diagram of the problem

u = v= 0

u =

v=

0

u(y)B

C D

A

E

T wT= Figure 1. (b) Boundary conditions of the computational

domain.



The governing equations for incompressible laminar flow are solved by stream function-vorticity formulation. The transient non dimensional governing equations in the conservative form are, Stream function equation

2ψ ω∇ = − (1) Vorticity equation

22

( ) ( ) 1Re Re

u v Grt x y yω ω ω θω∂ ∂ ∂ ∂+ + = ∇ −

∂ ∂ ∂ ∂ (2)

Energy equation in the fluid region,

2( ) ( ) 1Re Pr

u vt x yθ θ θ θ∂ ∂ ∂+ + = ∇

∂ ∂ ∂ (3)

where ψ =stream function, u yψ∂

=∂

;

vxψ∂

= −∂

; v ux y

ω ∂ ∂= −∂ ∂

,

The variables are scaled as, uuU

= vvU

= ; xxh

= ; yyh

= ;U hωω = ;

tth U

= ; w

T TT T

θ ∞

∞

−=

−;

with the over bar indicating a dimensional variable and U and h, denoting the average jet velocity at nozzle exit and the jet width, respectively. The boundary conditions needed for the numerical simulation have been prescribed. The inlet slot height is assumed as h = 0.05. Along AE (Fig. 1. (b)) parabolic inlet profile is assumed. AB and DE are solid walls and no-slip conditions are assumed for velocity along the walls. AB is at higher temperature and other wall (DE) is insulated. Stream wise gradients are set as zero at exit (BC) and normal gradients are zero is followed at entrainment boundary CD. The Nusselt number and average Nusselt number expressions are given by:

0

( )y

Nu xyθ

=

∂= −

∂ (4)

0

1 ( )L

Nu Nu x dxL

= ∫

The computational domain considered here is clustered cartesian grids. The unsteady vorticity transport equation (Eq. 2) and energy equation (Eq. 3) are solved by ADI method. To validate the numerical procedure, natural convection flow problem is solved and results are compared with De Vahl Davis [12]. Further The mixed convection code is tested by setting Gr=0 The flow becomes forced convection and the results are compared with experimental results of Quintana et al. [7] for velocity (Fig. 2 (a)) and temperature (Fig. 2 (b)). Good agreements at different downstream locations have been obtained with similarity profile of Glauert [13]. RESULTS AND DISCUSSION The domain has been chosen as 30h in streamwise direction and 20h in normal direction. Systematic grid refinement study is carried out with various levels of 61x61, 73x73, 85x85, 97x97, 105x105 and 121x121 (Fig. 3). The variation in Nu is less than 1% for level 5 and 6 and level 5 (105x105) is selected for the entire computations. Study is carried out with different Re, Pr and Gr. Since the clustered grids are used for the computations, Tecplot~9.0 is used for extracting the values for particular location. Detailed results are presented for streamline contour, isotherm contour, similarity profile and Nusselt number.



o o o o o o o o o o o o o o o o o o o ooooooooooooooooooooooooooooooooooooooooooooo

oooooooo

oooooooo

ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

u/U

η

0 0.25 0.5 0.750

1

2

3

4

5

Quintana et alGlauertx/h= 9.90x/h = 12.90x/h = 16.31x/h = 20.08

o

max Figure 2(a): u velocity Similarity profile

oooooooooooooooooooooooooooooooooooo

oooo

oooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

θ

η

0.25 0.5 0.75 10

0.5

1

1.5

2

2.5

Similarityx/h = 12.90x/h = 16.31x/h = 20.08x/h = 24.11

o

Figure 2(b): Temperature Similarity profile

Figure 2. Similarity profiles: Re=400, Pr=1.4, Gr=0.0

Grid refinement level

Ave

rag

eN

u

0 1 2 3 4 5 6 7 810

10.5

11

11.5

12

Figure 3. Grid independence study: (Re=500, Pr=0.71,

Gr=104)

0.1038

0.09690.09000.08310.07610.0692

0.0623

0.0554

X

Y

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 4(a): Streamline contour Re=300

0.0969

0.0831

0.0623

X

Y

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 4(b): Re=300 (solid line), Re=600 (dashed line)

X

Nu

10 20 30

5

10

15

20

25

30

35

40

Re = 300Re = 400Re = 500Re = 600

Figure 4(c): Local Nusselt number

Fig 4: Effect of Re: Pr = 0.71, Gr =104



0.09100.0849

0.07890.07280.0667

0.0607

X

Y

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5(a): Streamline contour Gr = 103

0.28

8 2

0 .2470

0.16

47

0.06

18

X

Y

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5(b): Streamline contour Gr = 107

0.8125

0.5000

0.3125

0.1875

0.0625

0.0288

0.0048

X

Y

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5(c): Isotherm contour Gr = 103

0.0001

0.0001

0.0014

0.06250.0171

0.0004

X

Y

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 5(d): Isotherm contour Gr = 107

u/U

η

0 0.25 0.5 0.75 10

0.5

1

1.5

2

2.5

Gr = 103

Gr = 104

Gr = 105

Gr = 106

Gr = 107

max

Figure 5(e): u velocity similarity profile

x

Nu

10 20 30

20

40

60

80

Gr = 103

Gr = 104

Gr = 105

Gr = 106

Gr = 107

Figure 5(f): Local Nusselt number

Figure 5: Effect of Gr, Re=400, Pr= 0.71



-0.0196

-0.0027-0.0001

0.3533

0.3533

0.2087

0.1471

0.0809

0.0357

0.01370.0044

0.00180.0004

X

Y

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 6(a): u velocity contour: Pr = 0.01

-0.0087

-0.0030

-0.0010

-0.0003

-0.0000

0.3444

0.2596

0.1236

0.07010.0409

0.0157

0.0048

0.0005

0.3864

0.3656

0.35430.4491

0.50

83

X

Y

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 6(b): u velocity contour: Pr = 0.1

-0.0210

-0.0139

-0.0052

-0.0008

0.2151

0.0663

0.0094

0.0007

0.3513

0.1613

0.24

72

X

Y

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 6(c): u velocity contour: Pr = 10.0

u/U

η

0 0.25 0.5 0.75 10

0.5

1

1.5

2

2.5

Pr = 0.01Pr = 0.1Pr = 0.71Pr = 7.1Pr = 10.0Pr = 15.0

max

Figure 6 (d): u Similarity profile

θ

η

0 0.25 0.5 0.75 10

0.5

1

1.5

2

2.5

Pr = 0.01Pr = 0.1Pr = 0.71Pr = 6.0Pr = 7.1Pr = 10.0Pr = 15.0

Figure 6(e): Temperature similarity profile

X

Nu

10 20 30

20

40

60

80

100

120

Pr = 0.01Pr = 0.1Pr = 0.71Pr = 6.0Pr = 7.1Pr = 10.0Pr = 15.0

Figure 6(f): Local Nusselt number

Figure 6: Effect of Pr: Re = 400, Gr = 104

EFFECT OF REYNOLDS NUMBER Effect of Re in mixed convection flow of plane wall jet is shown in Figure 4. Figure 4 (a) shows the streamline contour for Re=300. The main flow spread along the wall and entrainment occurs and shears over the main flow. When Re is increased the flow deflects towards the bottom wall due to increased inertia force (Fig. 4(b)). Due to downstream friction at low Re flow spreads more in the normal direction. The local Nusselt number distribution along the bottom wall is shown in Fig. 4(c). Near the inlet Nu is more and it decreases in the downstream direction monotonically. When Re is increased Nu is increased. It is due to more entrainment near the inlet at high Re. However in the downstream direction the increment is less. EFFECT OF GRASHOF NUMBER Effect of Gr on velocity and temperature distributions is shown in Figure 5 for Re=400



and Pr=0.71. Effect of Gr on streamline contour is shown in Fig. 5(a) and Fig. 5(b). When Gr is increased, the streamline deflects more towards the bottom wall. The temperature difference between bottom wall and adjacent fluid is higher at high Gr, which induces more flow. Temperature contours are shown for different Gr in Fig. 5(c) and Fig. 5(d). At low Gr jet spreads well in the normal direction (Fig. 5(c)). When Gr is increased, the isotherm contours concentrated near the bottom wall Fig. 5 (d): Fig. 5 (e-f) shows the similarity profile for velocity and temperature distribution at x = 1.0. It is noticed, that when Gr is increased, the umax is shifted down (Fig. 5(e)). NusseIt number distribution is shown in Figure 5(f). When Gr is increased Nu is increased. The increment is sensitive for Gr>104. EFFECT OF PRANDTL NUMBER Effect of Pr on mixed convection of plane wall jet is presented in Figure 6. Effect of Pr on u velocity contour is shown in Fig. 6 (a-c). At higher Pr and the umax is shifted in the normal direction (Fig. 6 (d)). Figure 6 (e) shows the temperature similarity profile for Re = 400 and Gr =104 at x = 1.0. It is observed that at low Pr, it has a linear profile in the normal direction. When Pr is increased gradually, it is decreased and convection effects become predominant. However this reduction is less at high Pr (Pr above 0.71). Local Nusselt number distribution is shown in Figure 6 (e). Nu is higher near the inlet and further it is decreased and approaches asymptotic value in the downstream direction. When Pr is increased, Nu increases. However this increment is reduced at high Pr. CONCLUSIONS Laminar buoyancy assisting plane wall jet flow is studied. Effect of Re, Pr and Gr is reported in detail. The following conclusions are drawn from the study. When Re is increased flow is concentrate near the bottom wall. Nu is increased near the inlet when Re is increased. High Gr induces more flow in the downstream direction. When Gr is increased umax is shifted down. For higher Gr, Nu is increased and this is sensitive at Gr>104 . At high Gr, the flow comes into the contact of hot wall, it takes heat rapidly and this place is replaced by fresh fluid causing

high temperature difference at the wall, thereby increasing heat transfer. Increment in Pr causes higher entrainment. When Pr is increased umax is shifted in the normal direction. Nu is increased for higher Pr. REFERENCES [1] M.K. Moallemi and K.S. Jang. Prandtl number effects on laminar mixed convection heat transfer in a lid-driven cavity. International Journal of Heat and Mass Transfer, 35,pp.1881- 1892, 1992. [2] B. Hong, B.F. Armaly, and T.S. Chen. Laminar mixed convection in a duct with a backward facing step: the effects of inclination angle and prandtl number. International Journal of Heat and Mass Transfer, 12,pp.30593067, 1993. [3] F.J. Higuera. Opposing mixed convection flow in a wall jet over a horizontal plate. Journal of Fluid Mechanics, 342,pp335-375, 1997. [4] S. Marzouk, H. Mhiri, S.E. Golli, and G.L.Palec. Numerical study of momentum and heat transfer in a pulsed plane laminar jet. International Journal of Heat and Mass Transfer, 46, pp.4319- 4334, 2003. [5] C.G. Rao, C. Balaji, and S.P. Venkateshan. Conjugate mixed convection with surface radiation from a vertical plate with a discrete heat source. Journal of Heat Transfer, 123, pp.698-702, August 2001. [6] D. Angirasa. Interaction of low-velocity plane jets with buoyant convection adjacent to heated vertical surfaces. Numerical Heat Transfer, Part A, 35, pp.67-84, 1999. [7] D.L. Quintana, M. Amitay, A. Ortega, and I.J. Wygnanski. Heat transfer in the forced laminar wall jet. Journal of Heat Transfer, 119, pp.451-459, 1997. [8] P. Bhattacharjee and E. Loth. Simulations of laminar and transitional cold wall jets. International Journal of Heat and Fluid Flow, 25,pp.32-43, 2004. [9] P.R. Kanna and M.K. Das. Conjugate forced convection heat transfer from a flat plate by laminar plane wall jet flow. International Journal of Heat and Mass Transfer, 48,pp.2896-2910, 2005. [10] P.R. Kanna and M.K. Das. Conjugate heat transfer study of two-dimensional laminar incompressible offset jet flows. Numerical Heat Transfer: Part A. Article in press. [11] A.Bejan. Convection Heat Transfer. Wiely-Interscience, New York, first edition, 1984. [12] D. de Vahl Davis, Natural Convection of Air in a Square Cavity: A Bench Mark Solution, Int. J. Numer. Meth. Fluids, vol. 3, pp. 249- 264, 1983. [13] M. Glauert, The wall jet, J. Fluid Mech. 1 (1) (1956) 1–10.



HIGHER ORDER SOLUTION OF THE EULER EQUATIONS ON UNSTRUCTURED MESHES USING POLYNOMIAL RECONSTRUCTION

Mohamed Yousuf A. U. 1, Gundeti Lavan Kumar 2

1 M. Tech (Fluid and Thermal) 2004 Batch, Dept. of Mechanical Engineering

2 M. Tech (Fluid and Thermal) 2003 Batch, Dept. of Mechanical Engineering Indian Institute of Technology Guwahati

High order accurate solution methods have proven to be invaluable in solving Euler and Navier-Stokes

equations on unstructured meshes. Accurate reconstruction is the key ingredient in obtaining high

order spatial accuracy for many upwind finite-volume solvers. The modern upwind algorithms for

compressible flow are designed for capturing discontinuities accurately; higher order schemes often

produce nonphysical oscillations, which can be effectively suppressed by employing limiters.

Numerical example is presented for single airfoil flow to demonstrate the capabilities of piecewise

polynomial reconstruction over lower order accurate reconstruction procedures (piecewise linear and

piecewise constant).

INTRODUCTION Significant developments in algorithms for Euler and Navier–Stokes equations on unstructured grids have occurred in recent years. The primary motivation behind these developments is the ease with which unstructured grids can be generated around complex geometries in a relatively short turn-around time compared to that of block-structured grids. Unstructured-grid flow solvers, based on finite-volume discretization of the governing equations with upwind schemes, are preferred because of their robustness and their inherent ability to accurately represent the physics associated with linear and nonlinear waves. In Barth and Fredrickson [2], Barth [3] and Delanaye and Essers [4] high order reconstruction have been developed and implemented within the framework of a finite volume solver. INTEGRAL FORMULATION The integral conservation law form of the Euler equations is solved in a two-dimensional domain Ω with perimeter∂Ω :

ddt

uΩ∫ dS + F

∂Ω∫ ( , ) 0u n dl =r

..…. (1)

In this equation u is the vector of conserved variables for mass, momentum and energy. The vector ( , )F u n

r represents the inviscid flux

vector with normal nr

. FINITE VOLUME SCHEME In the finite volume method the solution domain is tessellated into a number of small non-overlapping sub domains. Each sub domain servers as a control volume in which mass, momentum and energy are conserved. We assume the present discussions that the solution unknowns are placed at centroids of finite volumes shown in Fig. 1.

Fig.1: The identification of more neighbors and flux

integration path showed by dashed line



The solution procedure for solving Eqn. (1) consists of following steps: Reconstruction. Given the pointwise values of the solution at cell centers of the mesh, reconstruct a polynomial approximation to the solution in each control volume. Flux Quadrature. From the piecewise polynomial description of the solution, approximate the flux integral in Eqn. (1) by numerical quadrature. The actual choice of quadrature rule used in the flux integration is dictated by the lower order of data reconstruction, i.e. one point quadrature formulas with linear reconstruction and two points Gauss quadrature with quadratic reconstruction. The Euler flux is supplanted by a numerical flux which is a function of two solution states. Roe approximate Riemann solver [1] is used for computations. Evolution. Given a numerical approximation to the flux integral, evolve the system in time using multistage time stepping explicit scheme. This results in new solution unknowns. SIMPLIFIED QUADRATIC RECONSTRUCTION A quadratic polynomial contains six degrees of freedom in two dimensions. This means that the support (stencil) of the reconstruction operator must contain at least six members. In refs [3] and [4] this is accomplished by increasing the physical support on the mesh until six or more members are included. For each control volume surrounding vertex or midside node u0, a quadratic polynomial of the form

0 0 0 01( , )2

T Tu x y u r u r H r= + ∆ ∇ + ∆ ∆ ….. (2)

must be reconstructed from surrounding data. In this equation u∇ is the usual solution gradient and H is the Hessian matrix of second derivatives

H= xx

xy

uu⎡⎢⎣

xy

yy

u

u⎤⎥⎥⎦

Enforcing Monotonicity of the Reconstruction

Consider the reconstructed quadratic polynomial for the control volume surrounding u0

0 0 0 01( , )2

T Tu x y u r u r H r= + ∆ ∇ + ∆ ∆

One approach to enforcing the monotonicity of the reconstruction is to introduce a parameterΦ into the reconstructed polynomial

0 0 0 0 01( , ) ( )2

T Tu x y u r u r H r= Φ + ∆ ∇ + ∆ ∆

With the goal of finding the largest admissible 0Φ Є [0, 1] while invoking a monotonicity

principle that the values of the reconstructed function must not exceed the maximum and minimum of neighboring nodal values and u0. To calculate 0Φ first compute

min0 0min( , )neighborsu u u= ,max0 0max( , )neighborsu u u=

Then require that min max

0 0 0( , )u u x y u≤ ≤ max0 0

00

min0 0

0 00

0

min 1, , ( ) 0

min 1, , ( ) 0

1,........................... ( ) 0

ii

ii

i

u u if u uu u

u u if u uu u

if u u

⎧ ⎛ ⎞−− >⎪ ⎜ ⎟−⎝ ⎠⎪

⎪ ⎛ ⎞−⎪Φ = − <⎨ ⎜ ⎟−⎝ ⎠⎪⎪ − =⎪⎪⎩

This limiting procedure is very effective in removing spurious oscillations although the discontinuous nature of the limiter can hinder steady-state convergence of the scheme. NUMERICAL RESULTS Transonic flow calculation for a freestream Mach number equal to 0.80 and 1.25o angle of incidence has been carried out. The solution consists of an upper and lower surface shock wave and a trailing edge slip line. The grid for all calculations is shown in Fig. 2.



-0.5 0 0.5 1 1.5

-1

-0.5

0

0.5

1

Fig.2: Close-up of grid about NACA0012

Solution Mach contours are shown in Figs. 3–5 for various order accurate schemes. The surface pressure coefficient distributions are plotted in Fig. 6. Residual history for various order schemes are plotted in Fig. 7. The solution obtained using piecewise constant reconstruction misses the lower surface shock wave and trailing edge slip line.

0.7

0.9

0.85

0.8

1.2

0.95

0.8

0.9

0.75

0.75

0.75

Fig. 3: Mach contours (piecewise constant)

0.68

9474

0.763158

0.836842

1.131

58

1.20526

0.984

211

0.83

6842

0.6894740.689474

Fig.4: Mach contours (piecewise linear) The piecewise linear reconstruction scheme detects upper and lower surface shock waves as well as the slip line. As expected the numerical solution obtained with piecewise quadratic reconstruction is superior to other methods. Both the upper and lower shocks are crisply captured.

0.688943

1.2

1.26227

0.9

0.732343

0.732343

0.732343

0.8

0.9

Fig. 5: Mach contours (piecewise polynomial)



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O

O

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X / C

-Cp

00

0

0.20.2

0.2

0.40.4

0.4

0.60.6

0.6

0.80.8

0.8

11

1

-1-1 -1

-0.5-0.5 -0.5

00 0

0.50.5 0.5

11 1

o Kamath Results

--- 1st order Computed Result

2nd order Computed Result_ _ _ 3rd order Computed Results

Fig. 6: Surface pressure distribution

Iterations

Res

idua

l

0 10000 20000 30000 40000 5000010-10

10-8

10-6

10-4

10-2

100

1st order2nd order3rd order

1 2

3

Fig. 7: Residual history

CONCLUSION The numerical results indicate that the higher order reconstruction method (piecewise quadratic) offer a substantial improvement over the basic low order (piecewise linear and piecewise constant) schemes. REFERENCES 1. Roe, P. L. Approximate Riemann Solvers, Parameters Vectors and Difference Schemes. J. Computational Physics, 43, pp.357-372, 1981. 2. Barth T. J. and Paul O. Frederickson. Higher Order Solution of the Euler Equations on Unstructured Grids Using Quadratic Reconstruction, AIAA-90- 0013, January 8-11, 1990/Reno, Nevada.

3. Barth T. J. Recent Developments in High Order K-Exact Reconstruction on Unstructured Meshes, AIAA-93-0668, January 11-14, 1993/Reno, Nevada. 4. Delanaye M. and Essers J. A. Quadratic-Reconstruction Finite Volume Scheme for Compressible Flows on Unstructured Adaptive Grids, AIAA, 35, No. 4, April 1997. 5. Jawahar, and Hemanth Kamath P., A High Resolution Procedure for Euler and Navier-Stokes Computations on Unstructured Grids, J. Computational Physics, 164, pp. 165-203, 2000.



MICROFLUIDICS: AN INTRODUCTION

Puneet Chhabra, B-Tech 3rd Year, Department of Mechanical Engineering


Microfluidics is the science of designing, manufacturing, and formulating devices and processes that deal with volumes of fluid on the order of nanoliters or picoliters on the basis of studies on the behavior of fluids at such scales. The devices themselves have dimensions ranging from millimeters down to micrometers and can be identified by the fact that it has one or more channels with at least one dimension less than 1 mm. Common fluids used in microfluidic devices include whole blood samples, bacterial cell suspensions, protein or antibody solutions and various buffers. It is a new science, having emerged only in the 1990s, but has diverse and widespread potential applications which are among the greatest engineering challenges of the century.

To start of, take the case of Lab-on-a-chip devices or micro-total-analysis-systems (µTAS) which are single chips, usually constructed out of silicon or Pyrex glass, that integrate multiple traditional macroscopic laboratory processes, such as sample pre-treatment, reaction, and detection, on a smaller scale. It is able to provide variety of interesting measurements including molecular diffusion coefficients, fluid viscosity, pH, chemical binding coefficients and enzyme reaction kinetics, quickly and more

economically than possible using standard lab technology.

Then there is a DNA microarray - a collection of microscopic DNA spots attached to a solid surface, such as glass, plastic or silicon chip forming an array. Scientists use DNA microarrays to measure the expression levels of large numbers of genes simultaneously. Measuring gene expression is relevant to many areas of biology and medicine, such as studying treatments, disease and developmental stages. Other applications include inkjet printers, surface micromachining, mechanical micromilling, capillary electrophoresis, isoelectric focusing, immunoassays, flow cytometry, sample injection of proteins for analysis via mass spectrometry, PCR amplification, cell manipulation, cell separation, cell patterning and chemical gradient formation. The use of microfluidic devices to conduct research has a number of significant advantages. A chip performs in a fraction of a minute an analysis that would take hours using traditional methods. And because the volume of fluids within these channels is very small, the amount of reagents and analytes used is quite small. The fabrications techniques used to construct



microfluidic devices are relatively inexpensive and are very amenable both to highly elaborate, multiplexed devices and also to mass production. Microfluidics hardware requires construction and design that differs from macroscale hardware. It is not generally possible to scale conventional devices down and then expect them to work in microfluidics applications. When the dimensions of a device or system reach a certain size as the scale becomes smaller, the particles of fluid, or particles suspended in the fluid, become comparable in size with the apparatus itself which dramatically alters system behavior.

For one, there's the sheer size issue to deal with. Fluids in such small volumes don't undergo the same turbulence they do in larger volumes. Due to the small dimensions of microchannels, the Re is usually much less than 100, often less than 1.0. In this Reynolds number regime, flow is completely laminar and no turbulence occurs. Then, there's the issue of pressure. Channels as small as a hair's width require thousands of times more pressure than millimeter-size channels to maintain similar flow. Capillary action changes the way in which fluids pass through microscale-diameter tubes, as compared with macroscale channels. Further, factors such as surface tension, energy dissipation, and electrokinetics (charging of the surface due to rubbing of ions that the fluid is made up of with the solid) start to dominate the system. In addition, there are unknown factors involved, especially concerning instabilities of flows, microscale heat transfer and mass transfer, the nature of which only further research can reveal. So far, microfluidics has made some impressive progress in dealing with these issues. There are several different approaches to moving the tiny streams (or, in some cases, droplets) across a channel, and of controlling the flow. For the

most part, the chips themselves are fabricated like those used in computers. Photolithography is used to etch channels into silicon or glass wafers. The etched wafers can be stacked to create more complex pathways. Research in the microfluidics is concentrated in two primary areas: experimental and numerical fluid dynamics in micro/nano domains and microfabricating novel microfluidic devices. Numerical simulations of microfluidic systems can be extremely valuable both in terms of providing a research tool and as an efficient design and optimization tool. By incorporating the complexities of channel geometry, fluid flow rates, diffusion coefficients and possible chemical interactions into a numerical model, the behavior of a particular system can be accurately predicted when an intuitive prediction may be extremely difficult. For example, a custom coded numerical model has been used to predict differences in the diffusive scaling laws across the depth of a microchannel. Microfluidic systems are still early in their development, but their potential is vast. Taking a real-world problem, like bioterrorism, and coming up with a bioagent-detection solution is a first big step. We're going to see even more uses for this technology in water analysis, home healthcare, and disease detection.

And it all starts with just a nanoliter of fluid and a chip that's no bigger than your fingernail.



CAMPUS PLACEMENT: AN OVERVIEW

Following companies have been recruiting the B.Tech/M.Tech students so far from the mechanical department:

Ashok Leyland BHEL BPCL Byte Consulting Cognizant Crompton Contata Solutions Delmia Solutions DRDO Evalueserve Fluent India Ltd. GSSL HPCL IBM Induslogic

Infosys Ingersoll Rand IOCL Ispat ISRO ITC INFOTECH L & T Ltd. Manhattan NTPC OnMobile PDIL Power Alstom Quark Qwest SAPIENT

Schlumberger Satyam Tata Motors Tata Tech T.C.S. Techspan Tecumseh TELCON Thermax Ltd. TVS Motors TVS-SUZUKI YASU Tech Wipro

Placement 2004-05 (B.Tech) Number of Students 24 Number of Companies 20 Number of Students Placed 23 Number of Students with two jobs or more 11

Placement 2005-06 (B.Tech)* Number of Students 46 Number of Companies 27 Number of Students Placed 43 Number of Students with two jobs or more 15

* As on March 15th, 2006. Many companies are yet to visit IITG campus for Placement.



B.TECH PROJECTS ALLOTTED FOR 2005-06 SESSION

(BTP Coordinator: Dr K S R K Murthy)

P.No. Supervisors Name & Roll Number Name of the Project

P1 DC & AD (Civil)

Maneesh Mishra (02010326) K J Rao (02010320)

Parallel Finite Element and GA for Optimization of Composite Structures

P2 DC Himanshu Bisht (02010315) Acoustic Emission for Tool Condition Monitoring

P3 AKD & Jiten Kalita (Math)

Saurabh Singh (02010343) Jatin Gupta (02010316)

Multilevel computation of viscous and inviscid flows

P4 MKD Rameswar M. Paswan (02010339) Study of natural convection in an enclosure filled with porous media

P5 AD & PKJ Rahul Swarnkar (02010336) Mithilendu K. Jha (02010328)

Numerical Simulation of Mixing of Single-Phase Flow in a Stirred Vessel

P6 AD L. Abhijeeth Reddy (02010323) K. Sarat Chandra (02010317)

Prediction of Laminar-Turbulent Transition using k-Є Model of Turbulence

P7 AD A. Lakshmi Kanth (02010301) Saurabh Maurya (02010342)

Prediction of Turbulent Round Jets in a Co-flowing Ambient

P8 USD Kumar Kunal (02010322) Praveen Kumar (0201033)

Meshless local Petrov-Galerkin analysis of flexible manipulator

P9 MP & USD Swetha M (02010324) Numerical simulation and optimization of pulsating heat pipes

P10 SCM Tanuj Kush (02010346) B Siva Rama Krishna (02010308)

Coupling of LBM and radiative transfer method solvers for conjugate mode problems on unstructured grids

P11 SCM Pritish Ranjan Parida (02010334) Amit Prasad (02010306) Rishi Raj (02010340)

Analysis of phase change of semitransparent materials using the lattice Boltzmann method and the discrete transfer method

P12 SCM Gorthi Raghuchaitanya (02010314) Nagavarapu A. Krishna (02010329) Nishant Gupta (02010331)

Lattice Boltzmann method for solving conjugate mode problems with variable thermophysical properties

P13 PM K Vinayesh Reddy 02010318 B. Rakesh Sharma 02010310 V Puneeth Kumar m (02010347)

Design, Fabrication and Analysys of Fluidized Bed Paddy Drier



P14 PM Madhurjya Das (02010325) Chakresh Gupta (02010311)

Study of heat transfer and pressure drop in an annular heat exchanger with porous inserts

P15 PSR & PKJ Anamika Chowdhary (02010309) Gajendra Pal Singh (02010313)

Effect of ultrasonic vibrations on solidification characteristics of Al based alloy

P16 UKS & MKD

Mayank Bhardwaj (02010327) Sandesh Gannavaram (02010341) Varadraj Srivastava (02010348)

Modeling of Turbulent Flows in Complex Geometries using k- Є model

P17 UKS Chandan Kr. Pandey (02010312) Parvesh Singh (02010332) Rajesh Kumar (02010338)

Performance Analysis of Turbojet and Turbofan Engines

P18 ADS A T Raghuram (02010302) Akshat Gupta (02010305) Raghav Malhotra (02010335)

Development of an inventory model for perishable goods with a review on the present day Inventory Models

P19 ADS Vikul Goyal (02010352) Soumen Das (02010345)

Modeling and Crash Test analysis of a small car body

P20 RT Ajeet Kumar Jha (02010304) Amit Sahai Pankaj (02010307) Neeraj Kumar (02010330)

Computer Aided Analysis of High-Speed Precision Rolling Bearings

P21 RT Y.V. S. Brahmam (02010351) K V Ramana (02010350)

Control of Rotor Systems by Active Magnetic Bearings



M.TECH PROJECTS ALLOTTED FOR 2005-06 SESSION

(MTP Coordinator: Dr Manmohan Pandey)

Sl. No. Roll No. Name of Student Guide (s) Title

1 4410301 Awagurthi Koushik SKD Dynamic Analysis of Flexible Manipulator

2 4410302 A S S R Karuna Kumar SCM, NS Thermal Characteristics of Porous Burners

3 4410303 A Sunil Kumar AKD, DAAD Large Eddy Simulation1

4 4410304 A U Mohammad Yousuf AKD Computation of Compressible Flows

5 4410305 Abhishek Yadu MP, SCM Numerical Simulation of Supercritical Water Cooled Reactor

6 4410306 Amit Garg MP Design Optimization of Primary Cycle of Advanced Heavy Water Reactor

7 4410307 Ankur Shrivastava PM Extraction and Production of Biodiesel from Non-edible Plants

8 4410309 Chandrakant Maheshwari USD Prediction of Dimensional Deviation in a Turning Process using FEM

9 4410310 G Balaji SKK Bulk Reaction Modelling of Lined Duct with Air Gap using FEM

10 4410311 Hari Sankar Botcha AD Numerical Simulation of Mixing of Single Phase Flow in a Stirred Vessel

11 4410312 Jogendra Prasad Malladi PKJ Mathematical Modelling of Grade Change during Continuous Casting Process

12 4410313 Komarala Kumar Raja MKD Study of Flow Characteristic in Near Field of Two Parallel Plane Jets and an Offset Jet

13 4410314 K V V N S K Mohan RT Computer Aided Analysis of High Speed Precision Rolling Bearings

14 4410316 Kinthali Suresh Kumar MKD Multi Grid Method Turbulence Modelling of Plane Wall Jet Flow and Conjugate Heat Transfer with Obstacle

15 4410317 Kiran Chandra Sahu SKD Dynamic Analysis of Soft Core Sandwich Beam

16 4410319 Lokesh Kumar Singhal SCM Disease Diagnostic Using Transient Radiative Transfer Analysis

17 4410320 Mahadevan P USD, PSR Analysis of Hot Forging and Experimental Validation

18 4410322 Meena Ramesh Ghashiram GSK, ADS Reverse Engineering Application for Turbine Blades

19 4410323 Mohammad Mastan Pasha DC Optimization of FRP Composite

20 4410324 Prasenjit Mallik SKK Stability of Porous Journal Bearing

21 4410325 R Somabhupal Reddy RT Design and Analysis of Crown Tapered Roller Bearing for Automobile and Aircraft Applications

1 Project numbers ME/F02/AKD-DAAD/03 and ME/D12/DC-DAAD/28 are being carried out partly in Germany under DAAD-Sandwich scheme.



22 4410326 R Vijayaraj Chakravarthy RT Experimental Estimation of Bearings/Seals Dynamic Characteristic

23 4410328 Raja Ramesh Jakkula DC, DAAD FE Analysis of Smart FRP Laminate Composites

24 4410329 Rajendra Kishore Oliganti GSK, ADS Modelling of Complex Objects using CAD for Rapid Prototyping

25 4410330 Rajkamal Tiwari MKD Three Dimensional Study of Heat Transfer in an arbitrary Geometry using Nanofluids

26 4410331 Salunkhe Milind Atmaram USD Analysis of Rolling Process using FEM

27 4410332 Sanjeev Kumar ADS Sound Transmission through Barriers

28 4410333 Sanka Sai Babu GSK Shape Optimization

29 4410334 Saraiah Thotla UKS, DM(CE) Performance Study of Wind Turbine

30 4410335 Satish Narayana K SKD Dynamic Analysis of Flexible Manipulation using FEM

31 4410336 Satya Narayan Chouksey KM Comparison of Various Finite Element Stress Smoothing Techniques within the singularity Dominated Zone

32 4410337 Sheikh Abdul Shajeed PM Heat Transfer Characteristic on Upper Splash Region of CFB unit

33 4410338 Souptick Chanda PSR, PKJ Microstructure and Mechanical Property Evolution of Micro alloyed Al-Cu alloy

34 4410339 Srinivasa Rao Purimitla PKJ, AD Numerical Modelling of Inclusion Separation Process in a Continuous Casting Tundish

35 4410340 Srinivasa Rao Thalapala SKK Stability of Circular-noncircular Journal Bearing with Surface Roughness

36 4410342 Sushen Kirtania DC FE Analysis of Composite Structure

37 4410343 Tanuja Sukhacharan Vaidya PM Characterization of Nano-Particles using Rotating

Fluidised Bed

38 4410344 Tapan Kumar Mishra AKD, MP Control of Laminar-Turbulent Transition in Two-Dimensional Flows

39 4410345 Votari Natraj UKS Design of a Fluid-Thermal System

40 4410346 Venkata Srikanth Manda KM, PSR Practical Determination of Mixed-Mode SIFs

41 4410348 Yerra Radha Krishna KM A study on Singular Elements

42 4410349 Prabodh Kumar Panigrahi UKS, CE Film Cooling of Turbine Blades



RESEARCH PUBLICATIONS BY STUDENTS (05-06)

• "Discrete Transfer Method Applied to Radiative Transfer in a Variable Refractive Index Participating Medium", N. Ananda Krishna and Subhash C. Mishra, presented in the 18th National & 7th ISHMT-ASME Heat and Mass Transfer Conference held at IIT Guwahati from 4-6 Jan. 2006.

• "Application of lattice Boltzmann method and the discrete transfer method to conduction and radiation problems involving variable thermal conductivity and variable refractive index", S. C. Mishra, N. A, Krishna, N. Gupta and G. R. Chaitanya presented as the keynote paper in the 50th Congress of Indian Society of Theoretical & Applied Mechanics held at IIT Kharagpur from 14-17 Dec, 2005.

• “Solution of steady state heat conduction problem by Radial Basis Function Neural Network.” Ashok Kumar Alwal, Kishore Aggarwal and U.S. Dixit, pp 737 –744, 18th National and 7th ISHMT-ASME Heat and Mass Transfer Conference held at IIT Guwahati from 4-6 Jan 2006.

• "Discrete Transfer Method Applied to Radiative Transfer in a Variable Refractive Index Semitransparent Participating Medium", N. Ananda Krishna and Subhash C. Mishra, Journal of Quantitative Spectroscopy and Radiative Transfer (JQSRT).

• "Study of Conduction-Radiation Heat Transfer Problems using lattice Boltzmann Method and Discrete Transfer Method", S. C. Mishra, N. A, Krishna, N. Gupta and G. R. Chaitanya, submitted to Journal of Quantitative Spectroscopy and Radiative Transfer (JQSRT), March 2006.

• “Analysis of transient conduction and radiation heat transfer with variable thermal conductivity using the lattice Boltzmann method and the discrete ordinate method”, N. Gupta, G. R. Chaitanya, S. C. Mishra, presented in the 18th National and 7th ISHMT-ASME Heat and Mass Transfer Conference to be held at IIT Guwahati during January 4-6 2006.

• “Application of lattice Boltzmann method and the discrete transfer method to conduction and radiation problems involving variable thermal conductivity and variable refractive index”, S. C. Mishra, N. A. Krishna, N. Gupta and G. R. Chaitanya, presented as the keynote paper in the 50th Congress of Indian Society of Theoretical & Applied Mechanics to be held at IIT Kharagpur from 14-17 Dec, 2005.

• “Analysis of conduction and radiation heat transfer with variable thermal conductivity using the lattice Boltzmann method and the discrete ordinate method”, N. Gupta, G. R. Chaitanya, S. C. Mishra, Journal of Thermo-physics and Heat Transfer.

• “Numerical Simulation of Supercritical Water Cooled Reactor using Lumped Parameter Model”Abhishek Yadu, Manmohan Pandey, Subhash C. Mishra, 16th Annual conference of Indian Nuclear society(INSAC-2005) 15-18 Nov, 2005.

• “Parametric Study of Supercritical Water Cooled Reactor Using Lumped Parameter Model” Abhishek Yadu, Manmohan Pandey, Subhash C. Mishra, 2nd International Congress on Computational Mechanics and Simulation, 8-10 Dec, 2006.

• “Parametric study of Thermal-Hydraulics for advanced heavy water reactor”, Amit Garg, Manmohan Pandey, Uday S. Dixit, 16th Annual Conference of Indian Nuclear Society, 2005 (INSAC-2005), 15-18 Nov, 2005.

• “Parametric instability regions of a sandwich beam using Higher Order Theory”, K.C. Sahu and S.K. Dwivedy, Indian Society of Theoritical and Applied Mechanics (ISTAM) Conference organized by IIT Kharagpur from 14-17 Dec, 2005.

• "Mixing And Segregation Behavior of Granular Flow in Unary and Binary Particulate Systems", R. Swarnkar, A. Mujumdar, P. S. Robi, M. Malik, National Seminar on Physics for Advanced Engineering & Technology (NSPAET), VNIT Nagpur, March 2005.



Seventh Convocation (30th May 2005)



ACTIVITIES OF MESA DURING 2005-06

Industrial Trip

MESA Talk

Interaction session with CAT qualifiers

Lecture on applied CFD



Working Members

Executive Committee

Dr. Niranjan Sahoo : Faculty Advisor Rahul Swarnkar : President Deepak Kumar : Vice President Rahul Kumar : Publication Secretary Ravi Kumar Patni : Secretary, Activity Group Uma Maheswar Vattikuti : B.Tech 2nd Year representative Prabodh Panigrahy : M.Tech representative

Website Committee

Deepak Kumar : Webmaster Kamal Kant Maurya : Member Atanu Bhuyan : Member

Publication Committee

Rahul Kumar : Publication Secretary Rahul Swarnkar : Editor 1 Deepak Kumar : Editor 2 Mohammad Shadan : Member Chaitanya K R S : Member Bikramjit S Bhatia : Member Ravi Gupta : Member

Activity Group Ravi Kumar Patni : Secretary, Activity Group Anas Viquar : Member Aditya Taneja : Member Kiran Prakash : Member Ravi Kumar Assudani : Member Rohit Mittal : Member Alok Verma : Member Gaurav Kumar : Member Ravi Kishore : Member

Batch Representatives Rahul Swarnkar : B.Tech final year Deepak Kumar : B.Tech 3rd year Uma Maheswar Vattikuti : B.Tech 2nd Year Atul Kumar Soti : B.Tech 1st year Prabodh Panigrahy : M.Tech 2nd year

Treasurer Sudhendu Azad : B.Tech 3rd year

Mechanical Engineering Students' AssociationDepartment of Mechanical Engineering Indian Institute of Technology Guwahati

Email: [email protected]: http://www.iitg.ernet.in/mesaFax:+91-361-2690762,+91-361-2582699

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