ME3122 Heat Transfer1. IntroductionDepartment of Mechanical EngineeringNational University of SingaporeAY2015/16 Semester 1Course Objective To develop proficiency in applying basic heattransfer concepts and principles related toconduction, convection and radiation to analyseand solve practical engineering problems involvingheat transfer processes.ME3122Heat Transfer 2 Identify, formulate and solve problems involving different heat transfer processes; Analyse, model heat conduction in one-dimensional cases and describe two- and three-dimensional heat conduction and be able to apply them for simple heat conduction problems; Identify, model and calculate the heat transfer at radiation and irradiated surfaces; Analyse and apply appropriate empirical correlations in connection with convection for both internal and external flows; Understand principles and different types ofheat exchangers and basic calculation of overall heat transfer coefficient.ME3122Heat Transfer 3Learning OutcomesLecturers & Tutors Lecturers A/Prof PS Lee Office: E2-02-07 Email: mpelps@nus.edu.sg Prof Shu ChangOffice: E2-03-07Email: mpeshuc@nus.edu.sg Tutors Pradeep Kumar Bal (a0135574@u.nus.edu) Chen Zhen (chenzhen@u.nus.edu)ME3122Heat Transfer 4Syllabus Conduction (PS Lee) Steady, one-dimensional heat conduction with and without energy generation Unsteady heat conduction, lumped system analysis Extended surfaces Radiation (PS Lee) Black and gray body radiation Radiation between diffuse surfaces Convection (Shu Chang) Hydrodynamic and thermal boundary layers Laminar and turbulent forced convection Reynolds analogy Free convection Heat Exchangers (Shu Chang) UA-LMTD Effective-NTUME3122Heat Transfer 5Textbook & References Textbook Heat and Mass Transfer: Fundamentals & Applications, 4thEdition by Cengel and A. J. Ghajar, McGraw-Hill, 2010 CL RBR (Loans Desk 1), QC320 Cen 2010 1 copy References Fundamentals of Heat and Mass Transfer, 7thEditionby Incropera, Dewitt, Bergmann and Lavine, John Wiley & Sons, 2011CL RBR (Loans Desk 1) QC320 Inc 2011 5 copies Heat Transfer, 10thEdition by J.P. Holman, McGraw Hill Higher EducationCL RBR (Loans Desk 1), QC320 Hol 2010 2 copiesME3122Heat Transfer 6Grading (%) Continual Assessment: 50% Lab Reports (2): 20% Quizzes (2): 30% Final Examination: 50%7 ME3122Heat TransferINTRODUCTION TO HEAT TRANSFER8 ME3122Heat TransferDifference between Thermodynamics and Heat Transfer Thermodynamics tells us How much heat is transferred? How much work is done? Final/equilibrium state of the system. Heat transfer tells us How (with what modes) heat is transferred? At what rate is heat transferred? Temperature distribution inside the body.ME3122Heat Transfer 9What is Heat Transfer?10 ME3122Heat Transfer Heat transfer is thermal energy in transit due to a temperature difference. Thermal energy is associated with the translation, rotation, vibration and electronic states of the atoms and molecules that comprise matter.It represents the cumulative effect of microscopic activitiesand is directly linked to the temperature of matter. The transfer of thermal energy as heat is always from the higher-temperature medium to the lower-temperature one. Heat transfer stops when the two mediums reach the same temperature. Heat can be transferred in three different modes: Conduction Convection Radiation All modes of heat transfer require the existence of a temperature difference.Application Areas of Heat TransferME3122Heat Transfer 11 Heat transfer is commonly encountered in engineering systems and other aspects of life. Heat transfer equipment such as heat exchangers, boilers, condensers, radiators, heaters, furnaces, refrigerators, and solar collectors are designed primarily on the basis of heat transfer analysis. A knowledge of heat transfer is necessary in order to evaluate cost, the feasibility, and the size of the equipment to transfer a specified amount of heat in a given time.Quantity Meaning Symbol UnitsThermal Energy Energy associated with microscopic behavior of matterU or u Jor J /kgTemperature A means of indirectly assessing the amount of thermal energy stored in matterT K or CHeat Transfer Thermal energy transport due to temperature gradientsHeat Amount of thermal energy transferred over a time interval t > 0Q JHeat Rate Thermal energy transfer per unit timeq W or J /sHeat Flux Thermal energy transfer per unit time and per unit surface areaq" W/m2Terminology12 ME3122Heat TransferModes of Heat Transfer13 ME3122Heat Transfer Conduction: Heat transfer in a solid or a stationary fluid (gas or liquid) due to the random motion of its constituent atoms, molecules and /or electrons. Convection: Heat transfer due to the combined influence of bulk and random motion for fluid flow over a surface. Radiation: Energy that is emitted by matter due to changes in the electron configurations of its atoms or molecules and is transported as electromagnetic waves (or photons).Conduction Conduction is the transfer of energy from the more energetic to less energetic particles of a substance due to interactions between the particles. Conduction can take place in solids, liquids, or gases. In gases and liquids, conduction is due to the collisions and diffusion of the molecules during their random motion. In solids, it is due to the combinations of vibrations of the molecules in a lattice and the energy transport by free electrons.ME3122Heat Transfer 14 Experiments have shown that the rate of heat conduction through a plane layer is proportional to the temperature difference across the layer and the heat transfer area, but is inversely proportional to the thickness of the layer.( )( )1 21 21 2where: thickness of plane wall, temperature dor: :cross-sectional area of plane wall :coniffstant of erence across the wall,pT Tq ALT TTq kA kAL xxT T TALkA= = AA =A = ( )roportionality known as of the material.Note: Thermal conductivity is a transport property, which thermal conductivi.tyk measures the ability ofamaterial to conduct heatConduction (cont.)ME3122Heat Transfer 15( )( )( )( )2In the limiting case of0,Heat Rate:Wwhere :Temperature gradientC/m or K/mHeat Fourier'sFlux:W/mNote: 1. The negativesign is because hea Law of Heat Cotn isdu coctionxxdTq kAdxdTdxq dTq kA dxA = ''= = 2. The rate of heat conduction through asolid is nducted in the direction of decreasing temperaturdirectly proportional to its thermal conductive.ity.Conduction (cont.)ME3122Heat Transfer 16Convection Energy transfer by random molecular motion (as in conduction) and bulk (macroscopic) motion of the fluid. Advection: transport due solely to bulk fluid motion. Types of convection Forced convection: flow is caused by external means, e.g fan, pump,wind Natural (free) convection: flow induced by buoyancy forces due to density differences arising from temperature variations in the fluid. Latent heat exchange associated with phase change boiling and condensation.ME3122Heat Transfer 17Convection (cont.) Relation of convection to flow over a surface and development of velocity and thermal boundary layers: Convective heat transfer between a surface and a fluid can be calculated by Newtons law of cooling:h: Convection heat transfer coefficient (W/m2K)ME3122Heat Transfer 18( )sq hT T'' = Edge of BLConvective heat transfer coefficients The heat transfer coefficient depends on surface geometry, nature of the fluid motion, as well as fluid properties.Flow h (W/m2K) Air, natural/free convection 6 30 Superheated steam or air, forced convection 30 300 Oil, forced convection60 1,800 Water, forced convection300 6,000 Water, boiling 3,000 60,000 Steam, condensing6,000 120,000ME3122Heat Transfer 19Radiation Thermal radiation is energy emitted by matter. Energy is transported by electromagnetic waves (or photons). Can occur from solid surfaces, liquids and gases. Does not require presence of a medium, e.g. solar energy travels through vaccum Radiation heat transfer at a gas/surface interface involves radiation emission, E, from the surface and the absorption of radiation incident from the surroundings (irradiation, G).ME3122Heat Transfer 20Radiation (cont.) For an ideal emitter, or blackbodyEb= oT4sStefan-Boltzmann lawwhere Ts: absolute temperature of surface (K)o: Stefan-Boltzmann constant (5.67x10-8W/m2K4) For a real (non-ideal) surfaceE = cEb= coT4s where c: surface emissivity (0 s c s 1) Energy absorption due to irradiation G:Gabs= oG = ooT4surwhere o: surface absorptivity (0 s o s 1) For a gray surface,o = cME3122Heat Transfer 21 Irradiation: Special case of surface exposed to large surroundings of uniform temperature, Tsur( )( )( )( )4 42 2If = , the net radiation heat flux from the surface due to exchange with the surroundings is:Note can expresswhere For combined convecrad b s surrad r s sur r s sur s surq E G T Tq h T T h T T T To cc o coco''= = ''= = + +( ) ( )tion and radiation,conv rad s r s surq q q hT T h T T'' '' ''= + = + Radiation (cont.)22 ME3122Heat TransferME3122Heat Transfer 23In a manufacturing plant, the walls and ceiling of an oven are made of 200 mm thick fire-clay brick having a thermal conductivity of 1.5 W/mK. During steady-state operation, measurements reveal an inner surface temperature of 1200C and an outer surface temperature of 200C. The internal dimensions of the oven are as follows: Length = 4m, Width = 3m and the Height = 3m. What is the rate of heat input required to maintain steady-state temperature inside the oven?Example 1Solution for Example 1ME3122Heat Transfer 244 m3 m3 m1200C 200C200 mm( )2ceiling4walls21200 200700 C21.5W/m KTotal heat transfer area,2 4 3 3 3 4 3 54mHeat flux, 200 12001.50.207500W/mRate of heat input required,7500mmo iTkAT T q dTq k kA dx tq+= = = = + + =| |'' = = = |\ .| |= |\ .==54 405kW =LL=Ti= To=An insulated pipe supplying steam from a boiler runs through a room where the air and walls are at 30C. The outer diameter of the pipe is 100 mm and its surface temperature is 250C. The natural convection heat transfer coefficient from the surface to the air is 20 W/m2K. Find the rate of heat transfer from the surface due to convection and radiation per unit length of pipe. For radiation heat loss, the outer surface of the pipe may be treated as blackbody surface.ME3122Heat Transfer 25Example 2Solution for Example 2ME3122Heat Transfer 26( )( )( )( )( )( )( )( )( )( )4 44 48Heat loss due to convection 20 0.10 250 301382.3 W/mHeat loss due to radiationNote:Absolute temp. in K5.67 10 0.1conv so sconvconvrad s suro s surradradq hAT Th D L T TqqLq AT TD L T TqqLttoott= = '= = == = '= = ( )4 4523 3031182.6 W/m 1382.3 1182.6 2565 W/mtotal conv radq q q=' ' '= + = + =Tsur = T= 30C250CDo= 100 mmh = 20 W/m2KTs=SteamExample 3The temperature in a house located at latitude 40N is maintained at 23C with a temperature controller. The temperature of the inner surfaces of walls, floors and the ceiling of the house are found to be at an average temperature of 12C in winter and 27C in summer. A person with an external body surface area of 1.2 m2 and temperature of 32C remains in standing position for fifteen minutes inside the room, where the temperature is 23C. Find the rate of radiation exchange between the person and surrounding surfaces. ME3122Heat Transfer 27Solution for Example 3ME3122Heat Transfer 28( )( )( )( )( )( )( )( )4 48 4 48 4The emittance of person (external surfaces of the skin) 0.95The rate of radiation heat exchange is given byFor summer,0.95 5.67 10 1.2 305 30035.8WFor winter,0.95 5.67 10 1.2 305 2s surq AT Tqqco== = == ( )485132.9WAlthough the thermostat setting is the same, one feels chilly in winterand warm in summer.=Ts=32oC = 305 K,Tsur=27oC = 300 KTsur=12oC = 285 KSummary of Heat Transfer ProcessesME3122Heat Transfer 29Conduction- Diffusion of energy due to random molecular motion- Fourier's Law of Conduction: Convection- Diffusion of energy due to random molecular motionplus energy transfer due to bulkxdTq kdx'' = ( )( )4 4 fluid motion- Newton's Law of Cooling: Radiation- Energy transfer by electromagnetic waves- Stefan-Boltzmann's Equation: ss surq hT Tq T T co'' = '' = Exercise 11. In a cold climate, a house is heated either using electricity or gas or coal to maintain the desired temperature. The roof of such a house is 5 m long and 7 m wide, and 0.20 m thick, and is made of concrete having a thermal conductivity of 0.8 W/mK. On a winter night , the temperatures of the inner and outer surfaces of the roof are measured as 16C and 2C, respectively, for a period of 8 hours. Determine (i) the rate of heat loss through the roof and (ii) the cost of heat loss to the home owner if the cost of electricity is $0.17 per kWh.2. An electrical heater, which consists of a rod 300 mm long and 10 mm in diameter, is placed in room at 12C in steady state operation. Heat is generated in the rod as a result of resistance heating and the surface temperature is 140C under steady state operation. The voltage drop and the current through the rod are measured and found to be 50 V and 2 A, respectively. Considering negligible heat losses by radiation, estimate the convective heat transfer coefficient between the outer surface of the rod and the air in the room.3. A blackbody at 25C is exposed to solar radiation and the temperature increased to 95C. Estimate the increase in radiation heat transfer. ME3122Heat Transfer 30Exercise 1.1In a cold climate, a house is heated either using electricity or gas or coal to maintain the desired temperature. The roof of such a house is 5 m long and 7 m wide, and 0.20 m thick, and is made of concrete having a thermal conductivity of 0.8 W/mK. On a winter night , the temperatures of the inner and outer surfaces of the roof are measured as 16C and 2C, respectively, for a period of 8 hours. Determine (i) the rate of heat loss through the roof and (ii) the cost of heat loss to the home owner if the cost of electricity is $0.17 per kWh.ME3122Heat Transfer 31Solution Outline for Exercise 1.1ME3122Heat Transfer 32in kWHeat loss from the roof, wherethickness of the roofAmount of heat lost during 8 hoursQ =no. of hours, kWhCost = (amount of energy in kWh) (unit cost of energy)i oT Tq kA ttq= =LLExercise 1.2An electrical heater, which consists of a rod 300 mm long and 10 mm in diameter, is placed in room at 12C in steady state operation. Heat is generated in the rod as a result of resistance heating and the surface temperature is 140C under steady state operation. The voltage drop and the current through the rod are measured and found to be 50 V and 2 A, respectively. Considering negligible heat losses by radiation, estimate the convective heat transfer coefficient between the outer surface of the rod and the air in the room.ME3122Heat Transfer 33Solution Outline for Exercise 1.2Neglect radiation heat loss.Under steady state operation, heat loss from the surface by convection equals energy generated within the rod due to resistance heating.q = energy generated = V I = (voltage drop, V) (current, A), Wq = heat lost by convection = hAs(Ts Ta), Wh = q / [As(Ts Ta)] = ,W/m2K ME3122Heat Transfer 34Exercise 1.3A blackbody at 25C is exposed to solar radiation and the temperature increased to 95C. Estimate the increase in radiation heat transfer.Solution OutlineCalculate emissive power at both temperatures. Increase in radiation heat transfer is equal to the difference in emissive power.E1= T14, W/m2E2= T24, W/m2Increase in radiation heat transfer = E2 E1ME3122Heat Transfer 35CONSERVATION OF ENERGYME3122Heat Transfer 36Conservation of Energy(First Law of Thermodynamics) An important tool in heat transfer analysis, often providing the basis for determining the temperature of a system. Alternative Formulations Time Basis: At an instant Over a time interval Type of System: Control volume Control surfaceME3122Heat Transfer 37Application to a Control Volume At an Instant of Time:ME3122Heat Transfer 38Note representation of system by a control surface (dashed line) at the boundaries.energy transfer across the control surfaceSurface Phenomena, :rate of thermal and/or mechanical due to heat transfer, fluid flow and/or work interactions.Volumetric Phenomenain outE E :rate of due to conversion from another enegy form (e.g., electrical, nuclear, or chemical); energy conversion process occurs within tthermal he systeenergy genem.:rate of crat nhioagstEEenergy storage in the system.Conservation of Enenge of Each term hras units of J /s or W.gyin out g stE E E E + = Application to a Control Volume (cont.) Over a Time Interval:ME3122Heat Transfer 39Each term has units of J .in out g stE E E E + = A Transient Process for a Closed System of Mass (M)Assuming Heat Transfer to the System (Inflow) and Work Done by the System (Outflow),Over a For negligible changes in potential or kinetic enertime intervalinsgyAttant an inoutstttE QE WQ W EQ W UdUq Wdt== = A = A =Internal thermal energySpecial Case Closed System40 ME3122Heat TransferSpecial Case Open System( )( )22Instant of TimeSteady State for Flow through an Open System without Phase Change or Generation:At anflow workentha:02 2For alpyid a ne lt tinouttmu pv V gz q mu pv V gz Wpvu pv i| || |+ + + + + + + = ||\ .\ .+ ( )( )( ) ( ) with:For gas constant specific heatincompressible liq an 0ud: iin out p in outin out p in outin outi i c T Tu u c T Tpv pv = = ~41 ME3122Heat Transfer For steady state conditions, no changes in kinetic or potential energy, no thermal energy generation, negligible pressure drop:Special Case Open System (cont.)( )Simplified steady-flow energy equationp out inq mc T T = 42 ME3122Heat Transfer( ) ( )( ) ( )2 202 20For systems with significant heat transfer:ininoutoutV Vgz gz ~ ~Surface Energy Balance A special case for which no volume or mass is encompassed by the control surface. Applies for steady-state and transient conditions. With no mass and volume, energy storage and generation are not pertinent to the surface energy balance. Consider surface of wall with heat transfer by conduction, convection and radiation.( )( )4 41 22 2 2 (Instant in Tim Conservation of Ene e):0g00r yin outcond conv radsurE Eq q qT Tk hT T T TLco ='' '' '' = = 43 ME3122Heat TransferL