experimental study for a mixed convection heat transfer from an isothermal horizontal triangular...

8/10/2019 Experimental Study for a Mixed Convection Heat Transfer from an Isothermal Horizontal Triangular Cylinder

1/16

International Journal of Engineering Sciences, 2(6) June 2013, Pages: 210-225

TI Journals

International Journal of Engineering Scienceswww.tijournals.com

ISSN2306-6474

* Corresponding author.

Email address: [email protected]

Experimental Study for a Mixed Convection Heat Transferfrom an Isothermal Horizontal Triangular Cylinder

M.A. Hassab1, M.A. Teamah

2, W.M.El-Maghlany

3, M.A.Kandil

4

1,3,4Faculty of Engineering, Alexandria University, Egypt. 2Arab Academy for Science and Technology and Maritime Transport, Egypt.

A R T I C L E I N F O A B S T R A C T

Keywords:

Mixed Convection

Isothermal Triangular

Attack Angle

Laminar mixed convection heat transfer from an isothermal horizontal triangular cylinder was

experimentally investigated. The experimental study includes designing and constructing the test

rig to fulfill the research requirements. Three equilateral triangular cylinders have been investigated

in the present study with side length of 37, 50 and 70 mm respectively. The mixed convection

experiments were established for Grashof numbers ranging from 26.32104 to 213.4610

4,

Reynolds number ranging from 75.3 to 1251.6, and the attack angles from 0o to 180

o. The

experimental results gave the average Nusselt number for air with Prandtl number of 0.7 as aworking fluid. The results are presented as Nusselt numbers for different values of triangular

cylinders side length and attack angle at different Reynolds number for mixed convection heat

transfer.

2013 Int. j. eng. sci. All rights reserved for TI Journals.

1. Introduction

The convective heat transfer is one of the most important subjects that have been studied both numerically and experimentally, because it

affects the performance of thermal equipment in numerous engineering applications. These include heat exchangers, natural circulation

boilers, nuclear reactors, solar heating systems, dry cooling towers, cooling of electronic equipment, etc. Oosthuizen and Bishop [1,2]

investigated numerically and experimentally the mixed convection heat transfer over a square cylinder and the measured results were

correlated for both assisting and opposing. A numerical study has been reported by Abd-Elsamie [3] for mixed convection from an

isothermal infinite circular cylinder to air in the range 1< Re < 500 and 0.6 < Gr < 210

6

. The average Nusselt numbers were presented forboth assisting and opposing flow. Oosthuizen and Madan [4] investigated experimentally the combined convection heat transfer from

isothermal circular cylinders in air which covered the flow regime of 102< Re < 3103and 2.510

4< Gr < 310

5. Oosthuizen and Paul [5]

studied experimentally the heat transfer rates from square cylinders in both of assisting and opposing flows. Armaly et al. [6] presented

correlation equations for mixed convection flow across horizontal cylinders and spheres in air for various ranges of Reynolds and Grashof

numbers. Abu-Hijleh [7] solved the problem of laminar mixed convection from an isothermal cylinder numerically using the finite

difference method in the range 1< Re < 200 and 0 < Gr/Re2< 35. Turki et al. [8] have numerically studied the effect of two blockage ratios

(BL=1/4 and 1/8) on the two dimensional unsteady flow past a square cylinder inside horizontal channel for Reynolds number ranging from

62 to 200 and Richardson number from 0 to 0.1 for air. The results were presented to show the effects of the blockage ratio, the Reynolds

and Richardson numbers on the flow pattern and the heat transfer from the square cylinder. A heat transfer correlation was obtained for

forced and mixed convection. Alowa [9] investigated experimentally and numerically the laminar mixed convection heat transfer from an

isothermal circular cylinder. The numerical solution covered Prandtl number from 0.01 to 100 for Grashof number, Gr ( 8103, 810

4and

8105) , Reynolds number, Re ranging from 10 to 10

3and attack angles of forced flow approaching the cylinder from (assisting

flow) to (opposing flow) with an interval of 30o . The experimental work was applied for laminar mixed convection from an

isothermal circular cylinder to air. Three cylinders diameters 12.5, 25.5 and 50 mm were used. Experimental and numerical correlations

were obtained for laminar mixed convection. Sharma and Eswaran [10] studied the effect of channel-confinement of various degrees of

blockage ratio ( 10 %, 30 % and 50 % ) on the upward flow and heat transfer characteristics around a heated / cooled square cylinder by

considering the effect of aiding / opposing buoyancy at -1 Ri 1 , for Re = 100 and Pr = 0.7. The influence of buoyancy and channel -

confinement on the recirculation length, drag and lift coefficients, pumping power, Strouhal number and heat transfer from the cylinder, was

also investigated. Dhiman et al. [11] investigated the effects of cross-buoyancy and of Prandtl number on the flow and heat transfer

characteristic of an isothermal square cylinder confined in a channel. Abbassi et al. [12] studied the mixed convection in a plane channel

heated from below in the presence of a triangular prism for Re=100 and for different values of Grashof number in air. Their studies have

shown that the effect of thermal buoyancy had a slight increase of the frequency of the vortex shedding and a 44% increase in the time

averaged Nusselt number. In a similar paper by Abbassi et al. [13]; mixed convection was studied for a differentially heated two

dimensional plane channel with a built in triangular prism. Their investigation showed that the time averaged Nusselt number can be


2/16

Experimental Study for a Mixed Convection Heat Transfer from an Isothermal Horizontal Triangular Cylinder

International Journal of Engineering Sciences, 2(6) June 2013

211

described by a linear function of ln (Re) for Reynolds number range 50-200 and for zero Grashof number in air. Mohsenzedh et al. [14]

investigated numerically the effect of tandem heated triangular cylinders in a plane channel for Reynolds number of 100, 250 and 300. Their

results showed that wall proximity has different effect on first and second triangle in fluid characteristics especially in lower gap spaced and

the same behavior was seen for heat transfer. The effect of wall proximity on forced convection in a plane channel with a built-in triangular

cylinder has recently been investigated numerically for Reynolds number 100-450 by Farhadi et al. [15]. Their results showed that the

vortex formation at the downstream of the obstacle has a main effect on the flow separation over the surface of the lower channel wall. We

hope that we can present some guidelines that will be helpful in such kind of thermal analysis in the different engineering applications.

2. Experimental set up and measuring technique

The experimental setup used in the present investigation is schematically shown in Fig.1. It consists of a steam generator, steam separator,

test triangular cylinder, air duct, air duct arrangements and instruments.

Figure1. General view of the experimental setup


3/16

M.A. Hassab et al.


212

2.1. Test Procedure

The steps to run the experimental test using the apparatus and instruments are sequentially compiled in the following:

Fill the steam generator with distilled water to the level marked onto the water level inspection glass tube. The water level

inside the generator should not be lower than the bottom sign to ensure that the electric heater element is always entirely

immersed in the water.

Adjust the inclination angle of the air duct to the required angle by means of the protractor fixed on the duct.

Switch on the main power supply (220 V for the voltage transformers and the temperature read out) and then switch on the

voltage transformer of the heater and adjust the required heater input power that can be determined by reading both of the

voltmeter and ammeter.

Observe the water temperature inside the steam generator through the temperature read out device. When the temperature of

the water reaches around 90oC, switch on the super-heater transformer to operate the super-heater and adjust its power to

the required superheating degree.

When the steam starts to flow out of the steam separator drainage, close the drainage valve. This means that there is nowater at the separator. The water level inside the generator should be continuously observed.

Switch on the main switch of the fan in the electric supply board, and then switch on the fan. Adjust the required air mass

flow rate by means of the gate valve that is inserted on the fan suction pipe. The air mass flow rate through the air duct can be

determined from the pressure difference in the orifice manometer.

For almost one hour, observe the test cylinder temperature and the input and output steam temperatures. When these temperatures

reach steady state, start to measure the primary mass flow rate of the condensate.

The condensate mass flow rate is accomplished in a way that once the collecting cup is set under the condensate drain, thestopwatch is switched on. When enough mass is collected, switch off the stopwatch and draw away the collecting cup

instantaneously.

Weigh the collected condensate, and evaluate the mass flow rate, repeat this process ( condensate mass flow rate ) until the

mass flow rate stays constant. In this situation, the steady state of the experiment is fully reached.

Record all measured temperatures, the atmospheric pressure, steam U-tube height difference hs, orifice U-tube height

difference, ho. Start the final measurement of the condensate mass flow rate. This represents the test condensate mass flow rate.

At the end of this measurement, the temperatures, atmospheric pressure, steam U-tube height difference, orifice U-tube height

difference are recorded again.

3. Data reduction

The dimensionless groups of this investigation will be calculated starting from the raw data. All the measured data are recorded twice,

before and after the condensate measurement. The average of the two measurements is considered.

3.1. Total Heat Transfer from the Outer Surface of the Test Cylinder

The source of heat transferred at the isothermal surface of the cylinder is due to the condensation of steam fed in it. This heat is transferred

through the cylinder wall and then to the air in the air duct. The steam fed into cylinder is superheated, and the condensate water might be

sub-cooled. Therefore, the total heat transferred from the cylinder surface is given as:

consatpfgsatsipctot T-TC+h+T-TCm=Q lv (1)

3.2. Convective Heat Transfer from the Test Cylinder

The heat transfer from the cylinder has three parts:

Heat transfer to the inside wall surfaces of the air duct by radiation, Qrad.

Heat conduction through the insulation at both ends of the cylinder, Qc,endand at the condensate transfer tube , Qc,ct .

Heat transfer to the air inside the air duct by convection, Qconv.

dd

d

devddevdevdev

dev

db,devb,

dd

d

wdwww

w

db,wb,

rad

A

1+

AF

1+

A

1+

A

1+

AF

1+

A

1=Q

_EE_EE (2)

ax

2co2ci

ax

1co1ci

ra

2co2ci

ra

1co1ci

end,cR

TT

R

TT

R

TT

R

TTQ (3)


4/16



213

ct

tube.cconct,c

R

TTQ

(4)

.ct,c.end,crad.totconvQQQQQ (5)

The average Nusselt number, TTbkQ

k

ahNu

wf

conv

f 13 (6)

4. Discussion

V.1 Heat transfer categories from the test cylinder

The heat transfer by convection from the test triangular cylinder is a portion of the whole heat released due to the condensation of the steam

fed inside the cylinder. The heat transfer from the test triangular cylinder is divided into three parts:

Radiation heat transfer between the exposed outer triangular cylinder surface and inside wall surfaces of the air duct, QRad.

Conduction heat transfer through the insulation existed at both ends of the triangular cylinder and the condensate transfer tube, QCond.

Convection heat transfer from the exposed triangular cylinder surface to the air duct, QConv.

The trend of the categories of the heat transfer and their ratios from the total heat transfer are shown in Figs.2 to 7 which is drawn for the

three triangular cylinder, a = 37, 50, 70 mm respectively at the attack angles of 0o, 45

o, 90

o, 135

o, 180

ofor each triangular cylinder. The

amounts of radiation heat transfer from the cylinder stay constant because the emissivity of both cylinder and duct surfaces are relatively

constant. Furthermore, the thermal conductivity of the Styrofoam insulation is constant and the temperature difference is almost unchanged.

Therefore, the heat transfer by conduction is unchanged with Reynolds number.Fig.2 to 4 shows that the heat transfer by convection

increases with the angle of attack. Through these conditions, the changeable part of heat transfer is the convection heat transfer because it is

affected by Gr, Re and the attack angle.

The trend of the ratios for categories of the heat transfer from the total heat transfer are shown in Fig.5 to 7, which is drawn for the three

triangular cylinders, these figures indicate that, the major heat transfer category is convection through side walls of the test triangular

cylinders.

V.2. Experimental results for the average Nusselt number

Figs. 8 to 13 show the experimental results for the average Nusselt number versus Reynolds number and Richardson number. As observed

in Fig. 4 for the smallest triangular cylinder, a = 37 mm, the average Nusselt number slightly increases for Re < 200 where natural

convection is dominant. As the Reynolds number increases (Re 200), the Nusselt number increases with a higher rate. This is because the

forced convection is dominant. For the same Reynolds number, as the attack angle of the air flow increases the Nusselt number decreases.

The Nusselt number at attack angles of 60o, 90

oand 120

ofor Reynolds number less than 250 has the smallest values. This is because the

effects of the duct walls. At low Re, the natural convection is dominant which directs the thermal plume vertically upwards. For these

angles, the thermal plume is unable to propagate entirely and it is entrapped under the top duct wall causing a reduction inNu . For attack

angles 150oand 180

o(opposing flow), the flows are opposing each other and at the minimum Re the natural convection dominates. As

Reynolds number increases, the convection approaches the mixed convection regime where the forced convection competes with the

natural convection. With increasing Re, the natural and forced convection reach a point at which both are equivalent and, at this situation

Nu reaches the lowest value, even less than natural one. Increasing Re, the forced convection is dominant and Nu returns to increase

again with the increase of Re. For the mixed convection, the buoyancy parameter Ri, which is known as the Richardson number; provides a

measure of the influence of free convection in comparison with the forced convection. It is defined as:

2

Re

Gr=Ri (7)

The Richardson number gives an indication whether the flow may be considered as forced or natural convection. So, if Ri is of a lower

order than one, the buoyancy force is relatively insignificant and forced convection flow is prevailed. On the other hand, if Ri is of a

significantly greater order than one, the buoyancy force effect is dominant and the flow will tend to be natural convect ion. Accordingly, the

experimental results are plotted as Nu versus Ri. These figures show that Richardson number mainly affects Nusselt number in the

mixed convection region. The Richardson number is defined as the ratio of Gr to Re2

. This means the ratio of buoyancy force to inertia

force. For natural flow dominant regime, the buoyancy force is higher than the inertia force that produces (Ri >1). While in forced flow


5/16

M.A. Hassab et al.


214

dominant regime the inertia force is higher than the buoyancy force which gives (Ri


6/16



215

Figure 3. Categories of heat transfer from the triangular cylinder versus Re. at various attack angles for a = 50 mm

Figure 4. Categories of heat transfer from the triangular cylinder versus Re. at various attack angles for a = 70 mm


7/16

M.A. Hassab et al.


216

Figure 5. Percentage ratio of heat transfer Categories from the triangular cylinder versus Re. at various attack angles for a = 37 mm



8/16



217


0 100 200 300 400 500 600

Re

11

12

13

14

15

16

17

18

Nu

Attack Angle (Deg)

0.0

30

45

6090

120

135

150

180

Figure 8.Experimental Nusselt number versus Reynolds number for a=37 mm, and Gr.=26.32 x 104for attack angle from 0

oto 180

o


9/16

M.A. Hassab et al.


218

0 5 10 15 20 25 30 35 40 45 50

Ri

11

12

13

14

15

16

17

18

Nu

Attack Angle (Deg)

0.0

30

45

60

90120

135

150

180

Figure 9. Experimental Nusselt number versus Richardson number for a=37 mm, and Gr. =26.32 x 104 for attack angle from 0

oto 180

o

100 200 300 400 500 600 700 800 900

Re

11

12

13

14

15

16

17

18

19

20

Nu

Attack Angle (Deg)

0.0

30

45

60

90

120

135

150

180

Figure 10.Experimental Nusselt number versus Reynolds number for a=50 mm, and Gr.=82.88 x 104 for attack angle from 0

oto 180

o


10/16



219

0 5 10 15 20 25 30 35 40 45 50

Ri

11

12

13

14

15

16

17

18

19

Nu

Attack Angle (Deg)

0.0

30

45

60

90

120135

150

180

Figure 11. Experimental Nusselt number versus Richardson number for a=50 mm, and Gr.=82.88 x 104for attack angle from 0

oto 180

o

100 200 300 400 500 600 700 800 900 1000 1100 1200 1300

Re

13

14

15

16

17

18

19

20

21

22

23

Nu

Attack Angle (Deg)

0.0

30

45

60

90

120

135

150

180

Figure 12.Experimental Nusselt number versus Reynolds number for a=70 mm, and Gr. =213.45 x 104for attack angle from 0

oto 180

o


11/16

M.A. Hassab et al.


220

0 5 10 15 20 25 30 35 40 45 50 55 60

Ri

13

14

15

16

17

18

19

20

21

22

23

24

Nu

Attack Angle (Deg)

0.0

30

45

60

90

120

135

150

180

Figure 13. Experimental Nusselt number versus Richardson number for a=70 mm and Gr. =213.45 x 104 for attack angle from 0

oto 180

o

0 200 400 600 800 1000 1200 1400

Re

12

14

16

18

20

22

24

Nu

Triangle side length

37 mm

50 mm

70 mm

Figure 14. Experimental Nusselt number versus Reynolds number for assisti ng flow


12/16



221

0 10 20 30 40 50 60

Ri

12

14

16

18

20

22

24

Nu

Triangle Side Length

37 mm

50 mm

70 mm

Figure 15. Experimental Nusselt number versus Richardson number for assisting flow

0 200 400 600 800 1000 1200 1400

Re

13

14

15

16

17

18

19

20

21

22

23

Nu


37 mm

50 mm

70 mm

Figure 16.Experimental Nusselt number versus Reynolds number for cross flow


13/16

M.A. Hassab et al.


222

Figure 17. Experimental Nusselt number versus Richardson number for cross flow

0 200 400 600 800 1000 1200 1400

Re

12

13

14

15

16

17

18

19

20

Nu


37 mm50 mm

70 mm

Figure 18. Experimental Nusselt number versus Reynolds number for opposing flow

0 10 20 30 40 50 60

Ri

13

14

15

16

17

18

19

20

21

22

23

Nu


37 mm

50 mm

70 mm


14/16



223

0 10 20 30 40 50 60

Ri

12

13

14

15

16

17

18

19

20

Nu


37 mm

50 mm

70 mm

Figure 19.Experimental Nusselt number versus Richardson number for opposing flow

References

[1] H. Oosthuizen and M.Bishop, An experimental study of mixed convection heat transfer from square cylinders, AIAA 22nd thermo physics

conference.8-10 June 1987 / Honolulu, Hawaii, pp. 1-7.

[2]

P.H. Oosthuizen and M.Bishop, A numerical study of mixed convective heat transfer from square cylinders, Proceedings of the Eleventh Canadian

Congress of Applied Mechanics. 31 May, 4 June 1987 / Edmanton.

[3]

T.M. Abd-Elsamie, Heat transfer by laminar convection from an infinite isothermal horizontal circular cylinder, M.Sc. Thesis, Mech. Eng. Dept.,Alex. University, Egypt, 1999.

[4] P.H. Oosthuizen and S. Madan, The effect of flow direction on combined convective heat transfer from cylinders to air, ASME, Journal of Heat

Transfer- 1971, Vol. 93, pp. 240-242.

[5]

P.H. Oosthuizen and J.T. Paul, Combined convective heat transfer from square cylinders , Proceedings of the Eighth Canadian Congress of

Applied Mechanics. 7-12 June 1981 / Moncton.

[6] B.F. Armaly, T.S. Chen and N.Ramachandran, Correlations for mixed convection flows across horizontal cylinders and spheres , Transactions of

the ASME, Journal of Heat Transfer-1988, Vol. 110, pp. 511-514.

[7] B. A. Abu-Hijleh, Laminar mixed convection correlations for an isothermal cylinder in cross flow at different angles of attack, Int. J. Heat MassTransfer-1999, Vol. 42, pp. 1383-1388.

[8] S. Turki, H. Abbassi and S.B. Nasrallah, Two-dimensional laminar fluid flow and heat transfer in a channel with a built in heated square cylinder,

Int. J. Thermal Sciences-2003, Vol. 42, pp.1105-1113.[9] M.I. Alowa, An experimental and numerical study of laminar mixed convection from a n isothermal horizontal circular cylinder, PhD Thesis, Mech.

Eng. Dept., Alex. University, Egypt, 2003.

[10] A. Sharma and V. Eswaran, Effect of channel-confinement and aiding / opposing buoyancy on the t wo-dimensional laminar flow and heat transferacross a square cylinder , Int. J. Heat Mass Transfer, 2005, Vol. 48, pp. 5310-5322.

[11] A.K. Dhiman, R.P. Chhabra and V. Eswaran, Steady mixed convection across a confined square cylinder , Int. Communications in Heat and Mass

Transfer-2008, Vol. 35, pp. 47-55.

[12]

H. Abbassi, S. Turki, S. Ben Nasrallah, Mixed convection in a plane channel with a built in triangular prism, Numer. Heat Transfer Part A, 2001,Vol.39 pp. 307-320.

[13] H. Abbassi, S. Turki, S. Ben Nasrallah, Channel flow past bluff-body: outlet boundary condition, vortex shedding and effects of buoyancy, Comput.

Mech. , 2002, Vol.28 pp. 10-16.[14] A. Mohsenzedh, M. Farhadi, K. Sedighi, Convective cooling of tandem triangular cylinders placed in a channel, Thermal Sci. , 2010, Vol.14, pp.

138-197.

[15] M. Farhadi, K. Sedighi, A.M. Korayem, Effect of wall proximity on forced convection in plane channel with a built-in triangular cylinder. Int, J.Thermal Sci. , 2010, Vol.49 pp. 1010-1018.


15/16

M.A. Hassab et al.


224

Nomencalture


16/16



225

experimental study for a mixed convection heat transfer from an isothermal horizontal triangular...

Documents