pressure and heat transfer over a series of in-line non-circular ducts in a parallel plate channel

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 9, Number 18 (2014) pp. 5125-5139

© Research India Publications

http://www.ripublication.com

Pressure and Heat Transfer over a Series

of In-line Non-Circular Ducts in a

Parallel Plate Channel S. D. Mhaske #1, S. P. Sunny #2, S. L. Borse #3, Y. B. Parikh#4

#1Department of Mechanical Engineering, Symbiosis Institute of Technology,

Pune, India. #2Department of Mechanical Engineering, Symbiosis Institute of Technology,

Pune, India. #3Department of Mechanical Engineering, Rajarshi Shahu College of Engineering,

Pune, India. #4Department of Mechanical Engineering, Symbiosis Institute of Technology,

Pune, India.

1 [email protected], 2 [email protected], 3 [email protected], 4 [email protected]

Abstract

Flow and heat transfer for two-dimensional laminar flow at low Reynolds number

for five in-line ducts of various cross-sections in a parallel plate channel are

studied in this paper. The governing equations were solved using finite-volume

method. A commercial CFD software, ANSYS Fluent 14.5 was used to solve this

problem. A total of three different non-conventional cross-sections and their

characteristics are compared with that of circular cross-section. Shape-1, Shape-2

and Shape-3 performed better for heat transfer rate than the circular cross-section,

but also offered higher resistance to the flow. Shape-1 offered less resistance to

flow at Re < 200 but post Re = 200 the resistance equalled to that of the Shape-3.

In overall, Shape-2 performed better when the heat transfer and resistance to flow

were considered.

Keyword- CFD, Flow over non-circular ducts, Heat transfer, Pressure drop,

Parallel Plates

I. INTRODUCTION

The quest for heat transfer enhancement in most of the engineering applications is a

never ending process. The need for better heat transfer and low flow resistance has led to

extensive research in the field of heat exchangers. Higher heat transfer and low pumping

5126 S. D. Mhaske et al

power are desirable properties of a heat exchanger. Tube shape and its arrangement highly

influences flow characteristics in a heat exchanger. Flow past cylinders, esp. circular, flat, oval

and diamond arranged in a parallel plate channel were extensively studied by Bahaidarah et al.

[1-3]. They carried domain discretization in body-fitted co-ordinate system while the governing

equations were solved using a finite-volume technique. Chhabra [4] studied bluff bodies of

different shapes like circle, ellipse, square, semi-circle, equilateral triangle and square

submerged in non-Newtonian fluids. Kundu [5] [6] investigated fluid flow and heat transfer

coefficient experimentally over a series of in-line circular cylinders in parallel plates using two

different aspect ratios for intermediate range of Re 220 to 2800. Grannis and Sparrow [7]

obtained numerical solutions for the fluid flow in a heat exchanger consisting of an array of

diamond-shaped pin fins. Implementation of the model was accomplished using the finite

element method. Tanda [8] performed experiments on fluid flow and heat transfer for a

rectangular channel with arrays of diamond shaped elements. Both in-line and staggered fin

arrays were considered in his study. Jeng [9] experimentally investigated pressure drop and

heat transfer of an in-line diamond shaped pin-fin array in a rectangular duct. Ota [10] studied

the Heat transfer characteristics and flow behaviours around an elliptic cylinder at high

Reynolds number. Chen et al. [11] [12] calculated flow and conjugate heat transfer in a high-

performance finned oval tube heat exchanger element have been calculated for a thermally and

hydrodynamically developing three-dimensional laminar flow. Computations have been

performed with a finite volume method based on the SIMPLEC algorithm for pressure

correction. Zdravistch [13] numerically predicted fluid flow and heat transfer around staggered

and in-line tube banks and found out close agreement experimental test cases. Tahseen et al.

[14] conducted numerical study of the two-dimensional forced convection heat transfer across

three in-line flat tubes confined in a parallel plate channel, the flow under incompressible,

steady-state conditions. They solved the system in the body fitted coordinates (BFC) using the

finite volume method (FVM). Gautier and Lamballais [15] proposed a new set of boundary

conditions to improve the representation of the infinite flow domain. Conventional tube/duct shapes have been investigated for fluid flow and heat transfer

characteristics. In this paper two-dimensional, steady state, laminar flow over non-

conventional non-circular (Shape-1, Shape-2 and Shape-3) in-line ducts confined in a parallel

plate channel is considered. The different geometries investigated are Circular, Shape-1,

Shape-2 and Shape-3. Only representative cases are discussed in this paper.

NOMENCLATURE

A area of heat transfer surfaces in a module (m2)

Cp specific heat (J/kg.K)

D blockage height of a tube inside the channel (m)

f module friction factor

f0 module friction factor for circular tubes

H height of the channel (m)

L module length (m)

k thermal conductivity (W/m.K)

l length of the tube cross-section along the flow direction (m)

Nu module average Nusselt number (= �̇�𝐶𝑝𝛥𝑇𝑏𝐻

𝑘𝐴(𝑇𝑤−𝑇𝑚))

Nu0 module average Nusselt number for the reference case of circular tubes

Nu+ heat transfer enhancement ratio (= Nu/Nu0)

Pressure and Heat Transfer over a Series of In-line Non-Circular Ducts 5127

Nu* heat transfer performance ratio

ṁ mass flow rate (kg/s)

p pressure (Pa)

Re Reynolds number (= ρVH/µ)

T temperature (K)

Tm average of module inlet bulk temperature and module outlet bulk temperature (K)

Tw temperature of heat transfer surfaces (K)

Uin velocity at the channel inlet (m/s)

�⃗� velocity field

y vertical distance from the channel bottom (m)

Δp pressure drop across a module (Pa)

Δp* normalized pressure drop (=Δp /ρ 𝑈ⅈ𝑛2 )

ΔTb change in bulk temperature across a module (K)

µ dynamic viscosity (N.s/m2)

ρ density

𝛻 del operator

II. MATHEMATICAL FORMULATION The governing mass, momentum, and energy conservation equations [1] for steady

incompressible flow of a Newtonian fluid are expressed as: Mass conservation:

𝛻 ⋅ �⃗� = 0 (1)

Momentum conservation:

�⃗� ⋅ (𝛻�⃗� ) = −𝛻𝑝 + 𝑣𝛻2�⃗� (2)

Energy Conservation:

𝜌𝐶𝑝�⃗� ⋅ (𝛻𝑇) = 𝑘𝛻2𝑇 (3)

A commercial CFD software, ANSYS Fluent 14.5 was used to solve the governing equations.

The pressure-velocity coupling is done by Semi-Implicit Method for Pressure Linked

Equations (SIMPLE) scheme.

III. GEOMETRIC CONFIGURATION A total of four different duct cross-sections namely Circular, Shape-1, Shape-2andShape-3

were analysed. The five in-line ducts were confined in a parallel-plate channel. The distance

between two consecutive ducts was kept constant. H/D, L/D and l /D ratio (shown in Fig. 1)

kept constant for all cross-sections of the ducts. The unobstructed length of the pipe before the

first and the last module kept as one module length and three module lengths respectively so

that the flow is fully developed. It is also ensured that the flow is fully developed when it enters

the channel. The ducts and the parallel plate channel walls were assumed to be of infinite extent

in the z-direction i. e. perpendicular to the paper. Hence, the flow could be considered as two-

dimensional. Since, the geometry is symmetric along the x-axis, only the lower half portion is

considered for the computation purpose.


(a)

(b)

(c)

(d)

Fig. 1. Various duct cross-sections studied in this work: (a) Circular cross-section ducts, (b) Shape-1 cross-section ducts, (c) Shape-2 cross-section ducts, (d) Shape-3 cross-section ducts

IV. GRID GENERATION

The grid for all the cases is generated using the Automatic Method with all Quadrilateral

elements in the Mesh Component System of the ANSYS Workbench 14.5 software. In the

numerical simulation, the grid of 11,000 nodes is found to be fair enough for grid independent

solution. Refining the grid proved to be unnecessary and resulting in utilizing more computer

resources. Fig. 2 shows the grid generated for all the configurations.

(a)

(b)


(c)

(d)

Fig. 2. Grid for geometries considered: (a) Circular cross-section ducts, (b) Shape-1

cross-section ducts, (c) Shape-2 cross-section ducts, (d) Shape-3 cross-section ducts

V. BOUNDARY CONDITIONS Fig. 3 represents the schematic of the boundary conditions for all the cross-sections used. A

fully developed flow with velocity profile (u = Uin) and with temperature (T = Tin) was

assigned for the flow at inlet. The temperature was kept different than that of the plate and duct

walls. A no slip (u = v = 0) boundary condition was given to the plate and duct surface. The

surface temperature of the plates and the ducts were taken to be constant (T = Tw). At the

symmetry normal component of velocity and normal gradient of other velocity components

were taken as zero. At the outflow boundary there is no change in velocity across boundary.

Fig. 3. Flow domains studied in this study with the boundary condition

VI. VALIDATION

The parallel-plate channel problem corresponds to the rectangular duct with infinite aspect

ratio. The calculated value of Nusselt number is 7.541. Comparing the calculated Nusselt

number with that of the theoretical Nusselt number value of 7.54 [16], shows that our computed

values are in good agreement with that of the theoretical values.

Using the geometric parameters L/D = 3 and H/D = 2 for circular cross-section, the

normalized pressure drop (Δp*) and Nusselt number for third module of the parallel plate

channel, when compared with the values of Kundu et al. [5] shows good agreement between

both the values.


Fig. 4. Validation with previous work Kundu et al. [5]: normalized pressure drop

across third module

TABLE I: Validation with previous work of Kundu et al. [6]: module average Nusselt

number for L/D= 3, H/D= 2

Re Second Module Third Module Fourth Module

Kundu et al. [6] 50

9.4 9.4 9.8

Present Work 9.51 9.48 9.48

Kundu et al. [6] 200

12.5 12.6 12.8

Present Work 12.68 12.63 12.64

VII. RESULTS AND DISCUSSIONS

The numerical simulation was carried out for Reynolds number ranging from 25-350 and

Prandtl number considered as 0.74.

A. Onset of Recirculation:

For any duct shape no separation of flow was observed below Re = 30. Circular duct displayed

the signs of recirculation at lowest Re value (Re = 32) [1]. The Shape-1 and Shape-2 ducts

displayed the onset of recirculation at Re value 45 while the Shape-3 showed the signs of

recirculation just under Re = 35, almost similar to the value of Circular duct.

As the values of Reynolds number is increased the recirculation region starts increasing.

At Re = 150 the length of the recirculation region is slightly smaller than the distance between

the two consecutive ducts in the flow direction while at Re = 350 the length of the recirculation

region is greater than the distance between the two consecutive ducts. Since there is no

obstruction to the flow downstream of the last duct the elliptic behaviour of the flow is observed

as shown in Fig. 5-8.


(a)

(b)

(c)

Fig. 5: Effect of Reynolds number on the streamline over Circular cross-section ducts:

(a) Re = 25, (b) Re = 150 and (c) Re = 350

(a)

(b)

(c)

Fig. 6: Effect of Reynolds number on the streamline over Shape-1 cross-section ducts:

(a) Re = 25, (b) Re = 150 and (c) Re = 350

(a)


(b)

(c)


(a) Re = 25, (b) Re = 150 and (c) Re = 350

(a)

(b)

(c)


(a) Re = 25, (b) Re = 150 and (c) Re = 350

B. Fluid Flow Characteristics:

From the Fig. 5-8 and the data from Table II we can observe that the streamlines past the ducts

1-4 are similar in nature. Also the Fig. 9 shows the normalized u-velocity profiles at module

inlet for modules 2,3,4 and 5 for the lower portion of the channel for various cases at Re = 150.

We can observe that the normalized u-velocity profiles at module inlet for modules 2, 3, 4 and

5 matches well with each other at all the Reynolds number. Hence, we can say that the flow is

periodically developed for inner modules. As the flow is periodically developed, the pressure

drop and Nusselt number values for inner modules are same we can say that the study of any

module from 2-5 is sufficient. In present study we have selected module 3.

Fig. 10 shows the normalized pressure drop (Δp*) as a function of Reynolds number. We

can observe that, as the value of Re increases there is a steep descend in normalized pressure

drop for all the ducts presented in this study. All the ducts show higher normalized pressure

drop than the Circular ducts. The Shape-3 duct shows highest normalized pressure drop. There

is geometric similarity between Shape-2 and Shape-3. Hence there is no significant normalized

pressure drop difference between Shape-2 and Shape-3 ducts until Re = 50, but as the Re value

increases normalized pressure drop difference between Shape-2 and Shape-3 ducts starts

increasing. Recirculation of flow plays a vital role in this behaviour of normalized pressure

drop.


The ratio of normalized pressure drop for noncircular duct module (Δp*) to that for the

circular duct module (Δp0*) is shown in Fig. 11. The Shape-1 ducts presents lower pressure

drop ratio than its counterparts for Re < 200. On the other hand the pressure drop ratio for

Shape-2 ducts dips considerably. The pressure drop ratio shown in Fig. 11 of Shape-1, Shape-

2 and Shape-3 ducts is higher than 1 for all the values of Reynolds number which means that

they offer higher flow resistance than Circular ducts. This will lead to higher pumping power

for heat exchanger with any of the above duct cross-section.

(a) (b)

(c) (d)

Fig. 9. Normalized u-velocity profiles at inlet of modules at Re=150

Fig. 10. Variation of normalized pressure drop (Δp*) with Re for third module


Fig. 11.Variation of Δp*/Δp0* with Re for third module

C. Heat Transfer Characteristics:

Fig. 12 presents the module average Nusselt number as a function of Re for module 3 for Shape-

1, Shape-2, Shape-3 and Circular ducts. The Nusselt number for Re < 50 increases rapidly as

the Re increases. The duct shape has a very little effect on heat transfer rate at Re < 50. Post

Re = 50 the Nusselt number varies exponentially with the cross-section of the duct. Shape-1,

Shape-2 and Shape-3 ducts showed higher heat transfer rate than the circular ducts. At higher

values of Re the recirculation of the flow takes place. This recirculation vortices do not transfer

heat energy to the main stream of flow. Hence, their contribution to heat transfer is very less.

Fig. 13 presents the heat transfer enhancement ratio (Nu+) as a function of Re for module

3 for Shape-1, Shape-2 and Shape-3 ducts. Shape-1, Shape-2 and Shape-3 ducts performed

better than the Circular ducts. Shape-2 ducts showed highest heat transfer enhancement ratio

(Nu+) post Re = 50.

Fig. 14 presents the heat transfer performance ratio (Nu*) as a function of Re for module

3 for Shape-1, Shape-2 and Shape-3 ducts. Nu* represents heat transfer enhancement per unit

increase in pumping power. At Re < 40 Shape-1 ducts performed better than its counterparts,

but post Re = 40 Shape-2 performs better.

Fig. 12. Variation of Nu with Re for third module


Fig. 13. Variation of Nu+ with Re for third module

Fig. 14. Variation of Nu* with Re for third module


TA

BL

E I

I: C

om

par

iso

n o

f n

orm

aliz

ed p

ress

ure

dro

p a

nd

mod

ule

av

erag

e N

uss

elt

nu

mb

er f

or

all

the

geo

met

ric

tub

e sh

apes

Sh

ape-

3

Nu

*

0.9

76

0.9

77

0.9

77

0.9

76

0.9

80

1.0

19

1.0

20

1.0

19

1.0

20

1.0

21

1.0

43

1.0

31

1.0

33

1.0

32

1.0

39

1.0

62

1.0

29

1.0

32

1.0

31

1.0

34

Nu

+

1.0

47

1.0

47

1.0

47

1.0

47

1.0

50

1.0

87

1.0

85

1.0

84

1.0

85

1.0

84

1.1

00

1.0

92

1.0

89

1.0

90

1.0

89

1.1

11

1.0

90

1.0

84

1.0

89

1.0

76

Nu

7.2

07

7.2

16

7.2

05

7.2

07

7.2

52

10

.313

10

.330

10

.281

10

.283

10

.311

12

.473

12

.254

12

.128

12

.128

12

.166

13

.979

13

.150

12

.984

13

.000

12

.900

Δp

*/Δ

p0*

1.2

34

1.2

32

1.2

32

1.2

33

1.2

29

1.2

16

1.2

05

1.2

03

1.2

04

1.1

96

1.1

73

1.1

86

1.1

73

1.1

79

1.1

51

1.1

43

1.1

88

1.1

62

1.1

79

1.1

28

Δp

*

9.8

96

9.9

97

9.9

92

9.9

89

9.9

92

5.5

19

5.4

32

5.4

28

5.4

19

5.3

78

3.7

61

3.1

91

3.2

00

3.1

80

3.0

64

3.2

82

2.4

00

2.4

06

2.3

91

2.2

64

Sh

ape-

2

Nu

*

0.9

76

0.9

76

0.9

77

0.9

74

0.9

83

1.0

20

1.0

17

1.0

19

1.0

17

1.0

18

1.0

47

1.0

29

1.0

37

1.0

31

1.0

38

1.0

64

1.0

30

1.0

41

1.0

36

1.0

37

Nu

+

1.0

48

1.0

46

1.0

46

1.0

44

1.0

53

1.0

89

1.0

82

1.0

83

1.0

82

1.0

82

1.1

00

1.0

90

1.0

90

1.0

91

1.0

87

1.1

06

1.0

95

1.0

87

1.0

95

1.0

78

Nu

7.2

11

7.2

10

7.2

02

7.1

88

7.2

76

10

.325

10

.298

10

.267

10

.259

10

.285

12

.474

12

.232

12

.133

12

.131

12

.140

13

.916

13

.215

13

.017

13

.072

12

.918

Δp

*/Δ

p0*

1.2

38

1.2

31

1.2

30

1.2

32

1.2

31

1.2

15

1.2

05

1.2

01

1.2

06

1.1

99

1.1

58

1.1

89

1.1

60

1.1

82

1.1

47

1.1

22

1.2

00

1.1

38

1.1

81

1.1

21

Δp

*

9.9

27

9.9

92

9.9

78

9.9

84

10

.006

5.5

13

5.4

30

5.4

19

5.4

26

5.3

89

3.7

15

3.1

98

3.1

65

3.1

88

3.0

53

3.2

22

2.4

23

2.3

58

2.3

95

2.2

51

Sh

ape-

1

Nu

*

0.9

96

0.9

96

0.9

96

0.9

95

0.9

77

1.0

16

1.0

13

1.0

14

1.0

12

1.0

15

1.0

26

1.0

10

1.0

12

1.0

04

1.0

24

1.0

34

1.0

07

1.0

07

1.0

01

1.0

23

Nu

+

1.0

26

1.0

25

1.0

25

1.0

25

1.0

05

1.0

45

1.0

42

1.0

42

1.0

43

1.0

42

1.0

52

1.0

44

1.0

44

1.0

47

1.0

42

1.0

61

1.0

48

1.0

45

1.0

56

1.0

31

Nu

7.0

59

7.0

63

7.0

57

7.0

59

6.9

45

9.9

15

9.9

12

9.8

82

9.8

83

9.9

08

11

.934

11

.716

11

.622

11

.648

11

.638

13

.360

12

.647

12

.506

12

.609

12

.361

Δp

*/Δ

p0*

1.0

93

1.0

91

1.0

90

1.0

93

1.0

90

1.0

88

1.0

88

1.0

86

1.0

94

1.0

83

1.0

80

1.1

04

1.0

97

1.1

35

1.0

54

1.0

82

1.1

28

1.1

14

1.1

77

1.0

24

Δp

*

8.7

66

8.8

54

8.8

46

8.8

58

8.8

58

4.9

39

4.9

02

4.9

01

4.9

24

4.8

70

3.4

63

2.9

70

2.9

94

3.0

61

2.8

06

3.1

06

2.2

79

2.3

09

2.3

87

2.0

57

Cir

cula

r Nu

o

6.8

82

6.8

90

6.8

83

6.8

85

6.9

08

9.4

86

9.5

17

9.4

82

9.4

79

9.5

09

11

.340

11

.224

11

.134

11

.123

11

.172

12

.588

12

.070

11

.973

11

.937

11

.988

Δp

0*

8.0

20

8.1

18

8.1

13

8.1

04

8.1

28

4.5

38

4.5

07

4.5

10

4.5

00

4.4

96

3.2

08

2.6

90

2.7

29

2.6

97

2.6

62

2.8

71

2.0

20

2.0

71

2.0

28

2.0

08

Mo

du

le

Re

= 2

5

1

2

3

4

5

Re

= 5

0

1

2

3

4

5

Re

= 1

00

1

2

3

4

5

Re

= 1

50

1

2

3

4

5


TA

BL

E I

I: C

on

tinu

ed

Sh

ape-

3

Nu

*

1.0

76

1.0

26

1.0

25

1.0

33

1.0

15

1.0

79

1.0

20

1.0

16

1.0

31

1.0

07

1.0

81

1.0

10

1.0

07

1.0

25

1.0

04

1.0

82

1.0

00

0.9

98

1.0

20

1.0

01

Nu

+

1.1

22

1.0

86

1.0

77

1.0

92

1.0

52

1.1

24

1.0

78

1.0

67

1.0

91

1.0

43

1.1

27

1.0

65

1.0

59

1.0

87

1.0

41

1.1

31

1.0

52

1.0

51

1.0

82

1.0

40

Nu

15

.769

13

.776

13

.604

13

.706

13

.087

17

.657

14

.254

14

.063

14

.323

13

.062

19

.558

14

.606

14

.432

14

.868

12

.943

21

.418

14

.883

14

.722

15

.352

12

.790

Δp

*/Δ

p0*

1.1

33

1.1

87

1.1

59

1.1

83

1.1

15

1.1

31

1.1

80

1.1

60

1.1

88

1.1

11

1.1

34

1.1

72

1.1

63

1.1

92

1.1

13

1.1

39

1.1

63

1.1

68

1.1

96

1.1

21

Δp

*

3.0

39

1.9

78

1.9

79

1.9

69

1.8

60

2.8

86

1.7

12

1.7

10

1.7

04

1.6

15

2.7

79

1.5

26

1.5

25

1.5

21

1.4

50

2.7

00

1.3

88

1.3

91

1.3

87

1.3

29

Sh

ape-

2

Nu

*

1.0

74

1.0

35

1.0

36

1.0

43

1.0

24

1.0

81

1.0

32

1.0

29

1.0

46

1.0

16

1.0

88

1.0

26

1.0

23

1.0

43

1.0

19

1.0

95

1.0

25

1.0

15

1.0

40

1.0

15

Nu

+

1.1

12

1.1

05

1.0

79

1.1

04

1.0

61

1.1

18

1.1

06

1.0

71

1.1

09

1.0

56

1.1

26

1.1

03

1.0

63

1.1

07

1.0

65

1.1

36

1.1

06

1.0

55

1.1

07

1.0

67

Nu

15

.622

14

.011

13

.625

13

.858

13

.199

17

.560

14

.629

14

.108

14

.550

13

.230

19

.539

15

.136

14

.490

15

.147

13

.243

21

.515

15

.648

14

.774

15

.699

13

.120

Δp

*/Δ

p0*

1.1

08

1.2

15

1.1

29

1.1

85

1.1

15

1.1

06

1.2

30

1.1

25

1.1

91

1.1

24

1.1

09

1.2

44

1.1

23

1.1

98

1.1

42

1.1

14

1.2

56

1.1

21

1.2

05

1.1

62

Δp

*

2.9

75

2.0

26

1.9

28

1.9

73

1.8

60

2.8

21

1.7

84

1.6

59

1.7

10

1.6

34

2.7

16

1.6

20

1.4

72

1.5

29

1.4

86

2.6

42

1.4

99

1.3

34

1.3

98

1.3

78

Sh

ape-

1

Nu

*

1.0

46

1.0

07

1.0

00

1.0

03

1.0

07

1.0

57

1.0

07

0.9

90

0.9

92

1.0

03

1.0

68

1.0

06

0.9

82

0.9

76

1.0

08

1.0

79

1.0

04

0.9

74

0.9

60

1.0

12

Nu

+

1.0

78

1.0

54

1.0

42

1.0

65

1.0

11

1.0

97

1.0

57

1.0

36

1.0

57

1.0

09

1.1

15

1.0

57

1.0

29

1.0

42

1.0

19

1.1

35

1.0

56

1.0

24

1.0

25

1.0

28

Nu

15

.154

13

.361

13

.162

13

.369

12

.575

17

.222

13

.982

13

.643

13

.873

12

.643

19

.350

14

.499

14

.027

14

.257

12

.676

21

.500

14

.939

14

.339

14

.543

12

.648

Δp

*/Δ

p0*

1.0

96

1.1

46

1.1

30

1.2

00

1.0

14

1.1

16

1.1

56

1.1

44

1.2

11

1.0

19

1.1

39

1.1

61

1.1

54

1.2

16

1.0

33

1.1

63

1.1

62

1.1

61

1.2

19

1.0

50

Δp

*

2.9

42

1.9

10

1.9

30

1.9

97

1.6

91

2.8

48

1.6

77

1.6

85

1.7

38

1.4

82

2.7

91

1.5

12

1.5

12

1.5

53

1.3

45

2.7

56

1.3

87

1.3

82

1.4

14

1.2

45

Cir

cula

r

Nu

0

14

.053

12

.681

12

.630

12

.548

12

.435

15

.706

13

.225

13

.175

13

.125

12

.525

17

.352

13

.717

13

.625

13

.681

12

.435

18

.945

14

.149

14

.009

14

.185

12

.299

Δp

0*

2.6

84

1.6

67

1.7

07

1.6

64

1.6

68

2.5

51

1.4

50

1.4

74

1.4

35

1.4

54

2.4

50

1.3

02

1.3

11

1.2

77

1.3

02

2.3

70

1.1

94

1.1

90

1.1

60

1.1

86

Mo

du

le

Re

= 2

00

1

2

3

4

5

Re

= 2

50

1

2

3

4

5

Re

= 3

00

1

2

3

4

5

Re

= 3

50

1

2

3

4

5


VIII. CONCLUSION

In an environment wherein the heat transfer rate is critical, any of the above mentioned non-

conventional cross-section of the ducts (Shape-1, Shape-2 and Shape-3) will perform better

than that of the circular cross-section ducts. The duct shape has a very little influence on the

heat transfer rate at low Reynolds number. For optimal design of a heat exchanger for heat

transfer enhancement per unit increase in pumping power, Reynolds number and cross-section

of the duct must be carefully chosen. In overall, Shape-2 performed better when both, the heat

transfer rate and resistance to flow were considered.

ACKNOWLEDGEMENT

The authors would like to present their sincere gratitude towards the Faculty of Mechanical

Engineering in Symbiosis Institute of Technology, Pune and Rajarshi Shahu College of

Engineering, Pune.

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