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Gurpreet Kour Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 4( Version 8), April 2014, pp.13-16
www.ijera.com 13 | P a g e
CFD Based Evaluation Of Effectiveness Of Counter Flow Heat
Exchanger
Gurpreet Kour
M. Tech scholar, Thermal Engineering, BCET, Gurdaspur, Punjab, India.
Abstract
Engineers are continually being asked to improve effectiveness of heat transfer equipments. These requests may
arise as a result of the need to increase profitability or accommodate capital limitations. Processes which use
heat transfer equipment i.e. heat exchanger must frequently be improved for these reasons. Artifical roughness is
important technique for enhancing the effectiveness of heat exchanger. In this work effectiveness of smooth as
well as roughened tube in heat exchanger is theoretically investigated by using ring type roughness geometry.
The performance obtained is then compared with smooth tube. Ringed tube has a significant effect on
effectiveness of heat exchanger. The effectiveness is 3.2 times as compared with plane tube was reported. The
effectiveness found to be increased with increasing roughness and decreasing pitch between the rings.
Keywords- Heat exchanger, Effectiveness, CFD, Relative roughness.
NOMECLATURE
A Cross sectional area, m2
Cp Specific heat of water, kJ/kg K
D Diameter of inner tube, m
e Height of roughness element, m
e/D Relative roughness height(dimensionless)
L Length of test section, m
m Mass flow rate, kg/s
p Pitch of roughness element, m
p/D Relative roughness pitch (dimensionless)
q Heat transfer rate, KJ/s
Re Reynolds number (dimensionless)
Thi Hot water temperature at inlet, °K
Tho Hot water temperature at outlet, °K
Tci Cold water temperature at inlet, °K
Tco Cold water temperature at outlet, °K
V Velocity of water, ms-1
Greek letters
ρ Density of water, kg m-2
ɛ Effectiveness of heat exchanger,%
µ Dynamic viscosity of water, kg/s-1
m-1
I. INTRODUCTION
Heat transfer enhancement techniques are
frequently using in heat exchanger systems in order
to enhance heat transfer rate and to increase its
thermal performance. Heat transfer enhancement
techniques are divided into two categories active
method and passive method. In active method heat
transfer is improved by supplying extra energy to
fluids and to its equipment’s by use of mechanical
auxiliary elements i.e. rotating the surface, mixing
fluid with mechanical accessories and constituting
electrostatic in flow area. In passive method heat
transfer is improved by without any external energy
and including rough surfaces, extended surfaces and
coated surfaces. Among them coiled wire or twisted
tape inserts in swirl flow are most commonly used in
order to enhance heat transfer rate. The coiled wire or
twisted tape causes redevelopment of boundary layer
and increase the heat transfer surface area by
increasing turbulence. Numerous researches have
been carried out concerning effect of coiled wire,
twisted tape, dimpled tubes, sand grain roughness etc.
Taji et al. investigated heat transfer characteristics
and friction factor of horizontal double pipe heat
exchanger with coil wire inserts made up of different
materials. Effect of coil wire inside a horizontal tube
is studied by Garcia et al. in laminar, transition and
turbulent region with different pitch and wire
diameter. Heat transfer and friction correlations are
developed by Webb R.L et al. for turbulent flow in
tubes having a repeated-rib roughness.
CFD based theoretically evaluation of heat
exchanger effectiveness with plane tube and
roughened tube has been carried out in this work by
inserting ringed type tubes in wall of inner tube of
heat exchanger.
II. METHODOLOGY
The system consists of a counter flow heat
exchanger of stainless steel with smooth tube and
ringed tube shown in Fig. 1. The external surfaces of
heat exchanger are properly insulated. Flow rate in
both channels was adjusted to maintain same
Reynolds number. The effectiveness of heat
exchanger was calculated on the basis of temperature
drop. Solidworks flow simulation 2013 tool was used
in investigation.
Following assumptions has been used:
1. The fluids are in steady state conditions.
RESEARCH ARTICLE OPEN ACCESS
Gurpreet Kour Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 4( Version 8), April 2014, pp.13-16
www.ijera.com 14 | P a g e
2. Fluids do not undergo any phase change.
3. No slip boundary conditions in solid, fluid
interface.
4. Viscous and external heat transfer is neglected.
5. Thermo physical properties are constant.
Fig. 1. Counter flow heat exchanger
Boundary conditions:
Inlet temperature of cold fluid
298K
Inlet temperatures of hot fluid
348K
Internal diameter of inner tube (di)
0.017 m
Outer diameter of inner tube (do)
0.0214 m
Internal diameter of outer tube (Di)
0.042 m
Pitch (in mm)
10,20,30,40,50
Length
1.5m
Table 1: The range/value of operating parameters
S
No.
Operating parameter Range/value
1. Reynold number (Re) 3000-20,000
2. Relative roughness height
(e/D)
0.029-0.117
3. Relative roughness pitch
(p/D)
0.588-2.94
4. Mass flow rate (ṁ) 0.016-0.1
kg/s
5. Temperature of hot water
(o
K)
348 o
K
6. Temperature of cold
water(o
K)
298 o
K
III. DATA REDUCTION
In this work, effectiveness and heat transfer
rate was calculated by using the following equation:
maxq
q
  (1)
max min ( )hi ciq c T T  (2)
( ) ( )c pc hi co c ph co ciq m C T T m C T T    (3)
( )c c pc co ciq m C T T  (4)
( )h h ph ho hiq m C T T  (5)
IV. RESULT AND DISCUSSION
Results obtained w.r.t. in analyzing the
effect of relative roughness height (e/D),
Effectiveness, Relative relevant pitch (p/D), Mass
flow rate and Reynolds number under the said
theoretical study have been presented.
0
10
20
30
40
50
60
0 5000 10000 15000 20000 25000
Effectiveness,ɛ(%)
Reynolds number, Re
e/D=0.0117
e/D=0.0588
e/D=0.029
Smooth tube
Fig. 2: Variation of effectiveness as a function of
Reynolds no. for range of relative roughness
height (e/D).
Fig. 2 shows the variation of effectiveness as
a function of Reynolds number of smooth and
roughened tube. It can be seen that effectiveness
increases monotonously with decrease in mass flow
rate of water for smooth as well as roughened tube. It
can be seen that effectiveness for the tube fitted with
coil wire insert are higher than that of plain tube for
given Reynolds number.
0
10
20
30
40
50
60
5000 10000 15000 20000 25000 30000
Effectiveness,ɛ(%)
Reynold number(Re)
p/D=0.588
p/D=1.176
p/D=1.764
p/D=2.35
p/D=2.94
smooth tube
e/D=0.117
Fig. 3: Variation of effectiveness as a function of
Reynolds number.
Gurpreet Kour Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 4( Version 8), April 2014, pp.13-16
www.ijera.com 15 | P a g e
Fig. 3 shows the variation of effectiveness as
a function of Reynolds number of water for smooth
and roughened tube for range of relative roughness
pitch (p/D) at fixed relative relevant roughness (e/D)
of 0.117.
10
20
30
40
50
60
0.02 0.07 0.12 0.17
Effectiveness,ɛ(%)
Relative roughnessheight(e/D)
Re=3273.2
Re=6501.2
Re=9901.3
Re=13048.0
3
Re=16517.8
Re=19784.9
p/D=0.588
Fig. 4: Variation of effectiveness as a function of
mass flow rate for range of relative roughness
height (e/D).
Fig. 4 shows the variation of effectiveness as
a function of Reynolds number of relative roughness
height (e/D) in range of 0.029 -0.117.
Fig. 5 shows the effectiveness for roughened
tube is considerably higher as compared to smooth
tube.
Fig. 6 shows the variation of effectiveness as
a function of relative relevant pitch (p/D) for range of
Reynolds number and relative relevant roughness
(e/D) is kept fixed at 0.117.
10
20
30
40
50
60
0.02 0.07 0.12 0.17
Effectiveness,ɛ(%)
Relative roughness height(e/D)
Re=3273.2
Re=6501.2
Re=9901.3
Re=13048.03
Re=16517.8
Re=19784.9
p/D=0.588
Fig. 5: Variation of effectiveness as a function of
relative relevant height (e/D).
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Effectiveness,ɛ(%)
Relative relavent pitch(p/D)
Re=3273.2
Re=6501.2
Re=9901.3
Re=13048.3
Re=16517.8
Re=19784.10
e/D=0.117
Fig. 6: Variation of effectiveness as a function of
relative relevant pitch (p/D).
V. CONCLUSION
Numerical simulation of counter flow heat
exchanger using computational fluid dynamics (CFD)
is a very representative. This study offers a good
understanding of temperature distribution and fluid
flow under turbulent conditions for the range of
Reynolds number. Effectiveness increases for the
roughened tube as compared to that of the smooth
tube.
 The effectiveness increases monotonously with
decrease in mass flow rate of water for smooth as
well as roughened tube. It can be observed that
enhancement in effectiveness is considerably
large at lower values of flow rate of water.
 Effectiveness increases with decrease in reynolds
number of water for smooth as well roughened
tube. It has been observed that effectiveness
increases with decrease of reynolds number.
 The effectiveness increases with increase in
relative roughness height (e/D) at fixed relative
relevant pitch (p/D).
 The effectiveness increases at lesser value of
pitch .i.e., at 10 mm is higher due to increase in
number of rings which increases the turbulence
in the region.
REFERENCES
[1]. Achenbach E. and Heinecke E., 1981. On
vortex shedding from smooth and rough
cylinders in the range of Reynolds numbers
6,000 – 50, 00,000. Journal of Fluid
Mechanics, Vol. 109, 239-251.
[2]. Chan Woo Park, Hyun Churl Cho, Yong
Tae Kang, 2004. The effect of heat transfer
additive and surface roughness of micro-
scale hatched tubes on absorption
Gurpreet Kour Int. Journal of Engineering Research and Applications www.ijera.com
ISSN : 2248-9622, Vol. 4, Issue 4( Version 8), April 2014, pp.13-16
www.ijera.com 16 | P a g e
performance. Elsevier science Ltd.
Vol.27(3),264-270.
[3]. Gunes Sibel, Ozceyhan Veysel, Buyukalaca
Orhan, 2010. Heat transfer enhancement in
a tube with equilateral triangle cross
sectioned coiled wire inserts. Vol. 34, Issue
6, 684–691.
[4]. Gamrat G., Favre-Marinet M., Le Person S.,
Baviere R and Ayela F., 2008. An
experimental study and modelling of
roughness effects on laminar flow in micro
channels. Journal of Fluid Mechanics. Vol.
594, 399-423.
[5]. Garcia A., Vicente P.G., Viedma A., 2005.
Experimental study of heat transfer
enhancement with wire coil inserts in
laminar-transition turbulent regimes at
different prandtl number. Intenational
journal of heat and mass transfer,Vol. 4,
640-651.
[6]. Gunes S., Ozceyhan V., Buyukalaca O.,
2010. Heat transfer enhancement in a tube
with equilateral triangle cross sectioned
coiled wire inserts. Experimental Thermal
and Fluid Science, 684–691.
[7]. Herwig H., Gloss D and Wenterodt T., 2008.
A new approach to understanding and
modelling the influence of wall roughness on
friction factors for pipe and channel flows.
Journal of Fluid Mechanics, Vol. 613,35-53.
[8]. Hans V.S., Saini R.P., Saini J.S., Heat
transfer and friction factor correlations for
a solar air heater duct roughened artificially
with multiple v-ribs. Elsevier science Ltd,
Vol. 84, Issue 6, 898–911.
[9]. John Matsson, 2010. Introduction to solid
works flow simulation. SDC publications.
[10]. Kumar Sharad, Saini R.P., 2009. CFD based
performance analysis of a solar air heater
duct provided with artificial roughness.
Elsevier science Ltd, Vol. 34, Issue 5, 1285–
1291.
[11]. Karwa, Solanki R., S.C. and Saini J.S.,
1999. Heat Transfer Coefficient and
Friction Factor Correlations for the
Transitional Flow Regime in Rib-Roughened
Rectangular Ducts. International Journal of
Heat and Mass Transfer, 1597-1615.
[12]. Shashank S., Choudhari, Taji S.G., 2013.
Experimental Studies on Effect of Coil Wire
Insert On Heat Transfer Enhancement and
Friction Factor of Double Pipe Heat
Exchanger. International Journal of
Computational Engineering Research, Vol.
3(5).
[13]. Webb R.L., Eckert E.R.G.., Goldstein R.J.,
1971. Heat transfer and friction in tubes and
repeated-rib roughness. Elsevier Science
ltd. Vol. 14(4), 601-617.

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  • 1. Gurpreet Kour Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 4( Version 8), April 2014, pp.13-16 www.ijera.com 13 | P a g e CFD Based Evaluation Of Effectiveness Of Counter Flow Heat Exchanger Gurpreet Kour M. Tech scholar, Thermal Engineering, BCET, Gurdaspur, Punjab, India. Abstract Engineers are continually being asked to improve effectiveness of heat transfer equipments. These requests may arise as a result of the need to increase profitability or accommodate capital limitations. Processes which use heat transfer equipment i.e. heat exchanger must frequently be improved for these reasons. Artifical roughness is important technique for enhancing the effectiveness of heat exchanger. In this work effectiveness of smooth as well as roughened tube in heat exchanger is theoretically investigated by using ring type roughness geometry. The performance obtained is then compared with smooth tube. Ringed tube has a significant effect on effectiveness of heat exchanger. The effectiveness is 3.2 times as compared with plane tube was reported. The effectiveness found to be increased with increasing roughness and decreasing pitch between the rings. Keywords- Heat exchanger, Effectiveness, CFD, Relative roughness. NOMECLATURE A Cross sectional area, m2 Cp Specific heat of water, kJ/kg K D Diameter of inner tube, m e Height of roughness element, m e/D Relative roughness height(dimensionless) L Length of test section, m m Mass flow rate, kg/s p Pitch of roughness element, m p/D Relative roughness pitch (dimensionless) q Heat transfer rate, KJ/s Re Reynolds number (dimensionless) Thi Hot water temperature at inlet, °K Tho Hot water temperature at outlet, °K Tci Cold water temperature at inlet, °K Tco Cold water temperature at outlet, °K V Velocity of water, ms-1 Greek letters ρ Density of water, kg m-2 ɛ Effectiveness of heat exchanger,% µ Dynamic viscosity of water, kg/s-1 m-1 I. INTRODUCTION Heat transfer enhancement techniques are frequently using in heat exchanger systems in order to enhance heat transfer rate and to increase its thermal performance. Heat transfer enhancement techniques are divided into two categories active method and passive method. In active method heat transfer is improved by supplying extra energy to fluids and to its equipment’s by use of mechanical auxiliary elements i.e. rotating the surface, mixing fluid with mechanical accessories and constituting electrostatic in flow area. In passive method heat transfer is improved by without any external energy and including rough surfaces, extended surfaces and coated surfaces. Among them coiled wire or twisted tape inserts in swirl flow are most commonly used in order to enhance heat transfer rate. The coiled wire or twisted tape causes redevelopment of boundary layer and increase the heat transfer surface area by increasing turbulence. Numerous researches have been carried out concerning effect of coiled wire, twisted tape, dimpled tubes, sand grain roughness etc. Taji et al. investigated heat transfer characteristics and friction factor of horizontal double pipe heat exchanger with coil wire inserts made up of different materials. Effect of coil wire inside a horizontal tube is studied by Garcia et al. in laminar, transition and turbulent region with different pitch and wire diameter. Heat transfer and friction correlations are developed by Webb R.L et al. for turbulent flow in tubes having a repeated-rib roughness. CFD based theoretically evaluation of heat exchanger effectiveness with plane tube and roughened tube has been carried out in this work by inserting ringed type tubes in wall of inner tube of heat exchanger. II. METHODOLOGY The system consists of a counter flow heat exchanger of stainless steel with smooth tube and ringed tube shown in Fig. 1. The external surfaces of heat exchanger are properly insulated. Flow rate in both channels was adjusted to maintain same Reynolds number. The effectiveness of heat exchanger was calculated on the basis of temperature drop. Solidworks flow simulation 2013 tool was used in investigation. Following assumptions has been used: 1. The fluids are in steady state conditions. RESEARCH ARTICLE OPEN ACCESS
  • 2. Gurpreet Kour Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 4( Version 8), April 2014, pp.13-16 www.ijera.com 14 | P a g e 2. Fluids do not undergo any phase change. 3. No slip boundary conditions in solid, fluid interface. 4. Viscous and external heat transfer is neglected. 5. Thermo physical properties are constant. Fig. 1. Counter flow heat exchanger Boundary conditions: Inlet temperature of cold fluid 298K Inlet temperatures of hot fluid 348K Internal diameter of inner tube (di) 0.017 m Outer diameter of inner tube (do) 0.0214 m Internal diameter of outer tube (Di) 0.042 m Pitch (in mm) 10,20,30,40,50 Length 1.5m Table 1: The range/value of operating parameters S No. Operating parameter Range/value 1. Reynold number (Re) 3000-20,000 2. Relative roughness height (e/D) 0.029-0.117 3. Relative roughness pitch (p/D) 0.588-2.94 4. Mass flow rate (ṁ) 0.016-0.1 kg/s 5. Temperature of hot water (o K) 348 o K 6. Temperature of cold water(o K) 298 o K III. DATA REDUCTION In this work, effectiveness and heat transfer rate was calculated by using the following equation: maxq q   (1) max min ( )hi ciq c T T  (2) ( ) ( )c pc hi co c ph co ciq m C T T m C T T    (3) ( )c c pc co ciq m C T T  (4) ( )h h ph ho hiq m C T T  (5) IV. RESULT AND DISCUSSION Results obtained w.r.t. in analyzing the effect of relative roughness height (e/D), Effectiveness, Relative relevant pitch (p/D), Mass flow rate and Reynolds number under the said theoretical study have been presented. 0 10 20 30 40 50 60 0 5000 10000 15000 20000 25000 Effectiveness,ɛ(%) Reynolds number, Re e/D=0.0117 e/D=0.0588 e/D=0.029 Smooth tube Fig. 2: Variation of effectiveness as a function of Reynolds no. for range of relative roughness height (e/D). Fig. 2 shows the variation of effectiveness as a function of Reynolds number of smooth and roughened tube. It can be seen that effectiveness increases monotonously with decrease in mass flow rate of water for smooth as well as roughened tube. It can be seen that effectiveness for the tube fitted with coil wire insert are higher than that of plain tube for given Reynolds number. 0 10 20 30 40 50 60 5000 10000 15000 20000 25000 30000 Effectiveness,ɛ(%) Reynold number(Re) p/D=0.588 p/D=1.176 p/D=1.764 p/D=2.35 p/D=2.94 smooth tube e/D=0.117 Fig. 3: Variation of effectiveness as a function of Reynolds number.
  • 3. Gurpreet Kour Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 4( Version 8), April 2014, pp.13-16 www.ijera.com 15 | P a g e Fig. 3 shows the variation of effectiveness as a function of Reynolds number of water for smooth and roughened tube for range of relative roughness pitch (p/D) at fixed relative relevant roughness (e/D) of 0.117. 10 20 30 40 50 60 0.02 0.07 0.12 0.17 Effectiveness,ɛ(%) Relative roughnessheight(e/D) Re=3273.2 Re=6501.2 Re=9901.3 Re=13048.0 3 Re=16517.8 Re=19784.9 p/D=0.588 Fig. 4: Variation of effectiveness as a function of mass flow rate for range of relative roughness height (e/D). Fig. 4 shows the variation of effectiveness as a function of Reynolds number of relative roughness height (e/D) in range of 0.029 -0.117. Fig. 5 shows the effectiveness for roughened tube is considerably higher as compared to smooth tube. Fig. 6 shows the variation of effectiveness as a function of relative relevant pitch (p/D) for range of Reynolds number and relative relevant roughness (e/D) is kept fixed at 0.117. 10 20 30 40 50 60 0.02 0.07 0.12 0.17 Effectiveness,ɛ(%) Relative roughness height(e/D) Re=3273.2 Re=6501.2 Re=9901.3 Re=13048.03 Re=16517.8 Re=19784.9 p/D=0.588 Fig. 5: Variation of effectiveness as a function of relative relevant height (e/D). 0 10 20 30 40 50 60 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Effectiveness,ɛ(%) Relative relavent pitch(p/D) Re=3273.2 Re=6501.2 Re=9901.3 Re=13048.3 Re=16517.8 Re=19784.10 e/D=0.117 Fig. 6: Variation of effectiveness as a function of relative relevant pitch (p/D). V. CONCLUSION Numerical simulation of counter flow heat exchanger using computational fluid dynamics (CFD) is a very representative. This study offers a good understanding of temperature distribution and fluid flow under turbulent conditions for the range of Reynolds number. Effectiveness increases for the roughened tube as compared to that of the smooth tube.  The effectiveness increases monotonously with decrease in mass flow rate of water for smooth as well as roughened tube. It can be observed that enhancement in effectiveness is considerably large at lower values of flow rate of water.  Effectiveness increases with decrease in reynolds number of water for smooth as well roughened tube. It has been observed that effectiveness increases with decrease of reynolds number.  The effectiveness increases with increase in relative roughness height (e/D) at fixed relative relevant pitch (p/D).  The effectiveness increases at lesser value of pitch .i.e., at 10 mm is higher due to increase in number of rings which increases the turbulence in the region. REFERENCES [1]. Achenbach E. and Heinecke E., 1981. On vortex shedding from smooth and rough cylinders in the range of Reynolds numbers 6,000 – 50, 00,000. Journal of Fluid Mechanics, Vol. 109, 239-251. [2]. Chan Woo Park, Hyun Churl Cho, Yong Tae Kang, 2004. The effect of heat transfer additive and surface roughness of micro- scale hatched tubes on absorption
  • 4. Gurpreet Kour Int. Journal of Engineering Research and Applications www.ijera.com ISSN : 2248-9622, Vol. 4, Issue 4( Version 8), April 2014, pp.13-16 www.ijera.com 16 | P a g e performance. Elsevier science Ltd. Vol.27(3),264-270. [3]. Gunes Sibel, Ozceyhan Veysel, Buyukalaca Orhan, 2010. Heat transfer enhancement in a tube with equilateral triangle cross sectioned coiled wire inserts. Vol. 34, Issue 6, 684–691. [4]. Gamrat G., Favre-Marinet M., Le Person S., Baviere R and Ayela F., 2008. An experimental study and modelling of roughness effects on laminar flow in micro channels. Journal of Fluid Mechanics. Vol. 594, 399-423. [5]. Garcia A., Vicente P.G., Viedma A., 2005. Experimental study of heat transfer enhancement with wire coil inserts in laminar-transition turbulent regimes at different prandtl number. Intenational journal of heat and mass transfer,Vol. 4, 640-651. [6]. Gunes S., Ozceyhan V., Buyukalaca O., 2010. Heat transfer enhancement in a tube with equilateral triangle cross sectioned coiled wire inserts. Experimental Thermal and Fluid Science, 684–691. [7]. Herwig H., Gloss D and Wenterodt T., 2008. A new approach to understanding and modelling the influence of wall roughness on friction factors for pipe and channel flows. Journal of Fluid Mechanics, Vol. 613,35-53. [8]. Hans V.S., Saini R.P., Saini J.S., Heat transfer and friction factor correlations for a solar air heater duct roughened artificially with multiple v-ribs. Elsevier science Ltd, Vol. 84, Issue 6, 898–911. [9]. John Matsson, 2010. Introduction to solid works flow simulation. SDC publications. [10]. Kumar Sharad, Saini R.P., 2009. CFD based performance analysis of a solar air heater duct provided with artificial roughness. Elsevier science Ltd, Vol. 34, Issue 5, 1285– 1291. [11]. Karwa, Solanki R., S.C. and Saini J.S., 1999. Heat Transfer Coefficient and Friction Factor Correlations for the Transitional Flow Regime in Rib-Roughened Rectangular Ducts. International Journal of Heat and Mass Transfer, 1597-1615. [12]. Shashank S., Choudhari, Taji S.G., 2013. Experimental Studies on Effect of Coil Wire Insert On Heat Transfer Enhancement and Friction Factor of Double Pipe Heat Exchanger. International Journal of Computational Engineering Research, Vol. 3(5). [13]. Webb R.L., Eckert E.R.G.., Goldstein R.J., 1971. Heat transfer and friction in tubes and repeated-rib roughness. Elsevier Science ltd. Vol. 14(4), 601-617.