Improvement of the effectiveness of heat exchanger is the demand of compact and efficient cooling devices. In that respect, a numerical study of fluid flow and heat transfer has been conducted with different arrangements of simple vortex generator (VG) in a rectangular microchannel Reynolds number (Re) in the range between 200 and 1100. The combined effect of spanwise and pitchwise distance of VG on heat transfer is investigated rigorously to observe the dependence of heat transfer on both. By processing the numerical predictions through gene expression programing and genetic algorithm optimization, the output variations in heat transfer, or Nusselt number, and friction factor with Re and locations of VGs in the channel are predicted in the form of explicit equations. The predicted monotonic increase of the outputs with Re shows heat transfer enhancement of 40–135% at the cost of increased pressure drop by 62–186.7% with respect to channels without VGs.

References

1.
Tuckerman
,
D. B.
, and
Pease
,
R.
,
1981
, “
High-Performance Heat Sinking for VLSI
,”
IEEE Electron Device Lett.
,
2
(
5
), pp.
126
129
.
2.
Peng
,
X.
,
Wang
,
B.
,
Peterson
,
G.
, and
Ma
,
H.
,
1995
, “
Experimental Investigation of Heat Transfer in Flat Plates With Rectangular Microchannels
,”
Int. J. Heat Mass Transfer
,
38
(
1
), pp.
127
137
.
3.
Peng
,
X.
, and
Peterson
,
G.
,
1996
, “
Convective Heat Transfer and Flow Friction for Water Flow in Microchannel Structures
,”
Int. J. Heat Mass Transfer
,
39
(
12
), pp.
2599
2608
.
4.
Wang
,
B.
, and
Peng
,
X.
,
1994
, “
Experimental Investigation on Liquid Forced-Convection Heat Transfer Through Microchannels
,”
Int. J. Heat Mass Transfer
,
37
, pp.
73
82
.
5.
Judy
,
J.
,
Maynes
,
D.
, and
Webb
,
B.
,
2002
, “
Characterization of Frictional Pressure Drop for Liquid Flows Through Microchannels
,”
Int. J. Heat Mass Transfer
,
45
(
17
), pp.
3477
3489
.
6.
Qu
,
W.
, and
Mudawar
,
I.
,
2002
, “
Experimental and Numerical Study of Pressure Drop and Heat Transfer in a Single-Phase Micro-Channel Heat Sink
,”
Int. J. Heat Mass Transfer
,
45
(
12
), pp.
2549
2565
.
7.
Kuppusamy
,
N. R.
,
Mohammed
,
H.
, and
Lim
,
C.
,
2013
, “
Numerical Investigation of Trapezoidal Grooved Microchannel Heat Sink Using Nanofluids
,”
Thermochim. Acta
,
573
, pp.
39
56
.
8.
Kuppusamy
,
N. R.
,
Mohammed
,
H.
, and
Lim
,
C.
,
2014
, “
Thermal and Hydraulic Characteristics of Nanofluid in a Triangular Grooved Microchannel Heat Sink (TGMCHS)
,”
Appl. Math. Comput.
,
246
, pp.
168
183
.
9.
Xia
,
G.
,
Chai
,
L.
,
Zhou
,
M.
, and
Wang
,
H.
,
2011
, “
Effects of Structural Parameters on Fluid Flow and Heat Transfer in a Microchannel With Aligned Fan-Shaped Reentrant Cavities
,”
Int. J. Therm. Sci.
,
50
(
3
), pp.
411
419
.
10.
Xia
,
G.
,
Zhai
,
Y.
, and
Cui
,
Z.
,
2013
, “
Numerical Investigation of Thermal Enhancement in a Micro Heat Sink With Fan-Shaped Reentrant Cavities and Internal Ribs
,”
Appl. Therm. Eng.
,
58
(
1
), pp.
52
60
.
11.
Zhai
,
Y.
,
Xia
,
G.
,
Liu
,
X.
, and
Li
,
Y.
,
2014
, “
Heat Transfer in the Microchannels With Fan-Shaped Reentrant Cavities and Different Ribs Based on Field Synergy Principle and Entropy Generation Analysis
,”
Int. J. Heat Mass Transfer
,
68
, pp.
224
233
.
12.
Schubauer
,
G. B.
, and
Spangenberg
,
W.
,
1960
, “
Forced Mixing in Boundary Layers
,”
J. Fluid Mech.
,
8
(
1
), pp.
10
32
.
13.
Johnson
,
T.
, and
Joubert
,
P.
,
1969
, “
The Influence of Vortex Generators on the Drag and Heat Transfer From a Circular Cylinder Normal to an Airstream
,”
ASME J. Heat Transfer
,
91
(
1
), pp.
91
99
.
14.
Ahmed
,
H.
,
Mohammed
,
H.
, and
Yusoff
,
M.
,
2012
, “
An Overview on Heat Transfer Augmentation Using Vortex Generators and Nanofluids: Approaches and Applications
,”
Renewable Sustainable Energy Rev.
,
16
(
8
), pp.
5951
5993
.
15.
Bi
,
C.
,
Tang
,
G.
, and
Tao
,
W.
,
2013
, “
Heat Transfer Enhancement in Mini-Channel Heat Sinks With Dimples and Cylindrical Grooves
,”
Appl. Therm. Eng.
,
55
(
1
), pp.
121
132
.
16.
Zhao
,
X.
,
Tang
,
G.
,
Ma
,
X.-W.
,
Jin
,
Y.
, and
Tao
,
W.
,
2014
, “
Numerical Investigation of Heat Transfer and Erosion Characteristics for H-Type Finned Oval Tube With Longitudinal Vortex Generators and Dimples
,”
Appl. Energy
,
127
, pp.
93
104
.
17.
Deb
,
P.
,
Biswas
,
G.
, and
Mitra
,
N.
,
1995
, “
Heat Transfer and Flow Structure in Laminar and Turbulent Flows in a Rectangular Channel With Longitudinal Vortices
,”
Int. J. Heat Mass Transfer
,
38
(
13
), pp.
2427
2444
.
18.
Fiebig
,
M.
,
1995
, “
Vortex Generators for Compact Heat Exchangers
,”
J. Enhanced Heat Transfer
,
2
(
1–2
), pp. 43–61.
19.
Fiebig
,
M.
,
1998
, “
Vortices, Generators and Heat Transfer
,”
Chem. Eng. Res. Des.
,
76
(
2
), pp.
108
123
.
20.
Fiebig
,
M.
,
1997
, “
Vortices and Heat Transfer
,”
ZAMM: J. Appl. Math. Mech./Z. Angew. Math. Mech.
,
77
(
1
), pp.
3
18
.
21.
Wu
,
J.
, and
Tao
,
W.
,
2008
, “
Numerical Study on Laminar Convection Heat Transfer in a Rectangular Channel With Longitudinal Vortex Generator. Part A: Verification of Field Synergy Principle
,”
Int. J. Heat Mass Transfer
,
51
(
5
), pp.
1179
1191
.
22.
Wu
,
J.
, and
Tao
,
W.
,
2008
, “
Numerical Study on Laminar Convection Heat Transfer in a Channel With Longitudinal Vortex Generator. Part B: Parametric Study of Major Influence Factors
,”
Int. J. Heat Mass Transfer
,
51
(
13
), pp.
3683
3692
.
23.
Allison
,
C.
, and
Dally
,
B.
,
2007
, “
Effect of a Delta-Winglet Vortex Pair on the Performance of a Tube–Fin Heat Exchanger
,”
Int. J. Heat Mass Transfer
,
50
(
25
), pp.
5065
5072
.
24.
Chen
,
Y.
,
Fiebig
,
M.
, and
Mitra
,
N.
,
2000
, “
Heat Transfer Enhancement of Finned Oval Tubes With Staggered Punched Longitudinal Vortex Generators
,”
Int. J. Heat Mass Transfer
,
43
(
3
), pp.
417
435
.
25.
Chu
,
P.
,
He
,
Y.
,
Lei
,
Y.
,
Tian
,
L.
, and
Li
,
R.
,
2009
, “
Three-Dimensional Numerical Study on Fin-and-Oval-Tube Heat Exchanger With Longitudinal Vortex Generators
,”
Appl. Therm. Eng.
,
29
(
5
), pp.
859
876
.
26.
Kwak
,
K.
,
Torii
,
K.
, and
Nishino
,
K.
,
2003
, “
Heat Transfer and Pressure Loss Penalty for the Number of Tube Rows of Staggered Finned-Tube Bundles With a Single Transverse Row of Winglets
,”
Int. J. Heat Mass Transfer
,
46
(
1
), pp.
175
180
.
27.
Li
,
J.
,
Wang
,
S.
,
Chen
,
J.
, and
Lei
,
Y.-G.
,
2011
, “
Numerical Study on a Slit Fin-and-Tube Heat Exchanger With Longitudinal Vortex Generators
,”
Int. J. Heat Mass Transfer
,
54
(
9
), pp.
1743
1751
.
28.
Torii
,
K.
,
Kwak
,
K.
, and
Nishino
,
K.
,
2002
, “
Heat Transfer Enhancement Accompanying Pressure-Loss Reduction With Winglet-Type Vortex Generators for Fin-Tube Heat Exchangers
,”
Int. J. Heat Mass Transfer
,
45
(
18
), pp.
3795
3801
.
29.
Wu
,
J.
, and
Tao
,
W.
,
2007
, “
Investigation on Laminar Convection Heat Transfer in Fin-and-Tube Heat Exchanger in Aligned Arrangement With Longitudinal Vortex Generator From the Viewpoint of Field Synergy Principle
,”
Appl. Therm. Eng.
,
27
(
14
), pp.
2609
2617
.
30.
Yang
,
K.-S.
,
Li
,
S.-L.
,
Chen
,
Y.
,
Chien
,
K.-H.
,
Hu
,
R.
, and
Wang
,
C.-C.
,
2010
, “
An Experimental Investigation of Air Cooling Thermal Module Using Various Enhancements at Low Reynolds Number Region
,”
Int. J. Heat Mass Transfer
,
53
(
25
), pp.
5675
5681
.
31.
Zeng
,
M.
,
Tang
,
L.
,
Lin
,
M.
, and
Wang
,
Q.
,
2010
, “
Optimization of Heat Exchangers With Vortex-Generator Fin by Taguchi Method
,”
Appl. Therm. Eng.
,
30
(
13
), pp.
1775
1783
.
32.
Chomdee
,
S.
, and
Kiatsiriroat
,
T.
,
2006
, “
Enhancement of Air Cooling in Staggered Array of Electronic Modules by Integrating Delta Winglet Vortex Generators
,”
Int. Commun. Heat Mass Transfer
,
33
(
5
), pp.
618
626
.
33.
Yang
,
K.-S.
,
Jhong
,
J.-H.
,
Lin
,
Y.-T.
,
Chien
,
K.-H.
, and
Wang
,
C.-C.
,
2010
, “
On the Heat Transfer Characteristics of Heat Sinks: With and Without Vortex Generators
,”
IEEE Trans. Compon. Packag. Technol.
,
33
(
2
), pp.
391
397
.
34.
Chomdee
,
S.
, and
Kiatsiriroat
,
T.
,
2007
, “
Air-Cooling Enhancement With Delta Winglet Vortex Generators in Entrance Region of In-Line Array Electronic Modules
,”
Heat Transfer Eng.
,
28
(
4
), pp.
372
379
.
35.
Ma
,
J.
,
Huang
,
Y. P.
,
Huang
,
J.
,
Wang
,
Y. L.
, and
Wang
,
Q. W.
,
2010
, “
Experimental Investigations on Single-Phase Heat Transfer Enhancement With Longitudinal Vortices in Narrow Rectangular Channel
,”
Nucl. Eng. Des.
,
240
(
1
), pp.
92
102
.
36.
Liu
,
C.
,
Teng
,
J.-T.
,
Chu
,
J.-C.
,
Chiu
,
Y.-L.
,
Huang
,
S.
,
Jin
,
S.
,
Dang
,
T.
,
Greif
,
R.
, and
Pan
,
H.-H.
,
2011
, “
Experimental Investigations on Liquid Flow and Heat Transfer in Rectangular Microchannel With Longitudinal Vortex Generators
,”
Int. J. Heat Mass Transfer
,
54
(
13
), pp.
3069
3080
.
37.
Chen
,
C.
,
Teng
,
J.-T.
,
Cheng
,
C.-H.
,
Jin
,
S.
,
Huang
,
S.
,
Liu
,
C.
,
Lee
,
M.-T.
,
Pan
,
H.-H.
, and
Greif
,
R.
,
2014
, “
A Study on Fluid Flow and Heat Transfer in Rectangular Microchannels With Various Longitudinal Vortex Generators
,”
Int. J. Heat Mass Transfer
,
69
, pp.
203
214
.
38.
Ebrahimi
,
A.
,
Roohi
,
E.
, and
Kheradmand
,
S.
,
2015
, “
Numerical Study of Liquid Flow and Heat Transfer in Rectangular Microchannel With Longitudinal Vortex Generators
,”
Appl. Therm. Eng.
,
78
, pp.
576
583
.
39.
Datta
,
A.
,
Sanyal
,
D.
, and
Das
,
A. K.
,
2016
, “
Numerical Investigation of Heat Transfer in Microchannel Using Inclined Longitudinal Vortex Generator
,”
Appl. Therm. Eng.
,
108
, pp.
1008
1019
.
40.
Ebrahimi
,
A.
,
Rikhtegar
,
F.
,
Sabaghan
,
A.
, and
Roohi
,
E.
,
2016
, “
Heat Transfer and Entropy Generation in a Microchannel With Longitudinal Vortex Generators Using Nanofluids
,”
Energy
,
101
, pp.
190
201
.
41.
Al-Asadi
,
M. T.
,
Alkasmoul
,
F.
, and
Wilson
,
M.
,
2016
, “
Heat Transfer Enhancement in a Micro-Channel Cooling System Using Cylindrical Vortex Generators
,”
Int. Commun. Heat Mass Transfer
,
74
, pp.
40
47
.
42.
Yadav
,
V.
,
Baghel
,
K.
,
Kumar
,
R.
, and
Kadam
,
S.
,
2016
, “
Numerical Investigation of Heat Transfer in Extended Surface Microchannels
,”
Int. J. Heat Mass Transfer
,
93
, pp.
612
622
.
43.
Ferreira
,
C.
,
2002
, “
Gene Expression Programming in Problem Solving
,”
Soft Computing and Industry
,
Springer-Verlag
,
London
, pp.
635
653
.
44.
Dey
,
P.
, and
Das
,
A. K.
,
2016
, “
A Utilization of GEP (Gene Expression Programming) Metamodel and PSO (Particle Swarm Optimization) Tool to Predict and Optimize the Forced Convection Around a Cylinder
,”
Energy
,
95
, pp.
447
458
.
45.
Nazari
,
A.
, and
Riahi
,
S.
,
2013
, “
Predicting the Effects of Nanoparticles on Compressive Strength of Ash-Based Geopolymers by Gene Expression Programming
,”
Neural Comput. Appl.
,
23
(
6
), pp.
1677
1685
.
46.
Azarkish
,
H.
,
Sarvari
,
S.
, and
Behzadmehr
,
A.
,
2010
, “
Optimum Design of a Longitudinal Fin Array With Convection and Radiation Heat Transfer Using a Genetic Algorithm
,”
Int. J. Therm. Sci.
,
49
(
11
), pp.
2222
2229
.
47.
Dey
,
P.
, and
Das
,
A. K.
, “
Prediction and Optimization of Unsteady Forced Convection Around a Rounded Cornered Square Cylinder in the Range of Re
,”
Neural Comput. Appl.
(published online).
48.
Copiello
,
D.
, and
Fabbri
,
G.
,
2009
, “
Multi-Objective Genetic Optimization of the Heat Transfer From Longitudinal Wavy Fins
,”
Int. J. Heat Mass Transfer
,
52
(
5
), pp.
1167
1176
.
49.
Fabbri
,
G.
,
1997
, “
A Genetic Algorithm for Fin Profile Optimization
,”
Int. J. Heat Mass Transfer
,
40
(
9
), pp.
2165
2172
.
50.
Hajabdollahi
,
F.
,
Rafsanjani
,
H. H.
,
Hajabdollahi
,
Z.
, and
Hamidi
,
Y.
,
2012
, “
Multi-Objective Optimization of Pin Fin to Determine the Optimal Fin Geometry Using Genetic Algorithm
,”
Appl. Math. Modell.
,
36
(
1
), pp.
244
254
.
51.
Ge
,
Y.
,
Liu
,
Z.
, and
Liu
,
W.
,
2016
, “
Multi-Objective Genetic Optimization of the Heat Transfer for Tube Inserted With Porous Media
,”
Int. J. Heat Mass Transfer
,
101
, pp.
981
987
.
52.
Ge
,
Y.
,
Liu
,
Z.
,
Liu
,
W.
, and
Chen
,
G.
,
2015
, “
Active Optimization Design Theory and Method for Heat Transfer Unit and Its Application on Shape Design of Cylinder in Convective Heat Transfer
,”
Int. J. Heat Mass Transfer
,
90
, pp.
702
709
.
53.
Zeng
,
X.
,
Ge
,
Y.
,
Shen
,
J.
,
Zeng
,
L.
,
Liu
,
Z.
, and
Liu
,
W.
,
2017
, “
The Optimization of Channels for a Proton Exchange Membrane Fuel Cell Applying Genetic Algorithm
,”
Int. J. Heat Mass Transfer
,
105
, pp.
81
89
.
54.
Zheng
,
Z.-J.
,
Li
,
M.-J.
, and
He
,
Y.-L.
,
2015
, “
Optimization of Porous Insert Configurations for Heat Transfer Enhancement in Tubes Based on Genetic Algorithm and CFD
,”
Int. J. Heat Mass Transfer
,
87
, pp.
376
379
.
55.
Okhotin
,
A.
,
Pushkarskij
,
A.
, and
Gorbachev
,
V.
,
1972
, “
Thermophysical Properties of Semiconductors
,” Atomizdat, Moscow, Russia.
56.
Lan
,
J.
,
Xie
,
Y.
, and
Zhang
,
D.
,
2012
, “
Flow and Heat Transfer in Microchannels With Dimples and Protrusions
,”
ASME J. Heat Transfer
,
134
(
2
), p.
021901
.
57.
Gee
,
D. L.
, and
Webb
,
R.
,
1980
, “
Forced Convection Heat Transfer in Helically Rib-Roughened Tubes
,”
Int. J. Heat Mass Transfer
,
23
(
8
), pp.
1127
1136
.
58.
Guo
,
J.
,
Xu
,
M.
, and
Cheng
,
L.
,
2011
, “
Second Law Analysis of Curved Rectangular Channels
,”
Int. J. Therm. Sci.
,
50
(
5
), pp.
760
768
.
59.
Davis
,
L.
,
1991
,
Handbook of Genetic Algorithms
, Van Nostrand Reinhold, New York.
60.
Deb
,
K.
,
2001
,
Multi-Objective Optimization Using Evolutionary Algorithms
,
Wiley
,
Chichester, UK
.
61.
Deb
,
K.
,
Pratap
,
A.
,
Agarwal
,
S.
, and
Meyarivan
,
T.
,
2002
, “
A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II
,”
IEEE Trans. Evol. Comput.
,
6
(
2
), pp.
182
197
.
62.
Song
,
K.
,
Liu
,
S.
, and
Wang
,
L.
,
2016
, “
Interaction of Counter Rotating Longitudinal Vortices and the Effect on Fluid Flow and Heat Transfer
,”
Int. J. Heat Mass Transfer
,
93
, pp.
349
360
.
You do not currently have access to this content.