A numerical study was conducted to investigate convective heat transfer and laminar fluid flow in the developing region of two-dimensional parallel-plate channels with arrays of transverse hemicircular grooves cut into the plates. Air with uniform velocity and temperature enters the channel whose plates are at a uniform temperature. The finite-volume method is used to perform the computational analysis accounting for the traditional second-order-accurate QUICK and SIMPLE schemes. Steady-state results are presented for parallel-plate channels with and without hemicircular grooves for comparison purposes. The study revolves around four controlling parameters: (1) the height of the channel, (2) the relative groove depth, (3) the number of grooves, and (4) the Reynolds number. A prototypical 120cm-long channel contains two series of 3, 6, and 12 transverse grooves with four relative groove depths δD of 0.125, 0.25, 0.375, and 0.5. Three ratios of channel height to groove print diameter HD of 0.5, 1, and 2 are employed. Computations are performed for Reynolds numbers based on the hydraulic diameter ranging from 1000 to 2500. It is found that the grooves enhance local heat transfer relative to a flat passage at locations near their downstream edge. The maximum heat transfer enhancement occurs at an optimal depth of the grooves. For purposes of engineering design, generalized correlation equations for the Nusselt number in terms of the pertinent Re, δD, and the number of grooves N were constructed using nonlinear regression theory.

1.
Gnielinski
,
V.
, 1998, “
Forced Convection in Ducts
,”
Handbook of Heat Exchanger Design
,
G. F.
Hewitt
, ed.,
Begell House
,
New York
, Chap. 4.
2.
Sekulic
,
D. P.
, and
Shah
,
R. K.
, 2002,
Fundamentals of Heat Exchanger Design
,
Wiley
,
New York
.
3.
Simons
,
R. E.
,
Antonnetti
,
V. W.
,
Nakayawa
,
W.
, and
Oktay
,
S.
, 1997, “
Heat Transfer in Electronic Packages
,”
Handbook of Microelectronics Packaging
, 2nd ed.,
R. R.
Tummala
, ed.,
Chapman and Hall
,
New York
, pp.
1.315
1.403
.
4.
Bar-Cohen
,
A.
,
Watwe
,
A. A.
, and
Prasher
,
R. S.
, 2003, “
Heat Transfer in Electronic Equipment
,”
Handbook of Heat Transfer
,
A.
Bejan
and
A. D.
Kraus
, eds.,
Wiley
,
New York
, Chap. 13.
5.
Chung
,
Y. M.
,
Tucker
,
P. G.
, and
Luo
,
K. H.
, 2001, “
Large-Eddy Simulation of Complex Internal Flows
,”
Direct and Large-Eddy Simulations IV
,
B. J.
Geurts
,
R.
Friedrich
and
O.
Metais
, eds.,
Kluwer Academic
,
The Netherlands
.
6.
Chung
,
Y. M.
,
Luo
,
K. H.
, and
Sandham
,
N. D.
, 2002, “
Numerical Study of Momentum and Heat Transfer in Unsteady Impinging Jets
,”
Int. J. Heat Fluid Flow
0142-727X,
23
, pp.
592
600
.
7.
Berner
,
C.
,
Durst
,
F.
, and
McEligot
,
D. M.
, 1984, “
Flow Around Baffles
,”
ASME J. Heat Transfer
0022-1481,
106
, pp.
743
749
.
8.
Webb
,
B. W.
, and
Ramadhyani
,
S.
, 1985, “
Conjugate Heat Transfer in a Channel With Staggered Ribs
,”
Int. J. Heat Mass Transfer
0017-9310,
28
, pp.
1679
1687
.
9.
Kelkar
,
K. M.
, and
Patankar
,
S. V.
, 1987, “
Numerical Prediction of Flow and Heat Transfer in a Parallel-Plate Channel With Staggered Fins
,”
ASME J. Heat Transfer
0022-1481,
109
, pp.
25
30
.
10.
Lazardis
,
A.
, 1988, “
Heat Transfer Correlation for Flow in a Parallel-Plate Channel With Staggered Fins
,”
ASME J. Heat Transfer
0022-1481,
110
, pp.
801
802
.
11.
Cheng
,
C. H.
, and
Huang
,
W. H.
, 1989, “
Laminar Forced Convection Flows in Horizontal Channels With Transverse Fins Placed in the Entrance Region
,”
Numer. Heat Transfer, Part A
1040-7782,
16
, pp.
77
100
.
12.
Ghaddar
,
N. K.
,
Karczak
,
K. Z.
,
Mikic
,
B. B.
, and
Patera
,
A. T.
, 1986, “
Numerical Investigation of Incompressible Flow in Grooved Channels, Part 1. Stability and Self-Sustained Oscillations
,”
J. Fluid Mech.
0022-1120,
163
, pp.
99
127
.
13.
Ghaddar
,
N. K.
,
Megan
,
M.
,
Mikic
,
B. B.
, and
Patera
,
A. T.
, 1986, “
Numerical Investigation of Incompressible Flow in Grooved Channels, Part 2. Resonance and Oscillatory Heat-Transfer Enhancement
,”
J. Fluid Mech.
0022-1120,
168
, pp.
541
567
.
14.
Amon
,
C. H.
, and
Mikic
,
B. B.
, 1990, “
Numerical Prediction of Convective Heat Transfer in Self-Sustained Oscillatory Flows
,”
J. Thermophys. Heat Transfer
0887-8722,
4
, pp.
239
246
.
15.
Amon
,
C. H.
, 1992, “
Heat Transfer Enhancement by Flow Destabilization in Electronic Chip Configurations
,”
ASME J. Electron. Packag.
1043-7398,
144
, pp.
35
40
.
16.
Wirtz
,
R. A.
,
Huang
,
F.
, and
Greiner
,
M.
, 1999, “
Correlation of Fully Developed Heat Transfer and Pressure Drop in a Symmetrically Grooved Channel
,”
ASME J. Heat Transfer
0022-1481,
121
, pp.
236
238
.
17.
Greiner
,
M.
, 1987, “
Flow Field Destabilization and Heat Transfer Enhancement in Grooved Channels
,”
FED (Am. Soc. Mech. Eng.)
0888-8116,
52
, pp.
131
138
.
18.
Greiner
,
M.
,
Faulkner
,
R. J.
,
Van
,
V. T.
,
Tufo
,
H. M.
, and
Fischer
,
P. F.
, 2000, “
Simulations of Three-Dimensional Flow and Heat Transfer in a Symmetrically Grooved Channel
,”
ASME J. Heat Transfer
0022-1481,
122
, pp.
653
660
.
19.
Greiner
,
M.
,
Fischer
,
P. F.
,
Tufo
,
H. M.
, and
Wirtz
,
R. A.
, 2002, “
Three-Dimensional Simulations of Enhanced Heat Transfer in a Flat Passage Downstream From a Grooved Channel
,”
ASME J. Heat Transfer
0022-1481,
124
, pp.
169
176
.
20.
Greiner
,
M.
,
Fischer
,
P. F.
, and
Tufo
,
H. M.
, 2002, “
Two-Dimensional Simulations of Enhanced Heat Transfer in an Intermittently Grooved Channel
,”
ASME J. Heat Transfer
0022-1481,
124
, pp.
538
545
.
21.
McGarry
,
M.
,
Campo
,
A.
, and
Hitt
,
D. L.
, 2004, “
Numerical Simulations of Heat and Fluid Flow in Grooved Channels With Curved Vanes
,”
Numer. Heat Transfer, Part A
1040-7782,
46
, pp.
41
54
.
22.
Mahmood
,
P. M.
, and
Ligrani
,
P. M.
, 2002, “
Heat Transfer in a Dimpled Channel: Combined Influences of Aspect Ratio, Temperature Ratio, Reynolds Number, and Flow Structure
,”
Int. J. Heat Mass Transfer
0017-9310,
45
, pp.
2011
2020
.
23.
Ligrani
,
P. M.
,
Harrison
,
J. L.
,
Mahmood
,
G. I.
, and
Hill
,
M. L.
, 2001, “
Flow Structure Due to Dimple Depressions on a Channel Surface
,”
Phys. Fluids
1070-6631,
13
, pp.
3442
3451
.
24.
Mahmood
,
G. I.
,
Hill
,
M. L.
,
Nilson
,
D. L.
,
Ligrani
,
P. M.
,
Moon
,
H. K.
, and
Glezer
,
B.
, 2001, “
Local Heat Transfer and Flow Structure on and Above a Dimpled Surface in a Channel
,”
ASME J. Turbomach.
0889-504X,
123
, pp.
115
123
.
25.
Won
,
S. Y.
, and
Ligrani
,
P. M.
, 2004, “
Numerical Predictions of Flow Structure and Local Nusselt Number Ratios Along and Above Dimpled Surfaces With Different Dimple Depths in a Channel
,”
Numer. Heat Transfer, Part A
1040-7782,
46
, pp.
549
570
.
26.
Park
,
J.
,
Desam
,
P. R.
, and
Ligrani
,
P. M.
, 2004, “
Numerical Predictions of Flow Structure Above a Dimpled Surface in a Channel
,”
Numer. Heat Transfer, Part A
1040-7782,
45
, pp.
1
20
.
27.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
Hemisphere
,
Washington, DC
.
28.
Poling
,
B. E.
,
Prausnitz
,
J. M.
and
O’Connell
,
J. P.
, 2001,
The Properties of Gases and Liquids
,
McGraw-Hill
,
New York
, pp.
A.5
A.19
.
29.
Shah
,
R. K.
, and
London
,
L. A.
, 1978,
Laminar Flow and Heat Transfer in Ducts
,
Academic
,
New York
.
30.
Burgess
,
N. K.
,
Oliveira
,
M. M.
, and
Ligrani
,
P. M.
, 2004, “
Nusselt Number Behavior on Deep Dimpled Surfaces Within a Channel
,”
ASME J. Heat Transfer
0022-1481,
125
, pp.
11
18
.
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