Steady-state experiments are performed to study the convection heat transfer from four in-line simulated chips in a vertical rectangular channel using water as the working fluid. The experimental data cover a wide range for laminar flow under natural, mixed, and forced convection conditions with the Reynolds number based on the channel hydraulic diameter ranging from 40 to 2220 and on the heat source length ranging from 50 to 2775. The heat flux ranges from $0.1W∕cm2to0.6W∕cm2$. The effects of heat flux, flow rates, and chip number are investigated and results indicate that the Nusselt number is strongly affected by the Reynolds number. To develop empirical correlations, the appropriate value of the exponent $n$ of $ReD$ is determined to collapse all the lines into a single line to show the independence of heat flux. Based on experimental results, the empirical correlations are developed for relations using $Nuℓ$, $ReD$, and $GrD$. The results are compared to predictions from a three-dimensional numerical simulation, and a numerical correlation is also developed.

1.
Braaten
,
M. E.
, and
Patankar
,
S. V.
, 1985, “
Analysis of Laminar Mixed Convection in Shrouded Arrays of Heated Blocks
,”
Int. J. Heat Mass Transfer
0017-9310,
28
, pp.
1699
1709
.
2.
Türkoğlu
,
H.
, and
Yücel
,
N.
, 1995, “
Mixed Convection in Vertical Channels With a Discrete Heat Source
,”
Heat Mass Transfer
0947-7411,
30
, pp.
159
166
.
3.
Wang
,
Y.
, and
Vafai
,
K.
, 1999, “
Heat Transfer and Pressure Loss Characterization in a Channel With Discrete Flush-Mounted and Protruding Heat Sources
,”
Exp. Heat Transfer
0891-6152,
12
, pp.
1
16
.
4.
Meinders
,
E. R.
,
Van Der Meer
,
T. H.
, and
Hanjalic
,
K.
, 1998, “
Local Convective Heat Transfer From an Array of Wall-Mounted Cubes
,”
Int. J. Heat Mass Transfer
0017-9310,
41
, pp.
335
346
.
5.
Du
,
S.-Q.
,
Bilgen
,
E.
, and
Vasseur
,
P.
, 1998, “
Mixed Convection Heat Transfer in Open Ended Channels With Protruding Heaters
,”
Int. J. Heat Mass Transfer
0017-9310,
34
, pp.
263
270
.
6.
Tso
,
C. P.
,
Xu
,
G. P.
, and
Tou
,
K. W.
, 1999, “
An Experimental Study on Forced Convection Heat Transfer From Flush-Mounted Discrete Heat Sources
,”
ASME J. Heat Transfer
0022-1481,
121
, pp.
326
332
.
7.
Tou
,
K. W.
,
Xu
,
G. P.
, and
Tso
,
C. P.
, 1998, “
Direct Liquid Cooling of Electronic Chips by Single-Phase Forced Convection of FC-72
,”
Exp. Heat Transfer
0891-6152,
11
, pp.
121
134
.
8.
Bhowmik
,
H.
,
Tso
,
C. P.
,
Tou
,
K. W.
, and
Tan
,
F. L.
, 2004, “
General Convection Heat Transfer From Discrete Heat Sources in a Rectangular Channel
,”
Proc. 4th European Thermal Science Conf.
, FCH 3, pp.
1
10
.
9.
Tso
,
C. P.
,
Tou
,
K. W.
, and
Bhowmik
,
H.
, 2004, “
Experimental and Numerical Thermal Transient Behavior of Chips in a Liquid Channel During Loss of Pumping Power
,”
ASME J. Electron. Packag.
1043-7398,
126
(
4
), pp.
546
553
.
10.
Incropera
,
F. P.
,
Kerby
,
J. S.
,
Moffatt
,
D. F.
, and
,
S.
, 1986, “
Convection Heat Transfer From Discrete Heat Sources in a Rectangular Channel
,”
Int. J. Heat Mass Transfer
0017-9310,
29
, pp.
1051
1058
.
11.
Willingham
,
T. C.
, and
Mudawar
,
I.
, 1970, “
Forced Convection Boiling and Critical Heat Flux From a Linear Array of Discrete Heat Sources
,”
Int. J. Heat Mass Transfer
0017-9310,
35
, pp.
2879
2890
.
12.
Heindel
,
T. J.
,
,
S. R.
, and
Incropera
,
F. P.
, 1992, “
Liquid Immersion Cooling of a Longitudinal Array of Discrete Heat Sources in Protruding Substrates: 2-Forced Convection Boiling
,”
ASME J. Electron. Packag.
1043-7398,
114
, pp.
55
62
.
13.
Kline
,
S. J.
, and
McClintock
,
F. A.
, 1953, “
Describing Uncertainties in Single-Sample Experiments
,”
Mech. Eng. (Am. Soc. Mech. Eng.)
0025-6501,
75
, pp.
3
8
.
14.
Perry
,
J. H.
, 1963,
Chemical Engineer’s Handbook
,
4th ed.
McGraw-Hill
, New York.
15.
Greankoplis
,
C. J.
, 1972,
Mass Transport Phenomena
,
Holt, Rinehart & Winston
, New York.
16.
Shah
,
R. K.
, and
London
,
A. L.
, 1978, “
Laminar Flow Forced Convection in Ducts
,”
, Supplement No. 1,
, New York.
17.
Incropera
,
F. P.
, and
Dewitt
,
D. P.
, 1998,
Fundamentals of Heat and Mass Transfer
,
Wiley
, New York.
18.
Lloyd
,
J. R.
, and
Sparrow
,
E. M.
, 1970, “
Combined Natural and Forced Convection Flow on Vertical Surfaces
,”
Int. J. Heat Mass Transfer
0017-9310,
13
, pp.
434
438
.
19.
MacGregor
,
R. K.
, and
Emery
,
A. P.
, 1969, “
Natural Convection Through Vertical Plane Layers: Moderate and High Prandtl Number Fluids
,”
ASME J. Heat Transfer
0022-1481,
91
, pp.
391
403
.
20.
Fluent Inc.
, 1995,
Computational Fluid Dynamics Software
,
Lebanon
, NH.
21.
Patankar
,
S. V.
, 1980,
Numerical Heat Transfer and Fluid Flow
,
Hemisphere Publishing
, New York.