Computational heat transfer developed in parallel time-wise with computational fluid dynamics because they were both prompted by the emergence of electronic devices for computation in the middle of the twentieth century and by the subsequent rapid growth in capability and availability of those devices. The development of numerical methodologies for natural convection followed a somewhat different path because the fluid motion is generated by and intimately coupled with the thermal transport. The minihistories presented herein are representative rather than definitive because they trace the contributions of only one thread of investigators. They also differ from a review by virtue of identification of the human element, which is ordinarily excluded from archival technical accounts although it usually plays a critical role. They differ in a still another sense from the contributions of Spalding and of Harlow and their associates in that most of the advances were motivated by specific practical considerations rather than by computation itself.

References

1.
Martini
,
W. R.
, and
Churchill
,
S. W.
,
1960
, “
Natural Convection Inside a Horizontal Cylinder
,”
AIChE J.
,
6
, pp.
251
257
.10.1002/aic.690060217
2.
Hellums
,
J. D.
, and
Churchill
,
S. W.
,
1961
, “
Computation of Natural Convection by Finite Difference Methods
,”
International Developments in Heat Transfer, Part V
,
American Society of Mechanical Engineers
,
New York
, pp.
984
994
.
3.
Hellums
,
J. D.
, and
Churchill
,
S. W.
,
1962
, “
Transient and Steady State, Free and Natural Convection, Numerical Solutions: Part I. The Isothermal, Vertical Plate
,”
AIChE J.
,
8
, pp.
690
692
.10.1002/aic.690080525
4.
Hellums
,
J. D.
and
Churchill
,
S. W.
,
1962
, “
Transient and Steady State, Free and Natural Convection, Numerical Solutions: Part II. The Region Inside a Horizontal Cylinder
,”
AIChE J.
,
8
, pp.
692
695
, 719.10.1002/aic.690080526
5.
Tribus
,
M.
,
1961
, “
Report on Paper 118 in Section B
,”
Discussions, International Developments in Heat Transfer
,
American Society of Mechanical Engineers
,
New York
, p.
D-302
.
6.
Wilkes
,
J. O.
, and
Churchill
,
S. W.
,
1966
, “
The Finite Difference Computation of Natural Convection in a Rectangular Enclosure
,”
AIChE J.
,
12
, pp.
161
166
.10.1002/aic.690120129
7.
Aziz
,
K.
, and
Hellums
,
J. D.
,
1967
, “
Numerical Solution of the Three-Dimensional Equations of Motion for Laminar Convection
,”
Phys. Fluids
,
10
, pp.
314
324
.10.1063/1.1762111
8.
Hirasaki
,
G. J.
and
Hellums
,
J. D.
,
1968
, “
A General Formulation of the Boundary Conditions on the Vector Potential in Three-Dimensional Hydrodynamics
,”
Q. Appl. Math.
,
26
, pp.
331
342
.
9.
Samuels
,
M. R.
, and
Churchill
,
S. W.
,
1967
, “
Stability of a Fluid in a Rectangular Chamber Heated From Below
,”
AIChE J.
,
13
, pp.
77
85
.10.1002/aic.690130115
10.
Fromm
,
J. E.
,
1963
, Los Alamos Science Laboratory, Report No. La-2910.
11.
Chu
,
H. H.-S.
,
Churchill
,
S. W.
, and
Patterson
,
C. V. S.
,
1976
, “
The Effect of Heater Size, Location, Aspect Ratio, and Boundary Conditions on Two-Dimensional, Laminar, Natural Convection in Rectangular Channels
,”
ASME J. Heat Transfer
,
98
, pp.
194
201
.10.1115/1.3450518
12.
Chu
,
H. H.-S.
, and
Churchill
,
S. W.
,
1977
, “
The Development and Testing of a Numerical Method for Computation of Laminar Natural Convection in Enclosures
,”
Comput. Chem. Eng.
,
1
, pp.
103
108
.10.1016/0098-1354(77)80014-8
13.
Ozoe
,
H.
,
Yamamoto
,
K.
,
Churchill
,
S. W.
, and
Sayama
,
H.
,
1976
, “
Three-Dimensional, Numerical Analysis of Laminar Natural Convection in a Confined Fluid Heated From Below
,”
ASME J. Heat Transfer
,
98
, pp.
202
207
.10.1115/1.3450519
14.
Ozoe
,
H.
,
Sato
,
N.
, and
Churchill
,
S. W.
,
1979
, “
Experimental Confirmation of Computed, Three-Dimensional Streaklines for Natural Convection in an Inclined Rectangular Enclosure
,”
Int. Chem. Eng.
,
19
, pp.
454
462
[Kagaku Kogaku Ronbunshu,
5
, pp. 19–25 (1979) (in Japanese)].
15.
Ozoe
,
H.
,
Fujii
,
K.
,
Lior
,
N.
, and
Churchill
,
S. W.
,
1983
, “
Long Roll Cells Generated by Natural Convection in an Inclined Rectangular Enclosure
,”
Int. J. Heat Mass Transfer
,
26
, pp.
1427
1438
.10.1016/S0017-9310(83)80044-1
16.
Churchill
,
S. W.
,
Chao
,
P. K.-B.
, and
Ozoe
,
H.
,
1981
, “
The Extrapolation of Finite-Difference Calculations of Laminar Natural Convection in Enclosures to Zero Grid Size
,”
Numerical Heat Transfer
,
4
, pp.
39
51
.10.1080/01495728108961777
17.
Yamamoto
,
K.
,
Ozoe
,
H.
,
Chao
,
P. K.-B.
, and
Churchill
,
S. W.
,
1982
, “
The Computation and Dynamic Display of Three-Dimensional Streaklines for Natural Convection in Enclosures
,”
Comput. Chem. Eng.
,
6
, pp.
161
167
.10.1016/0098-1354(82)87010-5
18.
Ozoe
,
H.
,
Mouri
,
A.
,
Ohmuro
,
M.
,
Churchill
,
S. W.
, and
Lior
,
N.
,
1985
, “
Numerical Calculations of Laminar and Turbulent Natural Convection in Water in Rectangular Channels Heated and Cooled Isothermally on Opposing Vertical Walls
,”
Int. J. Heat Mass Transfer
,
28
, pp.
125
138
.10.1016/0017-9310(85)90014-6
19.
Booker
,
V. B.
,
1997
, “
An Experimental and Three-Dimensional Numerical Investigation of Czochralski Solidification of Single Silicon Crystals
,”
Ph.D. thesis
,
University of Pennsylvania
,
Philadelphia, PA
.
20.
Yi
,
K.-W.
,
Booker
,
V. B.
,
Eguchi
,
M.
,
Shyo
,
T.
, and
Kakimoto
,
K.
,
1995
, “
Structure of Temperature and Velocity Fields in the Si Melt of a Czochralski Crystal Growth System
,”
J. Crystal Growth
,
156
, pp.
383
392
.10.1016/0022-0248(95)00277-4
21.
Nakano
,
A.
,
Ozoe
,
H.
, and
Churchill
,
S. W.
,
1998
, “
Numerical Computation of Natural Convection for a Low-Prandtl Number Fluid in a Shallow Rectangular Region Heated From Below
,”
Chem. Eng. J.
,
71
, pp.
175
182
.10.1016/S1385-8947(98)00136-3
22.
Yamanaka
,
Y.
,
Kakimoto
,
K.
,
Ozoe
,
H.
, and
Churchill
,
S. W.
,
1998
, “
Rayleigh-Benard Oscillatory Natural Convection of Liquid Gallium, Heated From Below
,”
Chem. Eng. J.
,
71
, pp.
201
205
.10.1016/S1385-8947(98)00100-4
23.
Saville
,
D. A.
, and
Churchill
,
S. W.
,
1967
, “
Convection in Boundary Layers Near Horizontal Cylinders and Vertical Axisymmetric Bodies
,”
J. Fluid Mech.
,
29
, pp.
391
399
.10.1017/S0022112067000904
24.
Saville
,
D. A.
, and
Churchill
,
S. W.
,
1969
, “
Free Convection at Low Prandtl Numbers in Laminar Boundary Layers
,”
Ind. Eng. Chem. Fundam.
,
8
, pp.
329
332
.10.1021/i160030a024
25.
Saville
,
D. A.
, and
Churchill
,
S. W.
,
1970
, “
Simultaneous Heat and Mass Transfer in Free Convection Boundary Layers
,”
AIChE J.
,
16
, pp.
268
273
.10.1002/aic.690160220
26.
Lin
,
S.-J.
, and
Churchill
,
S. W.
,
1978
, “
Turbulent Free Convection From a Vertical, Isothermal Plate
,”
Numerical Heat Transfer
,
1
, pp.
129
145
.10.1080/10407787808913368
27.
Harlow
,
F. H.
, and
Nakayama
,
P. I.
,
1968
, “
Transport of Turbulence Energy Decay Rate
,”
University of California
,
Los Alamos, NM
,
Report No. LA-3854
.
28.
Jones
,
W. P.
, and
Launder
,
B. E.
,
1972
, “
The Prediction of Laminarization With a Two-Equation Model of Turbulence
,”
Int. J. Heat Mass Transfer
,
15
, pp.
301
314
.10.1016/0017-9310(72)90076-2
29.
Seider
,
W. D.
, and
Churchill
,
S. W.
,
1971
, “
Confined Jet Mixing in the Entrance of a Tubular Reactor
,”
AIChE J.
,
17
, pp.
704
712
.10.1002/aic.690170338
30.
Harlow
,
F. H.
, and
Welch
,
J. E.
,
1965
, “
Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid With Free Surface
,”
Phys. Fluids
,
8
, pp.
2182
2189
.10.1063/1.1761178
31.
Hazbun
,
E. A.
, and
Churchill
,
S. W.
,
1973
, “
Computation of Three-Dimensional Viscous Flow Between Convergent Travelling Surfaces
,”
AIChE J.
,
20
, pp.
486
497
.10.1002/aic.690190311
32.
Brown
,
M. A.
, and
Churchill
,
S. W.
,
1999
, “
Finite-Difference Computation of the Wave Motion Generated in a Gas by a Rapid Increases in the Bounding Temperature
,”
Comput. Chem. Eng.
,
23
, pp.
357
376
.10.1016/S0098-1354(98)00279-8
33.
Trilling
,
L.
,
1955
, “
On Thermally Induced Sound Fields
,”
J. Acoust. Soc. Am.
,
27
, pp.
425
431
.10.1121/1.1907920
34.
Maxwell
,
J. C.
,
1867
, “
On the Dynamical Theory of Gases
,”
Phil. Mag.
,
157
, pp.
49
88
.
35.
Joseph
,
D. D.
, and
Preziosi
,
L.
,
1989
, “
Heat Waves
,”
Rev. Mod. Phys.
,
61
, pp.
41
73
.10.1103/RevModPhys.61.41
36.
Joseph
,
D. D.
, and
Preziosi
,
L.
,
1990
, Addendum to the Paper “
Heat Waves
,”
Rev. Mod. Phys.
,
62
, pp.
375
391
.10.1103/RevModPhys.62.375
37.
Lord Rayleigh (Strutt
,
J. W.
),
1899
, “
On the Conduction of Heat in a Spherical Mass of Air Confined by Walls at High Temperature
,”
Phil Mag.
,
47
, pp.
314
325
.10.1080/14786449908621264
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