Abstract

The discrete Green's function (DGF) is a superposition-based descriptor of the relationship between the surface temperature and the convective heat transfer from a surface. The surface is discretized into a finite number of elements and the DGF matrix elements relate the heat transfer out of any element i to the temperature rise on every element j of the surface. For a given flow situation, the DGF is insensitive to the thermal boundary condition so it allows direct calculation of the heat transfer for any temperature distribution and noniterative solution of conjugate heat transfer problems. The diagonal elements of the matrix are determined solely by the local velocity field while the off-diagonals are determined by the spread of the thermal wake downstream of a heated element. An analytical DGF for the laminar flat-plate boundary layers is included as an example.

References

References
1.
Bergman
,
T. L.
,
Incropera
,
F. P.
,
Lavine
,
A. S.
, and
DeWitt
,
D. P.
,
2011
,
Introduction to Heat Transfer
,
Wiley
, Hoboken, NJ. 
2.
Holman
,
J. P.
,
1981
,
Heat Transfer
,
McGraw-Hill Science, Engineering & Mathematics
, New York.
3.
Hacker
,
J.
, and
Eaton
,
J.
,
1997
, “
Measurements of Heat Transfer in a Separated and Reattaching Flow With Spatially Varying Thermal Boundary Conditions
,”
Int. J. Heat Fluid Flow
,
18
(
1
), pp.
131
141
.10.1016/S0142-727X(96)00142-7
4.
Sellars
,
J.
,
Tribus
,
M.
, and
Klein
,
J.
,
1956
, “
Heat Transfer  to Laminar Flow in a Round Tube or Flat Conduit–the Graetz Problem Extended
,”
Trans. ASME
,
78
(
2
), pp.
441
448
.https://deepblue.lib.umich.edu/bitstream/handle/2027.42/7510/bad2050.0001.001.pdf?sequence=5
5.
Anderson
,
A. M.
, and
Moffat
,
R. J.
,
1992
, “
The Adiabatic Heat Transfer Coefficient and the Superposition Kernel Function: Part 1–Data for Arrays of Flatpacks for Different Flow Conditions
,”
ASME J. Electron. Packag.
,
114
(
1
), pp.
14
21
.10.1115/1.2905435
6.
Andreoli
,
V.
,
Cuadrado
,
D. G.
, and
Paniagua
,
G.
,
2018
, “
Prediction of the Turbine Tip Convective Heat Flux Using Discrete Green's Functions
,”
ASME J. Heat Transfer
,
140
(
7
), pp.
1
11
.10.1115/1.4039182
7.
Batchelder
,
K. A.
, and
Eaton
,
J. K.
,
2001
, “
Practical Experience With the Discrete Green's Function Approach to Convective Heat Transfer
,”
ASME J. Heat Transfer
,
123
(
1
), pp.
70
76
.10.1115/1.1336509
8.
Kays
,
W.
,
Crawford
,
M.
, and
Weigand
,
B.
,
2005
,
Convective Heat and Mass Transfer
,
McGraw-Hill Higher Education
,
Boston, MA
.
9.
Eckert
,
E.
,
1955
, “
Engineering Relations for Friction and Heat Transfer to Surfaces in High Velocity Flow
,”
J. Aeronaut. Sci.
,
22
(
8
), pp.
585
587
.https://doi.org/10.2514/8.3399
10.
Schultz
,
D. L.
, and
Jones
,
T.
,
1973
, “
Heat-Transfer Measurements in Short-Duration Hypersonic Facilities
,” Advisory Group for Aerospace Research and Development, Paris, France, Report No. AGARD-AG-165. 
11.
Lienhard
,
J.
,
2020
, “
Heat Transfer in Flat-Plate Boundary Layers: A Correlation for Laminar, Transitional, and Turbulent Flow
,”
ASME J. Heat Transfer
,
142
(
6
), p. 061805.  10.1115/1.4046795
12.
Kakac
,
S.
,
Yener
,
Y.
, and
Pramuanjaroenkij
,
A.
,
2013
,
Convective Heat Transfer
,
CRC Press, Boca Raton, FL
.
13.
Blasius
,
H.
,
1907
,
Grenzschichten in Flüssigkeiten Mit Kleiner Reibung
,
Druck Von BG Teubner
, Leipzig, Germany.
14.
Eaton
,
J. K.
, and
Milani
,
P. M.
,
2020
, “
The Discrete Green's Function for Convective Heat Transfer Part 2: Semi-Analytical Estimates of Boundary Layer Discrete Green's Function
,”
ASME J. Heat Transfer
,
142
(10), p. 102102.10.1115/1.4047516
15.
Mukerji
,
D.
, and
Eaton
,
J. K.
,
2005
, “
Discrete Green's Function Measurements in a Single Passage Turbine Model
,”
ASME J. Heat Transfer
,
127
(
4
), pp.
366
377
.10.1115/1.1844537
16.
Booten
,
C.
, and
Eaton
,
J. K.
,
2005
, “
Discrete Green's Function Measurements in Internal Flows
,”
ASME J. Heat Transfer
,
127
(
7
), pp.
692
698
.10.1115/1.1924567
17.
Booten
,
C. W.
, and
Eaton
,
J. K.
,
2007
, “
Discrete Green's Function Measurements in a Serpentine Cooling Passage
,”
ASME J. Heat Transfer
,
129
(
12
), pp.
1686
1696
.10.1115/1.2767749
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