A voltage applied across a uniform plate results in a uniform ohmic heat dissipation, useful for conducting heat transfer experiments or preventing unacceptably low temperatures on spacecraft components. Most experiments to date involve application of a known uniform heat flux to the surface of a model. Measurement of the resulting temperature distribution facilitates calculation of the heat transfer coefficient, h. The dependence of h on the boundary condition, however, may necessitate a specified nonuniform heat flux. In this paper, a novel methodology is developed for designing a nonuniform thickness heat flux plate to provide a specified spatially variable heat flux. The equations are derived to solve the two dimensional heat flux with a variable cross sectional area. After showing that this inverse heat transfer problem cannot be readily linearized, a methodology utilizing a smooth surface polynomial was applied. Then, for a prescribed, desired heat flux distribution, a 7th order polynomial (including 36 terms) yielded a normalized root mean squared error of 1% over the surface. This distributed heat flux could result in significant power and thus cost savings for a variety of applications.

References

References
1.
Kays
,
W. M.
, and
Crawford
,
M. E.
,
1993
,
Convective Heat and Mass Transfer
,
3rd ed.
,
McGraw-Hill
,
New York
.
2.
Whitaker
,
S.
,
1972
, “
Forced Convection Heat Transfer Correlations for Flow in Pipes, Past Flat Plates, Single Cylinders, Single Spheres, and for Flow in Packed Beds and Tube Bundles
,”
AIChE J.
,
18
, pp.
361
371
.10.1002/aic.690180219
3.
Liu
,
D.
, and
Li
,
Y.
,
2009
, “
A Novel Temperature Based Flat-Plate Heat Flux Sensor for High Accuracy Measurement
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, pp.
1242
1247
.
4.
Gilmore
,
D. G.
,
Lyra
,
J. C.
, and
Stultz
,
J. W.
,
2002
, “
Heaters
,”
Spacecraft Thermal Control Handbook
, Vol. 1, D. G. Gilmore, ed.,
The Aerospace Press
,
El Segundo, CA
, pp.
223
245
.
5.
Wiedner
,
B. G.
, and
Camci
,
C.
,
1996
, “
Determination of Convective Heat Flux on Steady-State Heat Transfer Surfaces With Arbitrarily Specified Boundaries
,”
ASME J. Heat Transfer
,
118
, pp.
850
856
.10.1115/1.2822580
6.
Mick
,
W. J.
, and
Mayle
,
R. E.
,
1988
, “
Stagnation Film Cooling and Heat Transfer Including Its Effect Within the Hole Pattern
,”
ASME J. Turbomach.
,
110
, pp.
66
72
.10.1115/1.3262169
7.
Mathworks
,
2011
,
Partial Differential Equation Toolbox User's Guide R2011b
,
Natick
,
MA
.
8.
Haynes
,
W. M.
,
2012
,
CRC Handbook of Chemistry and Physics
,
CRC
,
Boca Raton, FL
.
9.
Mathworks
,
2011
,
Optimization Toolbox User's Guide R2011b
,
Natick
,
MA
.
10.
Levenberg
,
K.
,
1944
, “
A Method for the Solution of Certain Non-Linear Problems in Least Squares
,”
Q. Appl. Math.
,
2
,
pp 164
168
.
11.
Marquardt
,
D.
,
1963
, “
An Algorithm for Least-Squares Estimation of Nonlinear Parameters
,”
J. Soc. Ind. Appl. Math.
,
11
, pp.
431
441
.10.1137/0111030
You do not currently have access to this content.