Coupled Radiative and Conductive Heat Transfer in a Two-Dimensional Rectangular Enclosure With Gray Participating Media Using Finite Elements

1984 ◽  
Vol 106 (3) ◽  
pp. 613-619 ◽  
Author(s):  
M. M. Razzaque ◽  
J. R. Howell ◽  
D. E. Klein
Keyword(s):  
Heat Transfer ◽  
Flux Distribution ◽  
Conductive Heat Transfer ◽  
Conductive Heat ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Heat Flux Distribution ◽  
Distributed Energy ◽  
Participating Media ◽  
Rectangular Enclosure

A numerical solution of the exact equations of coupled radiative/conductive heat transfer and temperature distribution inside a medium, and of the heat flux distribution at all the gray walls of a two-dimensional rectangular enclosure with the medium having uniform absorbing/emitting properties, using the finite element method, is presented. The medium can also have distributed energy sources. Comparison is made to the results of the P-3 approximation method.

Optimal Sizing of Planar Thermal Spreaders

1994 ◽  
Vol 116 (2) ◽  
pp. 296-301 ◽  
Author(s):  
S. Hingorani ◽  
C. J. Fahrner ◽  
D. W. Mackowski ◽  
J. S. Gooding ◽  
R. C. Jaeger
Keyword(s):  
Heat Transfer ◽  
Flux Distribution ◽  
Environmental Temperature ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Two Dimensional ◽  
Heat Flux Distribution ◽  
Optimal Thickness ◽  
Dimensionless Variables ◽  
Biot Numbers

Two-dimensional cylindrical and three-dimensional Cartesian thermal spreaders are studied. One of the surfaces is convectively coupled to a uniform environmental temperature while the opposite surface is subjected to a uniform heat flux distribution over a portion of its boundary. The problem is generalized through the introduction of appropriate dimensionless variables, and analytical solutions for the temperature field are presented for each coordinate system. The solutions depend on the usual geometric and heat transfer groups. It is found that, for a range of realistic Biot numbers and a given ratio of the spreader to heater dimensions, a dimensionless spreader thickness exists for which the temperature of the heater reaches a minimum value. Optimal thickness curves are presented for these ranges.

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