The accuracy of approximating radiative heat transfer using a temperature dependent thermal conductivity
Abstract
Radiative heat transfer across the gap between two coaxial cylinders can be approximated using an equivalent thermal conductivity that is a cubic polynomial in the temperatures T(sub 1) and T(sub 2) of the two surfaces (T(sub 1) greater than T(sub 2)). It is convenient to write the polynomial in terms of the average temperature, yielding T(sub avg(exp 3)) multiplied by an expression in T(sub avg)/T(sub 1). This expression has a value close to unity when the temperature difference is small and approaches 2 as the lower temperature approaches zero. The approximation is valid if the temperature of each surface is uniform. Numerical calculations showed that it is also reasonably accurate when the temperature varies with height on the cooler surface. An electrical circuit analogy shows that this should be generally true, but that the approximation may be poor when the hotter surface temperature is not uniform. The appendix shows the derivation of the view factors used in the radiative heat transport calculations.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 February 1993
 Bibcode:
 1993STIN...9414318C
 Keywords:

 Cylindrical Bodies;
 Radiative Heat Transfer;
 Surface Temperature;
 Temperature Dependence;
 Temperature Gradients;
 Thermal Conductivity;
 Equivalent Circuits;
 Mathematical Models;
 Polynomials;
 Thermodynamics;
 Fluid Mechanics and Heat Transfer