Paper presented at the 5th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 1-4 July, 2007.
Analysis of any heat transfer problem
that includes thermal radiation with absorption
and emission is always complicated by the
“action-at-a-distance” nature of thermal
radiation. This implies that the entire
temperature field has to be determined
simultaneously rather than focusing on a single
location and the immediate neighborhood about
that location as in a conduction-only problem.
This paper introduces the concept of the effective
optical depth (EOD) which limits the range
about a location over which a solution is
conducted rather than solving the entire
temperature field at once. In this study, we
investigate the error introduced in the solution of
a planar, gray, radiation-conduction heat transfer
problem with black and grey boundaries for a
range of EOD/optical thickness ratio from 0.01
to 10 and conduction-radiation parameter from
0.01 to 10. In general, the accuracy of the
predicted temperature profiles and total heat flux
was within a few percentage points and was
observed to be as high as 10% for small
EOD/optical thickness ratios. Computational
times using the finite element method were
estimated to be 12.5% or less using the EOD as
compared to solving the entire temperature field
for each element. This savings in computational
time may justify the small errors introduced by
using the EOD approximation.
