Applicability of stochastic process theory to heat conduction in solids with random temperature fields

Abstract

A few papers have appeared over the last two decades which consider problems of heat conduction in solids under various random conditions. These are reviewed and discussed with a view to understanding why the subject has not attracted more attention. On the assumption that the theoretical problems are indeed of relevance to practical heat transfer calculations, it is suggested that the analytical methods adopted by the majority of authors do not lend themselves easily to general application. In particular, a criterion applied to each method is the ease of its adaptability to numerical computer methods. It is found that one method, employing established techniques of stochastic process theory and spectral analysis, does meet the imposed criterion and can be applied in a systematic manner to a range of typical problems. This method, which is nominated as the spectral method, is shown also to have applications beyond random or stochastic conditions, being adaptable to the study of heat conduction in solids subjected to arbitrary conditions.