Monte Carlo method of solving heat conduction problems

Abstract

A new approach in the use of Monte Carlo to solve heat conduction problems was developed using a transport equation approximation to the heat conduction equation. The method was shown to be applicable to the solution of multimedia problems in complex geometries with no inherent limitations as to the geometric complexity of problems which can be solved. Nuclear radiation transport and heat conduction problems can be calculated with the same computer code; and, in the case where the nuclear reactions are the heat source, the problem can be performed in a coupled mode with a single computer run. The method was demonstrated for problems involving multimedia, internal sources, fixed temperature boundary conditions, convective boundary conditions, time-dependent sources, and for a coupled nuclear radiation-heat conduction problem. Comparisons were made to analytical solutions when they were available or could be generated. The adjoint formulation was found to be the most suitable mode of solution for the class of problems which was considered and therefore the method appears to be more useful for calculating temperatures at specific points rather than temperature distributions.