Application of Monte Carlo Method to Steady State Heat Conduction Problems

Abstract

The Monte Carlo method was used in modelling steady state heat conduction problems. The method uses the fixed and the floating random walks to determine temperature in the domain of the definition of the heat conduction equation, at a single point directly. A heat conduction problem with an irregular shaped geometry and prescribed boundary temperatures was analyzed. Computer programs for the analysis were coded using VAX FORTRAN on a VAX 4.4 mainframe. The fixed random walk and the
floating random walk methods gave comparable results of 507.260K and 506.980K respectively for temperature at a point. The Monte Carlo method also gave a result of 50.580C , similar to that of 50.000C for a particular node, with the Finite Difference method (using Gauss- Seidel iteration) for a 2-dimensional regular shaped heat conduction problem.

Keywords: Monte Carlo Method, Fixed Random Walk, Floating Random Walk, Modelling, Steady-State Heat Conduction

African Research Review Vol. 2 (4) 2008: pp. 31-53