Multidimensional Inverse Heat Conduction Using the Monte Carlo Method

Abstract

The Monte Carlo method is used to solve inverse heat conduction problems when the surface temperature is spatial and time dependent. The standard random walk is modified to deal with curved boundaries. The proposed random walk has all the characteristics of the floating random walk, except its step size is small. This is a uniquely flexible method with excellent accuracy and it is computationally fast. The method is used to solve one- and three-dimensional heat conduction problems and the results are presented. A procedure is described to improve the accuracy of the solution, then used to calculate heat transfer from a cylindrical surface cooled by a stream of air.