A Critical Evaluation of the Monte Carlo Method for Application to the Inverse Heat Conduction Problem

Abstract

The solutions of the Inverse Heat Conduction Problem using the Monte Carlo method, Green’s Function Solution Equation and the Alternative Green’s Function Solution Equation are compared. The Monte Carlo method is a simple technique that provides a method of determining the source of error and placement of sensors. However, in comparison with the exact solution, if attainable, the cost is a higher error in the solution. All the three methods use the function specification method in the sense that a functional form for the surface heat flux or temperature is assumed and the parameters defining the function are evaluated by minimizing the error functional. In the alternative method, the functional form also satisfies the boundary conditions, the unknown quantity in the problem. The input data for this comparison are experimentally measured temperatures in a stainless steel disk subjected to spray cooling.