Solution of inverse heat conduction problems using control volume approach

Abstract

A new method for solving multidimensional inverse heat conduction problems is presented. Using control volume methods, the partial heat conduction equation is replaced by a system of ordinary differential equations in time, which are then solved sequentially. The procedure is started at a spatial node where temperature sensor is located and sequentially marches through space to the surface node. The accuracy of the method was demonstrated by comparison of the calculated surface heat flux and temperature with the known exact solution. Two numerical experiments, one- and two-dimensional inverse heat conduction problems, are solved to illustrate the effectiveness, computational efficiency and good accuracy of the presented method. In the third example, the inverse formulation is applied to a set of experimental data. The method can easily be extended to three-dimensional cases.