A solution method for a nonlinear three-dimensional inverse heat conduction problem using the sequential gradient method combined with cubic-spline function specification

In this article, an inverse method for retrieving time- and space-varying heat flux on the surface of a three-dimensional slab with temperature-dependent thermophysical properties from temperature scanning on the opposite surface is investigated. The sequential gradient method, which implements the gradient method in a sequential manner, is employed to solve the nonlinear inverse heat conduction problem. To stabilize the solution algorithm, a cubic-spline function is specified in space and a constant or linear function is specified in time without the use of the regularization term. The proposed method is verified with presented computational results for several cases.