Deforming finite elements for the numerical solution of the nonlinear inverse heat conduction problem

Abstract

AbstractA numerical solution of the nonlinear inverse heat conduction problem is obtained using an in‐line method in conjuction with the measured thermocouple temperature history. The deforming finite elements technique is used to treat initial time delay in temperature response due to thermocouple location. In the absence of elements deformation, the method reduces to the conventional Galerkin formulation. A three‐time level implicit scheme, which is unconditionally stable and convergent, is employed for the numerical solution. The temperature‐dependent thermophysical properties in the resulting matrices are evaluated at the intermediate level. The complication of solving a set of nonlinear algebraic equations at each step is avoided. Illustration of the technique is made on the one‐dimensional problem with a thermal radiation boundary condition. The results demonstrate that the method is remarkable in its stability to predict surface condition without debilitation.