Finding a time-dependent reaction coefficient of a nonlinear heat source in an inverse heat conduction problem

In this article, we propose an approximate technique for reconstructing a time-dependent reaction coefficient together with the surface heat flux histories and temperature distribution in a nonlinear inverse heat conduction problem (IHCP). We assume that the initial condition and the transient heat flux on the accessible boundary along with the temperature measured at specified interior locations in the domain of the problem are given as the input data. By applying the given measurements in a transformation, the main problem is reformulated as a certain parabolic problem and later a procedure based upon deploying the Ritz approximation along with the collocation method is applied which converts the problem to a nonlinear system of algebraic equations. Accurate numerical results in dealing with the exact initial and boundary data are obtained and regarding the perturbed boundary data, the regularization method based on cubic spline approximation is used, which results in obtaining stable numerical derivatives.