Time-Dependent Heat Flux Estimation in Multi-Layer Systems by Inverse Method

Abstract

In this paper, the conjugate gradient method, coupled with the adjoint problem, is used to solve the inverse heat conduction problem and to estimate the time-dependent heat flux, using temperature distribution at a point in a three-layer system. Also, the effect of noisy data on the final solution is studied. The numerical solution of the governing equations is obtained by employing a finite difference technique. For solving this problem, the general coordinate method and body-fitted coordinate method are used. The irregular region in the physical domain (, ) is transformed into a rectangle in the computational domain (, ). The present formulation is general and can be applied to the solution of boundary inverse heat conduction problems over any region that can be mapped into a rectangle. The obtained results show the good accuracy of the presented method. Also, the solutions have good stability even if the input data includes noise. The problem is solved in an axisymmetric case. Applications of this model are in the thermal protection systems and heat shield systems.