In this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time- dependent heat flux using the temperature distribution at a point in a two layer system. Also, the effect of noisy data on 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 is used. The irregular region in the physical domain (r, z) 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 for few selected examples 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 axisymmetric case. Applications of this model are in the thermal protect systems (t.p.s.) and heat shield systems.

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