estimation of the time- dependent heat flux using temperature distribution at a point in a three layer system with none homogeneous boundary conditions

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 three layer system with none homogeneous boundary conditions. also, the effect of noisy data on final solution is studied. for solving this problem the general coordinate method is used. we solved the inverse heat conduction problem of estimating the transient heat flux, applied on part of the boundary of an irregular region. 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. applications of this model are in the thermal protect systems (t.p.s.) and heat shield systems.