Estimation of the time-dependent heat flux using the temperature distribution at a point by conjugate gradient method

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. Also, the effects of noisy data and position of measured temperature on final solution are 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. We solve the inverse heat conduction problem of estimating the transient heat flux, applied on part of the boundary of an irregular region. The irregular region in the physical domain (r,z) is transformed into a rectangle in the computational domain (ξ,η). 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 and that the results are nearly independent of sensor position.