An optimal control procedure for estimating the heat fluxes on the boundaries of functionally graded (FG) thick plates to reach the desired domain temperature distributions in a specified time interval of heating is presented. The conjugate gradient method (CGM) is employed for optimization, and the differential quadrature method as an accurate and numerically efficient method in conjunction with the forward finite-difference method are applied to solve the three-dimensional transient heat transfer, sensitivity, and adjoint problems. The validity of the presented optimal control problem is demonstrated by solving different numerical examples. Results show that excellent estimation on the boundary heat fluxes can be obtained with arbitrary initial guesses of these functions.
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