Simultaneous identification of the spatio-temporal dependent heat transfer coefficient and spatially dependent heat flux using an MCGM in a parabolic system

This paper aims to simultaneously identify the spatio-temporal dependent heat transfer coefficient γ(x,t) and the spatially dependent heat flux q(x) in a parabolic system. The simultaneous identification problem is formulated as a constrained minimization problem using the output least squares method with Tikhonov regularization. The differentiability of the solution and adjoint equations are investigated to obtain the gradient formulae and determine the step lengths, respectively. To illustrate the efficiency, accuracy, and robustness of the proposed algorithm, numerical results are investigated using the modified conjugate gradient method (MCGM).