Reconstruction of the heat transfer coefficients and heat fluxes in heat conduction problems

Abstract This paper studies the reconstruction of the spatial-dependent- heat transfer coefficient γ ( x ) and- heat flux q ( x ) , using the Levenberg–Marquardt (L-M) connected with the surrogate functional method and the modified conjugate gradient method (MCGM) (problem I). In addition to studying the reconstruction of γ ( x ) and space–time-dependent heat flux q ( x , t ) using the MCGM (problem II). The numerical results obtained by the L-M and MCGM demonstrate the efficiency, accuracy, and robustness of the proposed methods. The obtained results are compared with those obtained from an inverse approach connected with COMSOL Multiphysics under the same conditions. Finally, a conclusion and some remarks are presented.