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The purpose of this paper is to present novel search formulations in gradient‐type methods for prediction of boundary heat flux distribution in two‐dimensional nonlinear heat conduction problems.

The performance of gradient‐type methods is strongly contingent upon the effective determination of the search direction. Based on the definition of this parameter, gradient‐based methods such as steepest descent, various versions of both conjugate gradient and quasi‐Newton can be distinguished. By introducing new search techniques, several examples in the presence of noise in data are studied and discussed to verify the accuracy and efficiency of the present strategies.

The verification of the proposed methods for recovering time and space varying heat flux. The performance of the proposed methods via comparisons with the classical methods involved in its derivation.

The innovation of the present method is to use a hybridization of a conjugate gradient and a quasi‐Newton method to determine the search directions in gradient‐based approaches.