The present work is devoted to the analysis of non-linear heat transfer problems using the recent development of consective-interpolation procedure. Approximation of temperature is enhanced by taking into account both the nodal values and their averaged nodal gradients, which results in an improved finite element model. The novel formulation possesses many desirable properties including higher accuracy and higher-order continuity, without any change of the total number of degrees of freedom. The non-linear heat transfer problems equation is linearized and iteratively solved by the Newton-Raphson scheme. To show the accuracy and efficiency of the proposed method, several numerical examples are hence considered and analyzed.
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