Inverse and efficiency of heat transfer convex fin with multiple nonlinearities

In this article, we first propose the novel semi-analytical technique-modified Adomian decomposition method (MADM)-for a closed-form solution of the nonlinear heat transfer equation of convex profile with singularity where all thermal parameters are functions of temperature. The longitudinal convex fin is subjected to different boiling regimes, which are defined by particular values of n (power index) of heat transfer coefficient. The energy balance equation of the convex fin with several temperature-dependent properties are solved separately using the MADM and the spectral quasi-linearization method. Using the values obtained from the direct heat transfer method, the unknown parameters of the profile, such as thermal conductivity, surface emissivity, heat generation number, conduction-convection parameter, and radiation-conduction parameter are inversely predicted by an inverse heat transfer analysis using the simplex search method. The effect of the measurement error and the number of measurement points has been presented. It is found that present measurement points and reconstruction of the exact temperature distribution of the convex fin are fairly in good agreement.