Semianalytical investigation on heat transfer in porous fins with temperature‐dependent thermal conductivity via the homotopy perturbation Sumudu transform approach

A unique investigation has been undertaken to analyze the heat transmission by convective and radiative mechanisms in a fully saturated penetrable fin of a longitudinal structure positioned on a leaning surface. This study introduces the fusion of the realms of Homotopy perturbation and Sumudu transform techniques to address a previously unexplored problem involving a moving fin with temperature‐dependent thermal conductivity. In prior research papers, the Homotopy Perturbation Sumudu Transform Method (HPSTM) was utilized to obtain analytical solutions for fins featuring temperature‐dependent thermal conductivity. However, in our current study, we employ the HPSTM to tackle a novel problem involving a moving porous fin. This fin exhibits temperature‐dependent thermal conductivity and is subjected to convection and radiation effects. Through a comparison with numerical results, the present study has validated the dependability of its findings. The dimensionless temperature profile has been investigated by studying its relationship with several parameters. Here we observed that when the Peclet number ( Pe ) $({Pe})$ is augmented by 400%, there is a corresponding 1.11% increase in thermal outline at the fin's extremity. Enhancing the value of radiation parameter Nr ${Nr}$ by 400% declines the temperature of the fin tip by 14.079%. This study encourages the application of the Homotopy perturbation Sumudu transform technique in more complex fin problems.