Evaluating thermal behaviour and efficiency in stretching/shrinking fully wet longitudinal porous fin using the Hermite wavelet method

The present study focuses on the thermal behaviour and efficiency of a fully wet, moving longitudinal fin of rectangular profile equipped with a stretching/shrinking mechanism. The novelty of this work lies in employing the semi-analytical Hermite wavelet method to analyse complex heat transfer phenomena under dynamic fin conditions, which has not been extensively explored in existing literature. Utilizing the Darcy model, fluid-solid interactions are analysed, and the non-dimensionalized model equation is resolved effectively, addressing a second-order nonlinear ordinary differential equation with results validated against existing literature. The thermal profile of the fin is examined through graphical analysis, considering various parameters including the stretching/shrinking parameter, Peclet number, internal heat generation parameter, and other pertinent parameters. As Pe increases by 400%, the temperature distribution rises by 10.8% in the stretching fin, 8.54% in the stagnant fin, and 5.16% in the shrinking fin. Additionally, the temperature distribution decreases by 4.92% when comparing the stretching fin to the shrinking fin. Efficiency and thermal behaviour are found to be optimal under stretching conditions due to increased convective heat dissipation, minimal under shrinking due to reduced surface area, and moderate under stagnant conditions. The insights from this study are directed towards practical applications to fin design.