Wavelet collocation solution for fully wet semi-spherical porous fin

Study Focus: In this paper, the thermal behavior of a semi-spherical fin embedded in a porous medium is examined. The heat transfer coefficient is considered to be temperature-dependent and follows a power-law relationship. Modeling Approach: Heat transmission through the porous medium is modeled using Darcy’s law, with the flow velocity as a key factor. Methodology: The Legendre wavelet collocation method (LWCM) is employed to solve the governing equations and predict the temperature distribution within the fin. Results obtained from LWCM are compared to those from the least squares method and numerical methods, showing good agreement and validating the proposed method. The effects of various parameters on the temperature distribution in the fin are analyzed and presented through figures and tables. The study concludes that the Legendre wavelet collocation method is an efficient and powerful technique for obtaining analytical solutions for heat transfer problems in porous media.