Improve Analytical Solutions for Trapezoidal, Rectangular and Dovetail Shapes of Inclined Longitudinal Porous Fin

This study improved the approximate analytical solutions of the heat distribution and transport of inclined longitudinal porous fin in the presence of radiative and convective environments with rectangular, trapezoidal, and dovetail profiles. The model of Darcy, which mimics the interaction of fluids and solids, is utilized to obtain the equation of governing the heat transfer of the porous fin. To investigate the rectangular, trapezoidal, and dovetail profiles, a single equation has been solved through analysis of the mathematical model by using the optimal differential transform method (ODTM) which consist least squares differential transform method (LSDTM), and the Galerkin differential transform method (GDTM) while the BVP4c presents the numerical solution. A comparison is made between the approximate analytical and numerical solutions for different parameters. It results in that the solutions produced from LSDTM and GDTM are closer to the numerical solution than the solutions of DTM, nonlinear autoregressive exogenous-levenberg marquardt algorithm (NARX-LMA) and cascade feedforward backpropagated-levenberg marquardt algorithm (CFB-LMA). A comprehensive graphic analysis was conducted to examine the effect of variation in inclination angles, tapering at the tip, wet porous parameters, internal heat generation, progressive natural convection parameters, and dimensionless radiation parameters on the thermal profile and thermal transfer rate of the porous longitudinal fin. The split fin design achieves the greatest heat transfer rate, trailed by rectangular and trapezoidal fin profiles, assuming that internal heat generation is maintained to a minimum.