Heat transfer analysis of an inclined longitudinal porous fin of trapezoidal, rectangular and dovetail profiles using cascade neural networks

In this paper, the mathematical model of an inclined longitudinal porous fin of trapezoidal, rectangular, and dovetail profiles in the presence of convective and radiative environments is considered to study the heat transfer and heat distribution within the fin. The governing equation for the energy transfer in the porous fin is derived by using the Darcy model that simulates the interaction of fluids and solids. The mathematical model has been analyzed so that a common equation can be used to study the trapezoidal, rectangular, and dovetail profiles. Furthermore, to study the temperature distribution in the fin, a supervised machine learning algorithm is developed using Cascade feedforward backpropagated (CFB) neural networks and Levenberg–Marquardt (LM) algorithm. A reference solution of 1001 points for supervised learning of the design scheme is generated by using a numerical solver (RK-4), which is further utilized by the CFB-LM algorithm with the Log-Sigmoid activation function to train, validate and test the data properly. The design algorithm’s outcomes are compared to the results of the homotopy perturbation method, shooting method, and other machine learning algorithms. Extensive graphical and statistical analyses are conducted to study the influence of variations in inclination angle, tip tapering, wet porous parameter, internal heat generation, porosity, progressive natural convective parameter, and dimensionless radiative parameter on the thermal profile and heat transfer rate of the longitudinal porous fin. The dovetail fin profile achieves the maximum heat transfer rate, followed by rectangular and trapezoidal fin profiles, provided that internal heat production is kept to a minimum.