A hybrid GDQM–ANN framework for entropy generation prediction in radiative MHD flow through an inclined porous channel

Entropy generation analysis in magnetohydrodynamic (MHD) flow through an inclined porous channel is essential for optimizing the performance of thermal systems such as geothermal units, heat exchangers, and solar collectors. In this article, we study the magnetic field and mixed convection effects on entropy generation in an inclined channel partially filled with porous medium in the presence of thermal radiation. The governing energy and momentum equations are transformed into nonlinear ordinary differential equations through non-dimensionalization, followed by a perturbation expansion in the Brinkman number. These equations are numerically solved using the Generalized Differential Quadrature Method (GDQM) to obtain accurate solutions for the temperature, velocity, and entropy generation. In addition, a Levenberg–Marquardt (LM) based artificial neural network (ANN) is developed to accurately predict key nondimensional flow and thermal characteristics using datasets that are generated from GDQM. The effects of relevant physical parameters on temperature, velocity, and entropy are analyzed through graphical representations, while the skin friction coefficient and Nusselt number at the channel walls are presented in tabular form. The ANN models exhibit very good accuracy with the regression coefficients, \(R_0\approx 1\) and the best validation performance values of \(7.1161 \times 10^{-09}\) and \(1.7179 \times 10^{-09}\) , respectively. The close agreement between ANN predictions and GDQM results highlights that the proposed ANN models are fast, reliable, and computationally efficient alternatives to conventional numerical solvers for entropy optimization in MHD porous channel flows.