Deep neural network-based heat transfer analysis for magnetohydrodynamic Jeffery–Hamel flow of a couple stress fluid

This study investigates the thermal behavior for Jeffery–Hamel flow of a couple stress fluid under the influence of a magnetic field, employing an artificial neural network (ANN) methodology. The research evaluates how the variations in Reynolds number (Re), Eckert number (Ec), Prandtl number (Pr), couple stress parameter (S), magnetic parameter (M), and channel angle (α) alter the temperature distributions within the fluid. The governing coupled nonlinear differential equations for couple stress fluid in Jeffery–Hamel flow and heat transfer are solved using an artificial neural network (ANN) approach. The ANN is trained to satisfy the boundary value problem by minimizing the residuals of the governing equations and boundary conditions, providing an efficient mesh-free solution. The analysis reveals that increasing the magnetic parameter amplifies the Lorentz force, which leads to an increase in the fluid temperature across both divergent and convergent channels. It is observed that when the couple stress parameter is very low, an increase in channel angle raises fluid temperature. Conversely, for a large value of couple stress parameter, increasing the channel angle decreases fluid temperature in the divergent channel but increases it in the convergent channel. In the absence of a magnetic field (M = 0), enhancing the couple stress parameter results in a decrease in the fluid temperature for a divergent channel, while in a convergent channel, it leads to an increase in the fluid temperature. These insights offer a comprehensive understanding of the interplay between couple-stress fluid properties, magnetic field, heat transfer, and channel geometries, contributing to the optimization of thermal management in systems utilizing couple-stress fluids.