EXPLORING ATANGANA-BALEANU FRACTIONAL BEHAVIOR IN HYDROMAGNETIC FLOW: A NUMERICAL ITERATIVE GAUSS-SEIDEL APPROACH

Abstract

This research investigates the behavior of Atangana-Baleanu fractional derivatives in a hydromagnetic field within a horizontal channel characterized by variable viscosity and thermal conductivity, incorporating a constant heat source and heat diffusion. An iterative Gauss-Seidel numerical scheme, tailored to specific boundary conditions, has been employed to analyze the non-linear mathematical formulations, which have been simplified using similarity transformations. The study systematically examines the influence of key variables on flow velocity, flow temperature, and magnetic field behavior, with results presented both graphically and in tabular form. Notably, the findings reveal that a decrease in fluid viscosity reduces the momentum of fluid molecules while simultaneously enhancing heat transfer rates and decreasing shear stress. The implications of this research extend to various practical applications, including the design and control of hypervelocity vehicles and the management of blood circulation in human arteries, highlighting the significance of MHD phenomena in both engineering and biomedical contexts.