Distributed-order time-fractional analysis of non-Newtonian Sisko fluid flow under magneto-thermal effects

This article investigates the unsteady magnetohydrodynamic (MHD) boundary layer flow and heat transfer characteristics of a Sisko non-Newtonian fluid subjected to natural convection and thermal radiation effects. To accurately capture the hereditary and memory-dependent behavior of the fluid, a distributed-order time fractional model is introduced into the governing equations. The classical Cattaneo heat conduction model is generalized using distributed fractional derivatives to address non-Fourier heat transport phenomena. The flow configuration is considered a vertical plate in a thermally stratified environment with an applied transverse magnetic field and radiative heat flux. The governing coupled non-linear partial differential equations, including momentum and energy equations, are transformed into non-dimensional form and solved numerically using the finite difference method integrated with the L1 approximation scheme for distributed-order derivatives. A comprehensive parametric analysis is conducted to assess the influence of the magnetic field, radiation parameter, distributed fractional orders, and Sisko fluid index on the velocity and temperature profiles. The results demonstrate that increasing the magnetic field strength and fractional-order parameters leads to a suppression of the fluid velocity due to enhanced Lorentz forces and memory effects, while thermal radiation promotes heat transfer within the boundary layer. The study provides new insights into the thermal and flow behavior of Sisko fluids in electrically conducting and radiative environments, relevant to industrial processes involving polymeric fluids, biomedical applications, and thermal management systems.