Non-Newtonian fluid flow over a stretching sheet in a porous medium with variable thermal conductivity under magnetohydrodynamics influence

The magnetohydrodynamics (MHD) Williamson fluid model close to a moving surface is thoroughly analysed in this work, taking into account the effects of changing thermal conductivity, and diffusion. The overall dynamics of flow are affected by the major influence of thermal conductivity variations on heat transfer. The nonlinear partial differential equations governing the system are converted into ODEs by similarity transformations, taking into consideration the effects of porous media using the Darcy model. The Runge-Kutta fourth-order (RK4) method is used to numerically solve these equations, making it easier to examine incompressible fluid flow on the moving surface. The findings provide important new understandings of the intricate flow patterns and the development of shear layers brought about by the fluid-surface interaction at varied thermal conductivity levels. These results improve our understanding of fluid dynamics in geophysical and atmospheric environments and are essential for the design and optimisation of engineering applications with changeable thermal characteristics.