Finite element analysis on Hall and ion slip effects on transient MHD free convective rotating flow of Jeffrey's fluid with isothermal and ramped wall temperature

In this study, we look at ion slip and Hall effects for unsteady free convective MHD rotating Jeffrey fluids across a vertically infinite permeable plate with a temperature ramping wall. FEM is used to solve governing equations while considering initial and boundary conditions. This article considers two cases: isothermal plate and ramping wall temperature. Graphs demonstrate velocity and temperature behavior with implanted settings. We plotted velocity against relevant parameters. We also discovered that isothermal plates had significantly higher velocity and temperatures than ramps changing wall temperatures. The mainly authorized and energetic FEM to explain the dimensionless partial differential equations with boundary conditions. Following are the key steps that make up the method: Discretize the domain. Derivation of element equation assembly of element equation, imposition of boundary condition and solution of assembly equation. While numerous studies have explored MHD flow in non-Newtonian fluids, limited attention has been given to the combined effects of ion slip and Hall currents in the presence of both ramped and isothermal temperature profiles, especially for Jeffrey fluids over a rotating, permeable surface. Furthermore, the thermal response due to wall ramping has not been extensively analyzed using robust numerical tools like FEM in the context of unsteady convective flows with magnetic fields. Understanding the heat and momentum transport behavior under the influence of electromagnetic fields and fluid rotation has practical applications in engineering systems such as cooling of electronic devices, polymer processing, geothermal energy systems, and MHD generators. The findings provide deeper insight into how temperature ramping and isothermal conditions affect fluid flow and heat transfer, thereby offering useful guidelines for thermal management in industrial applications involving electrically conducting, non-Newtonian fluids.