Transient magnetohydrodynamic flow over a rotating vertical porous surface incorporating thermal radiation, hall and ion-slip effects: Using finite element method

The current study investigates the combined influence of thermal radiation, rotation, Hall and ion-slip effects, chemical reactions, and viscous dissipation on unsteady convective heat and mass transfer past a finite, non-reflective vertical plate. A mathematical model is developed by formulating the governing partial differential equations for momentum, energy, and concentration, which are solved numerically using the finite element method. The effects of the controlling physical parameters on velocity, temperature, and concentration fields are analyzed in detail, along with engineering quantities of interest such as the Nusselt number, Sherwood number, and resistive force. The motivation for this work stems from the need to better understand complex transport phenomena arising from the interaction of rotational motion, electromagnetic forces, and thermal effects in high-temperature and high-speed environments relevant to aerospace systems, rotating machinery, and advanced thermal management technologies. In particular, the inclusion of Hall current and ion-slip effects addresses an important gap in existing studies, as these parameters are rarely incorporated in unsteady convection models despite their significant impact on flow behavior and heat transfer. Furthermore, the role of time-dependent convection coupled with chemical reactions and viscous dissipation is examined to provide a more realistic representation of practical systems. The results offer valuable insights for the optimal design of energy and environmental systems, enabling improved prediction and control of fluid flow, solutal transport and thermal transfer in rotating and radiative environments. The research also delves into the significance of chemical reactions on velocity and concentration distributions. The chemical reaction parameter influences the concentration and velocity fields, with increased chemical reactions leading to reduced boundary layers, and the Sherwood number being enhanced due to increased interfacial mass transfer. The magnetic parameter and reaction coefficient tend to reduce the skin friction coefficient, while increasing the reaction coefficient declines the concentration distribution. In addition, temperature profiles are significantly impacted by the heat source and absorption parameters. A rise in the thermal source parameter typically improves the thermal transfer rate, although the expected outcome can vary depending on the balance of external heat and heat generated within the flow. Similarly, the viscous dissipation coefficient, represented by the Eckert number, affects both the temperature and velocity distributions. An increase in the Eckert number indicates an enhancement in the thermal and flow boundary layers due to increased thermal conductivity from viscous dissipation. This study investigates the significance of multiple parameters, including magnetic fields, radiation, rotation, chemical reactions, heat absorption, and viscous dissipation, on the flow of fluid moving through a porous medium with convective and diffusive boundary conditions. The effects of several parameters on the temperature, velocity, and concentration profiles are analyzed, with an analytical solution provided to better understand these interactions. The transmission of heat and mass rates in free and forced convective flows over vertical plates have been extensively investigated due to their relevance in engineering and industrial applications. Such flows arise in nuclear waste storage, geothermal systems, chemical processing industries, groundwater pollution control, and cooling of electronic and nuclear systems. In many of these applications, the working fluids are not pure but rather mixtures, leading to complex transport phenomena governed by heat sources, viscous dissipation (Eckert number), chemical reactions, and porous medium effects. Magnetohydrodynamics (MHD) plays a vital role in processes involving electrically conducting fluids, such as liquid metals used in casting, plastic extrusion, crystal growth, and metallurgical operations. The application of magnetic fields enables better control of fluid motion, heat transfer rates, and material quality. Similarly, convective mass and heat transference in porous media is of significant importance in drying processes, underground energy transport, post-accident heat removal systems, and nuclear waste management. In recent years, nanofluids engineered suspensions of nanoparticles in base fluids have fascinated considerable attention due to their enhanced thermal performance compared to conventional fluids. This has motivated extensive research into MHD nanofluid flow over stretching or moving surfaces under various physical effects.