MHD FLOWING OF CONVECTIVE HEAT FLOW ROTATING OF RECTANGULAR HOLLOW WITH ACHIEVE OF NON-ISOTHERMAL AND ISOTHERMAL HEDGE

Abstract

 The study investigates the magneto hydrodynamic (MHD) behaviour of convective heat flow in a rotating rectangular hollow enclosure subjected to both non-isothermal and isothermal boundary conditions. The interaction of thermal buoyancy, rotational forces, and externally applied magnetic fields produces a complex flow structure, significantly influencing heat transfer characteristics within the cavity. A two–dimensional incompressible electrically conducting fluid is considered, and the governing equations are formulated using the Bossiness approximation, incorporating Coriolis acceleration and Lorentz force effects. The rectangular hollow is examined under mixed boundary conditions, wherein selected walls are maintained at uniform isothermal temperatures, while others follow a non-isothermal spatial distribution. Numerical simulations are employed to evaluate the influence of key controlling parameters, including Hartmann number, Taylor number, Prandtl number, and Rayleigh number. The results reveal the critical role of magnetic damping in suppressing convective currents, while rotation enhances secondary circulatory structures depending on angular velocity. The interplay between isothermal and non-isothermal hedges yields distinct thermal stratifications and modifies heat transfer rates along the cavity walls. Overall, the analysis provides insights into optimizing thermal regulation in rotating MHD systems with relevance to advanced cooling technologies, geophysical flows, and energy-conversion devices..  In this study we assume the left vertical wall of the cavity is at temperature T_h (T_h +By^λ) and right vertical wall temperature T_c   (T_h> T_c) the top and bottom horizontal surfaces of the cavity are adiabatic. Darcy law is to be obeyed to the flow inside the porous medium the properties of the fluid and porous medium are homogeneous, isotropic and constant expect variation of fluid density with temperature. The fluid and porous medium are in thermal equilibrium and flux of heat radiation in y - direction is negligible in comparison to that in x-direction. Galerkin Finite Element Method of three nodded triangular elements has been used to convert the partial differential equations into the matrix form equations. Results are presented in terms of stream functions and isotherms for various values of Aspect ratios, Radiation parameters, Rayleigh numbers, Nusselt numbers and Power law exponents( ).