Computation of Non-isothermal Thermo-convective Micropolar Fluid Dynamics in a Hall MHD Generator System with Non-linear Distending Wall

Abstract

A theoretical model for steady non-isothermal convective heat transfer in non-Newtonian magnetized micropolar gas flow from a non-linear stretching/contracting wall in the presence of strong magnetic field is presented, as a simulation of an MHD (magnetohydrodynamic) Hall energy generator. Subsonic flow is considered, and compressibility effects neglected. The strength of the magnetic field which is applied in the general case obliquely to the wall is sufficient to invoke the collective effects of Hall current and Ohmic heating (Joule dissipation). Viscous heating is also included in the energy balance. Deploying similarity transformations, the governing equations are normalized into nonlinear ordinary differential equations with associated boundary conditions. The non-linear boundary value problem thus posed is then solved computationally with Nachtsheim–Swigert iteration technique along with the fourth-fifth order Runge–Kutta integration method. Verification of solutions is obtained with the semi-analytical Homotopy analysis method. Further validation is conducted with the semi-numerical Adomian decomposition method. In both cases excellent agreement is obtained with the Runge–Kutta shooting quadrature solutions. Additional validation is conducted with earlier Newtonian studies in the absence of micropolar, Hall current and dissipation effects. The influence of local Grashof number, local Hartmann number, Eringen microrotational parameter, Eringen coupling vortex parameter, Prandtl number and Eckert number on non-dimensional velocity components (primary, secondary and angular) and temperature within the boundary layer are graphically illustrated and interpreted at length. Furthermore, the effects of the thermophysical (e.g. non-isothermal power law index), electromagnetic parameters (e.g. Hall parameter) and geometric parameter (wall extension/contraction parameter) on the skin-friction coefficient (i.e. primary and secondary shear stress and wall couple stress) and surface heat transfer rate (Nusselt number) are evaluated. The study is relevant to near wall transport phenomena in novel MHD Hall power generators.