V3I9P2

ANALYSIS OF MHD HEAT TRANSFER IN A COAXIAL ANNULUS WITH TEMPERATURE-DEPENDENT POWER-LAW SURFACE HEAT FLUX AND NONLINEAR THERMAL RADIATION

Abdullahi Hussaini¹, Isah Bala Yabo², Huanhuan Liu³, Sahabi Zayyanu Yabo^1*

Abstract

This study presents a comprehensive theoretical analysis of magnetohydrodynamic (MHD) heat transfer in a vertical coaxial annulus filled with an electrically conducting, viscous, incompressible power-law fluid. The flow is driven by buoyancy forces arising from a temperature-dependent power-law surface heat flux applied at the walls. Thermal radiation is modelled using the nonlinear Rosseland diffusion approximation. Both steady and unsteady solutions are obtained the former via a regular perturbation method (assuming a small radiation parameter) and the latter via an implicit finite-difference scheme. The governing equations are reduced to a set of coupled nonlinear ordinary differential equations for the steady case and parabolic partial differential equations for the transient case. Key parameters include the Hartmann number, Grashof number, radiation parameter, suction/injection parameter, and power-law index. Results indicate that the magnetic field and suction suppress the flow, while buoyancy, radiation, and injection enhance it. The effects are more pronounced under isothermal wall conditions than under isoflux conditions. The findings offer useful insights for the design of thermal management systems involving non-Newtonian fluids in electromagnetic fields.

Keywords:

MHD; coaxial annulus; power-law fluid; nonlinear thermal radiation; Rosseland approximation; perturbation method; finite difference method