Gabriel Samaila, Abubakar Masha, Musa Kida, Salihu Lawan Aliyu and Abdulrahman Mustapha
Department of Mathematics and Computer Science, Kashim Ibrahim University, Maiduguri, Borno State, Nigeria.
*Corresponding author’s Email: mashafantami@gmail.com, doi.org/10.55639/607.020100126
ABSTRACT
This study investigates the combined effects of a transverse magnetic field, nonlinear thermal radiation through the full Rosseland approximation, and nonlinear Boussinesq buoyancy on free convection boundary layer flow adjacent to a vertical plate subject to a convective surface boundary condition. The governing nonlinear partial differential equations are transformed into a non-similar system and solved at two levels of truncation using the Runge Kutta-Fehlberg fourth-fifth order (RKF45) method embedded within a Newton-Raphson shooting framework. The influences of the Biot number (Bi), Grashof number (Gr), Prandtl number (Pr), thermal radiation parameter (R), magnetic interaction parameter (M), and the nonlinear Boussinesq parameter (δ) on the wall temperature, Nusselt number, and skin friction coefficient are examined for both the linear (LDT, δ = 0) and nonlinear (NDT, δ = 1) density temperature models. The Biot number emerges as the most dominant parameter, producing the largest simultaneous increases in wall temperature and Nusselt number across the range considered. The magnetic field is found to be a highly effective flow controller but a comparatively poor thermal controller, nearly doubling the skin friction coefficient with negligible change in wall heat flux as M increases. Higher Prandtl numbers compress the thermal boundary layer and enhance surface heat transfer, while increasing radiation expands the boundary layer and counterintuitively reduces wall heat flux. The nonlinear density-temperature model consistently predicts higher skin friction than the linear approximation, with discrepancies growing under intense convective heating to levels that could compromise structural safety assessments of heated MHD walls. These findings provide a physically complete and practically relevant framework for the thermal and mechanical design of MHD natural convection systems at high temperatures.
KEYWORDS
Thermal radiation, Magnetic field, Vertical plate, Non-linear approximation.