Magnetohydrodynamics Flow and Heat Transfer With Nonlinear Thermal Radiation Over a Moving Vertical Plate With Convective Boundary Conditions: A Numerical Analysis

ABSTRACT This piece of work provides an in‐depth analysis of magnetohydrodynamics (MHD) fluid flow and heat transport near a continuously moving vertical plate in the presence of nonlinear thermal radiation with convective boundary condition. A nonlinear dependence of thermal radiation on temperature enhances thermal transport, while convective boundary conditions govern heat transfer at the plate surface. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) through the application of a similarity transformation. To numerically solve these ODEs, we have used bvp4c method in MATLAB. The influences of dimensionless parameters on heat transfer and fluid flow are presented using tables and graphs. The key novelty of this study lies in analyzing the impact of nonlinear thermal radiation on MHD flow over a constantly moving vertical plate using the bvp4c method. When the fluid flows in the positive x‐direction and the plate moves in the opposite direction, the coefficient of skin friction decreases. Moreover, when the direction of the fluid and the plate is the same, both the velocity and the temperature profiles increase with greater nonlinear thermal radiation. Near the wall, the temperature gradient decreases as nonlinear thermal radiation intensifies, while it increases in the free stream. The thickness of the thermal boundary layer decreases, while the thickness of the velocity boundary layer increases with increasing magnetic parameter. Similarly, when the Grashof number increases, the velocity boundary layer becomes thicker, while the thermal boundary layer tends to become thinner. However, when the Prandtl number increases, the thermal boundary layer becomes thicker, whereas the velocity boundary layer tends to become thinner. Practically, these findings aid in optimizing heat transfer in engineering applications such as cooling systems, heat exchangers, aerospace thermal protection, and biomedical devices.