Solving Mixed Convection Boundary Layer Flow with Convective Boundary Condition bvp4c Solver

Abstract

This study examines mixed convection boundary layer flow toward a vertical plate with a convective boundary condition. The goals include employing similarity transformations to convert the controlling partial differential equations (PDEs) into ordinary differential equations (ODEs), and using the shooting method with bvp4c solver in MATLAB to acquire numerical solutions as well as comparing the results to those of previous study. It is found that the temperature and velocity profiles have been significantly affected by governing parameters, such as the mixed convection parameter and Prandtl number, as demonstrated by numerical simulations.  It has been noted that a higher value of the convective parameter γ results in greater temperature and velocity gradients at the surface, raising the surface shear stress and the rate of heat transfer. The results closely resemble those of previous study, demonstrating the method's correctness and the bvp4c solver's resilience when dealing with mixed convective flow issues. This work provides a solid numerical framework for further thermofluid system research and advances our understanding of mixed convection dynamics.