Solving Heat Transfer Problem on a Stretching/Shrinking Surface with Convective Boundary Condition Using bvp4c Solver

Abstract

The heat transfer problem over a stretching/shrinking surface with a convective boundary condition is studied in this work. The objectives are to verify the governing equations, to generate a numerical solution and to analyse the problem. Using similarity transformations, the governing partial differential equations (PDEs) for heat transfer and fluid flow are converted into ordinary differential equations (ODEs). The MATLAB's bvp4c solver is used to obtain a numerical solution to the generated ODEs. An analysis is done on how the stretching/shrinking parameter, convective parameter, and Prandtl number affected the thermal boundary layer. The findings indicate that the local Nusselt number increases as the shrinking parameter increases. The opposite behaviour happens for the stretching parameter. As for the convective parameter, it reduced the thermal boundary layer thickness and enhanced heat transfer performance when it increased significantly. Besides, increasing the Prandtl number enhanced heat transfer for both stretching and shrinking cases. Additionally, the study compared the results with previous research to confirm the validity of the findings.