Distribution of a Fluid over a flat plate slab by diffusion and Convection

Abstract

This study describes the distribution of a fluid over a flat slab by diffusion and convection. A second order differential equation, which describes this phenomenon, is selected from another paper that is mentioned in the introduction. A theoretical new model is designed in this study to get the mathematical solutions for it. This paper provides the analytical solution by using classic technique method and the numerical solution by using three methods that are matrix method, shooting method, and Successive over Relaxation Method (SOR) method. After the solutions are got, it will be a compression between the analytical and numerical solutions and also between the figure of the previous study and the figures of this study which is got from the results of the analytical and numerical solutions. In addition, there is an experiment is provided in this study to describe how to get the experimental data because the previous study has no experimental data. Finally, it can be concluded from the results that the analytical and numerical solution for equation (7) are match each other and the best step size is ( =0.1). The matrix and SOR methods are more accuracy and appropriate to solve the equation, but they need more work than shooting method.