Theoretical and numerical study of a fluid flow of a slightly rarefied gas-free stream past a moving wall inside a porous medium

Abstract

This study investigates the boundary layer flow problem arising in the viscous fluid flow of a slightly rarefied gas-free stream over a moving plate embedded in a porous medium. Previous works were mainly focused on numerically, and some properties of the solutions were discussed from numerical results. But, numerical solutions are only sometimes guaranteed the solution’s existence. In this work, we have adopted the famous topological shooting argument to prove the existence result of the solution. We have shown that the solution may be convex or concave depending on the parameter values. Also, for these reasons, there arise some difficulties. However, we have rectified all the challenges and proved that unique solutions exist for all the particular governing parameter values. Nevertheless, we found an exact solution for some specific parameter values. Furthermore, the Haar wavelet collocation method is used to address the numerical results of the nonlinear boundary value problem. We first validate the obtained results with the existing numerical outcomes. The impacts of permeability and slip parameters on the velocity profiles and shear stress are elucidated through tables and figures, and probable arguments are explained in detail.

Keywords:

• Free stream flow
• Haar wavelet collocation method porous medium
• similarity solution
• topological shooting argument

2010 MSC:

• 34B08
• 34B15
• 34B60
• 34C12
• 76D05