Numerical analysis of slip flow in a Permeable Wall Microchannel

In this work, a Newtonian fluid flow circulating in a rectangular microchannel with permeable walls is investigated under slip conditions. It should be clarified that this is a purely hydrodynamic problem, therefore, the objective of this work is to obtain the pressure field and velocity profiles in the longitudinal and transverse directions. Therefore, the fluid mechanics equations to be solved in this problem are the continuity and momentum equations in the $x$ and $y$ directions, which are presented in a dimensionless form and rewritten in their variational form in order to adapt them to FreeFem++, a free software which enables to obtain the solution to partial differential equation systems, obtaining results that are presented graphically in order to make a qualitative and quantitative comparison of different conditions in the permeability and slip properties in the microchannel walls. In this way, this study attempts to make a contribution to further applications in different researching areas and projects.