Ecoulement de succion dans un canal rectangulaire poreux

Abstract

study examines the flow of a moving fluid between two porous walls, a topic of importance in the fields of hydrodynamics and process engineering. To analyze this flow, we first applied the principle of mass conservation, leading to the establishment of the continuity equation. In parallel, the principle of conservation of momentum was used to derive the Navier-Stokes equations, which describe the dynamic beha- vior of the fluid. Given that the fluid under consideration is incompressible, we then introduced the current function, which proved advantageous ; indeed, this approach simplifies the system of equations by reducing the number of equations to be sol- ved from three to just one, known as the vorticity equation. We then applied the method of similar solutions to model the flow, transforming the original problem into a boundary problem defined on two bounds, making it easier to solve. To find the solution to this boundary problem, we used the Tir method, combined with the fourth-order Runge-Kutta algorithm ; this numerical approach was implemented using MATLAB software, which offers efficient tools for computation and simulation. In sum, this study provides a detailed analysis of fluid flow between porous walls, using fundamental principles of fluid dynamics.