Numerical analysis of a viscous steady laminar flow due to a mass transfer from a porous plate

Abstract

Considers the motion of a viscous fluid within the narrow gap under a floating disk above an infinite porous plate. The flow is caused by a uniform blowing from the porous surface. If we ignore edge effects, after scaling the variables, an expression for the vertical component of the velocity is found with two particularities in the sense of an asymptotic expansion and for a self‐similar solution. We obtain an expression for the pressure distribution under the disk. Then, with this solution, Navier‐Stokes equations are reduced into one non‐linear equation of the fourth order with two points boundary conditions. First, we used a development of this equation by Newton’s method. The purpose of this paper is to show that the numerical scheme of quasilinearization gives rapid convergence to solution of this boundary layer problem. The vertical force balance gives the prediction for the height of the disk floating above the porous surface when the mass of the disk is known. Without any previous hypothesis, “TRIO”, a general computer code for thermal and fluid flow analysis developed at the CEA (Commissariat à l’Energie Atomique), confirms our main hypothesis and all our results. These two numerical solutions are well in keeping with the analytical and experimental solutions of Hinch and Lemaitre in 1994.