On the Solution of a Parabolic PDE Involving a Gas Flow Through a Semi-Infinite Porous Medium

Abstract

Taking as start point the parabolic partial differential equation with the respective initial and boundary conditions, the present research focuses onto the flow of a sample of waste-water derived from a standard/conventional dyeing process. In terms of a highly prioritized concern, meaning environment decontamination and protection, in order to remove the dyes from the waste waters, photocatalyses like ZnO or TiO2 nanoparticles were formulated, due to their high surface energy which makes them extremely reactive and attractive. According to the basics of ideal fluid, the key point is the gas flow through an ideal porous pipe consisting of nanoparticles bound one to each other, forming a porous matrix/pipe. The modeling of the gas flow through a porous media is quite valuable because of its importance in investigating the gas-solid processes. The present study is a valid contribution to the existing literature, by developing a nonstandard line method for the partial differential equation, in order to obtain a numerical solution of unsteady flow of gas through nano porous medium. Hence, the physical problem is modeled by a highly nonlinear ordinary differential equation detailed on a semi-finite domain and represents a guidance for several questions originating in the gas flow theory. The findings of this study offered a facile approach to improve an attractive issue related to materials science/chemistry, like synthesis of ZnO or TiO2 nanoparticles forming an ideal nano porous pipe with efficiency in industrial waste waters decontamination.