Abstract
In this paper we study diffusion and convection filtration problem of one substance through the pores of a porous material which may absorb and immobilize some of the diffusing substances. As an example we consider round cylinder with filtration process in the axial direction. The cylinder is filled with sorbent i.e. absorbent material that passed through dirty water or liquid solutions. We can derive the system of two partial differential equations (PDEs), one expressing the rate of change of concentration of water in the pores of the sorbent and the other - the rate of change of concentration in the sorbent or kinetical equation for absorption. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM). This procedure allows reducing the 2-D axisymmetrical mass transfer problem decribed by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order. We consider also model 1-D problem for investigation the depending the concentration of water and sorbent on the time.
Highlights
The study of hydrodynamic flow and heat transfer through a porous media becomes much more interesting due to its wide and diverse applications [1],[7]
The numerical algorithms for modelling of liquid polymer injection are considered in the article [14], so that the liquid polymer is flowing through a porous medium
Many mathematical models are developed for the analysis of such processes, for example mathematical models of moisture movement in wood, when the wood is considered as porous media [6]
Summary
The study of hydrodynamic flow and heat transfer through a porous media becomes much more interesting due to its wide and diverse applications [1],. The numerical algorithms for modelling of liquid polymer injection are considered in the article [14], so that the liquid polymer is flowing through a porous medium. Many mathematical models are developed for the analysis of such processes, for example mathematical models of moisture movement in wood, when the wood is considered as porous media [6]. For the necessary engineering accuracy to solve above mentioned problems the conservative averaging method (CAM) with special integral hyperbolic and exponential type splines is used. In this paper we study the linear heat and moisture transfer processes in the porous multilayered media layer by using CAM with special integral hyperbolic type splines. In the article [16] the Langmuir expression was considered, correlating it with the saturation concentration and a Langmuir adsorption parameter p A contaminant transport model with Langmuir sorption under nonequilibrium conditions which is described by two coupled equations – advective-dispersion equation and nonequilibrium sorption equations is considered in [2]
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