Calculation of Heat and Moisture Distribution in the Porous Media Layer

Mathematical Modelling and Analysis

2018

Self Cite

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.

Section: Introductionmentioning

confidence: 99%

On Mathematical Modelling of the Solid-Liquid Mixtures Transport in Porous Axial-Symmetrical Container With Henry and Langmuir Sorption Kinetics

Kangro

Mathematical Modelling and Analysis

2018

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“…In this paper we study the linear heat and moisture transfer processes in the porous multilayered media layer by using CAM with special integral splines. In one layer similar process is analysed and decribed in [15], [16].…”

Section: Introductionmentioning

confidence: 99%

Special Splines of Hyperbolic Type for the Solutions of Heat and Mass Transfer 3-D Problems in Porous Multi-Layered Axial Symmetry Domain

Mathematical Modelling and Analysis

Buikis

Aboltins

et al. 2017

Self Cite

In this paper we study the problem of the diffusion of one substance through the pores of a porous multi layered material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. As an example we consider circular cross section wood-block with two layers in the radial direction. We consider the transfer of heat process. We derive the system of two partial differential equations (PDEs) - one expressing the rate of change of concentration of water vapour in the air spaces and the other - the rate of change of temperature in every layer. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM) with special integral splines. This procedure allows reduce the 3-D axis-symmetrical transfer problem in multi-layered domain described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.

“…A. Buikis was developed different assumptions for CAM along the vertical coordinate in the Cartesian coordinates using parabolic splines [3], [11]. We are expanding the usage of splines method with integral parabolic and exponential splines [16], [2] in addition, not only in Cartesian coordinates, but also in cylindrical coordinates too [1], [10], if it requires the model under consideration.…”

Section: Introductionmentioning

confidence: 99%

On Mathematical Modelling of the 2-D Filtration Problem in Porous Axial Symmetrical Cylinder

Kangro

Teirumnieka

et al. 2017

ETR

Self Cite

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 equation is 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 kinetically 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 axis-symmetrical mass transfer problem described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.