Numerical Modeling of Heat and Mass Transport with Inner Heat Exchange in Unsaturated Porous Media

2020 ◽  
Vol 27 ◽  
pp. 166-176
Author(s):  
Jozef Kačur ◽  
Patrik Mihala
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Heat Exchange ◽  
Inverse Problems ◽  
Water Transport ◽  
Heat Conductivity ◽  
Unsaturated Porous Media ◽  
Heat Transmission ◽  
Matrix Heat

We are focused to the numerical modelling of heat, contaminant and water transport in unsaturated porous media in 3D. The heat exchange between water and porous media matrix is taken into the account. The determination of heat energy transmission coefficient and matrix heat conductivity is solved by means of inverse problem methods. The mathematical model represents the conservation of heat, contaminant and water mass balance. It is expressed by coupled non-linear system of parabolic-elliptic equations. Mathematical model for water transport in unsaturated porous media is represented by Richard's type equation. Heat transport by water includes water flux, molecular diffusion and dispersion. A successful experiment scenario is suggested to determine the required parameters including heat transmission and matrix heat conductivity coefficients. Additionally we investigate contaminant transport with heat transmission and contaminant adsorption. The obtained experiments support our method suitable for solution of direct and inverse problems. This problem we have discussed previously in 1D model, but preferential streamlines in 1D thin tubes shadow accurate results in determination of required parameters. In our presented setting we consider a cylindrical sample which is suitable in laboratory experiments for inverse problems.

Determination of the Air−Water Interfacial Area in Wet “Unsaturated” Porous Media

Langmuir ◽  
1996 ◽  
Vol 12 (8) ◽  
pp. 2041-2044 ◽  
Author(s):  
Milind V. Karkare ◽  
Tomlinson Fort
Keyword(s):  
Porous Media ◽  
Interfacial Area ◽  
Unsaturated Porous Media

scholarly journals Reverse Task of Heat Conductivity for the Semilimited Bar

2019 ◽  
pp. 27-31
Author(s):  
O. Shevchenko
Keyword(s):  
Thermal Conductivity ◽  
Inverse Problem ◽  
Heat Exchange ◽  
Boundary Conditions ◽  
Heat Conductivity ◽  
Algebraic Equations ◽  
Newton's Law ◽  
Newton’S Law ◽  
Solid Bodies

The article concerns methods and formulas for the calculation of the coefficient of thermal conductivity of solid bodies using the known solutions of direct thermal conductivity tasks. The solution to the inverse problem of heat conductivity is based on the quite complicated methods including both hyperbolic functions and finite-difference methods. Under certain experimental conditions, the task is simplified at the regular thermal modes of 1, 2, or 3 types. Thus final formulas are simplified to algebraic equations. The simplification of the inverse problem of heat conductivity to algebraic equations is possible using other approaches. These me­thods are based on the analysis of the reference points, zero values of temperature distribution function, function inflection points, and its first and second derivatives. Here, we present formulas for the calculations of the temperature field on the assumption of the direct task solution for the half-bounded bar under the pulsed heating followed the re-definition of the boundary conditions. The article describes two methods in which solutions are reduced to simple algebraic formulas when using the specified points on hea­ting thermograms of test examples. These solutions allow algebraic deriving of simple relations for inverse problems of determination of thermophysical characteristics of solid bodies. The calculation formulas are given for the determination of the heat conductivity coefficient determination by two methods: by value of temperature, coordinate, and two moments at which this temperature is reached. The second method uses the values of two coordinates of the test sample in two different points where the equal temperature is reached at different points in time. The final solution of the equation is logarithmic. The analysis of known methods and techniques shows that experimental methods are oriented on the technical implementation and based on facilities of available equipment and instruments. Existing experimental techniques are based on specific constructions of measuring facilities. Simultaneously, there are well-studied methods of solution of thermal conductivity standard tasks set out in fundamental issues. The theoretical methods come from axioms, equations, and theoretical postulates, and they give the solution of inverse tasks of thermal conductivity. This work uses the solutions of direct tasks presented in the monograph by A.V.Lykov “The theory of heat conductivity”. These solutions have a good theoretical background and experts’ credit. The boundary conditions of the problem are next: the half-bounded thin bar is given. The side surface of the bar has a thermal insulation. At the initial moment, the instant heat source acts on the bar in its section at some distance from its end. Heat exchange occurs between the environment and the end of the bar according to Newton’s law. The initial (relative) temperature of the bar is accepted equal to zero. The heat exchange between the free end face of the bar and the environment is gone according to Newton’s law.

An Analytic Solution of Water Transport in Unsaturated Porous Media

2008 ◽  
Vol 11 (6) ◽  
pp. 591-601 ◽  
Author(s):  
M. Nasseri ◽  
M. R. Shaghaghian ◽  
Y. Daneshbod ◽  
H. Seyyedian
Keyword(s):  
Porous Media ◽  
Water Transport ◽  
Analytic Solution ◽  
Unsaturated Porous Media

scholarly journals Mathematical Modelling of Mass Transfer in Zones of Complete and Incomplete Saturation under the Action of Systematic Combined Drainage

2019 ◽  
pp. 86-87
Author(s):  
Anatolii Vlasyuk ◽  
Tatiana Tsvietkova
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Porous Media ◽  
Boundary Value Problem ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Finite Differences ◽  
Unsaturated Porous Media ◽  
Vertical Drains ◽  
The Mathematical Model

The mathematical model of a processes mass transfer in saturated and unsaturated porous media to the filtertrap in isothermal conditions to the system of vertical drains is presented. The numerical solution of the respective boundary value problem was obtained by the method of finite differences using the numerical method of conformal mappings in an inverse statement.

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