Numerical model of heat transfer in three phases of the poroelastic medium

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Abstract

In this paper, the results of numerical analysis of the thermal consolidation of a two phase medium, under the assumption of independent heat transfer in fluid and the solid phase of the medium, are presented. Three cases of pore fluid were considered: liquid, represented by water, and gas, represented by air and carbon dioxide. The mathematical model was derived from irreversible thermodynamics, with the assumption of a constant heat transfer between the phases. In the case of the accepted geometry of the classical dimensions of the soil sample and boundary conditions, the process leads to equalization of temperatures of the skeleton on the pore fluid. Heat transfer is associated with the fluid flow in the pores of the medium. In the case of gas as the pore fluid, a non-linear mathematical model of gas filtration through the pores of the medium was accepted. For the computing process, relationships between viscosity or density and temperature proposed by other authors were taken into account. Despite accepting mechanical constants of the solid phase that do not depend on temperature, the obtained model is nonlinear and develops the classical Biot–Darcy model.

REFERENCES

  • [1] Biot M.A., General Theory of three-dimensional Consolidation, J. Appl. Physics, 1941, Vol. 12.

  • [2] Biot M.A., Willis D.G., The Elastic Coefficients of the Theory of Consolidation, J. Appl. Mech., 1957, Vol. 24.

  • [3] Coussy O., Mechanics of Porous Continua, John Wiley & Sons, Ltd., 1995.

  • [4] Coussy O., Poromechanics, The Atrium, Southern Gate, Chichester, John Wiley & Sons, Ltd., 2004.

  • [5] Kisiel I., Derski W., Izbicki R., Mróz Z., Mechanics of Soils and Rocks, Series: Technical Mechanics, Vol. VII, PWN, Warszawa, (Polish Scientific Publishers), (in Polish), 1982.

  • [6] Strzelecki T., Bauer J., Auriault J.L., Constitutive Equation of a Das-Filled Two-Phase Medium, Transport in Porous Media, 1993, Vol. 10, 197–202.

  • [7] Strzelecki T., Kostecki S., Żak S., Modeling of flows through porous media, DWE, Wrocław, (Lower Silesia Educational Publishers), (in Polish), 2008.

Studia Geotechnica et Mechanica

The Journal of Wroclaw University of Technology

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