Hyperbolic models in the analysis of heat and moisture exchange in inhomogeneous porous materials
DOI:
https://doi.org/10.32347/2410-2547.2024.113.227-240Keywords:
Guyer-Krumhansl equation, heat and mass transfer, thin films, capillary-porous bodies, inhomogenuity, Knudsen number, hyperbolic equation of heat and moisture transferAbstract
The paper uses hyperbolic models for the analysis of heat and moisture exchange in inhomogeneous porous materials in which short heat pulses propagate. The heat transfer in sharply inhomogeneous media at room temperature is not described by Fourier and Cattaneo laws, but is modeled by Guyer-Krumhansl-type equations. The O.V. Lykov system of equations of interrelated heat and mass transfer taking into account the finiteness of heat and mass (moisture) transfer rates is solved using a one-dimensional formulation. However, the heat propagation velocity is of the order of the sound speed, so due to the short relaxation time, the solutions of the hyperbolic equation of thermal conductivity largely coincide with the solutions of the classical parabolic equation, although there are some significant differences. They depend on processes occurring on the surface (in thin layers) of porous bodies. The moisture diffusion rate in capillary-porous materials is approximately 106…107 and more times lower than the heat propagation rate, so, accordingly, the relaxation time of diffusion processes is much longer and should be considered in mass transfer equations. Exact analytical solutions of the one-dimensional Guyer-Krumhansl equation are obtained using the operator method. This equation is also used to study heat pulses of different shapes in the medium with respect to phonon/ballistic methods of heat transfer. The obtained results are used to model the heat and moisture propagation in thin films of capillary-porous bodies with account taken of molecular effects in systems of reduced dimension. The very short heat pulses propagation simulating isolated heat waves is modeled with reference to Knudsen number, as well as the solutions for the periodic initial function. The exact solutions of the above problems in the model of thin films of capillary-porous bodies are obtained.
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