The difference scheme for the numerical solution of boundary problem for a system of equations for non-isothermal filtration with a Caputo derivative of fractional order on time is developed. Stability of the differential scheme is proved. Computational experiment in the analysis of solutions obtained has been done. Physical processes pass slowly in the fractal medium with non-locality in time. It is explained by the fact the occasionally wandering particle is being eliminated from the start place slowly, since not all directions of the movement become available for it. Values of pressure and temperature depending on the coordinate of layer radius and time calculated, and graphs of the dynamics pressure and temperature changes according to the layer radius and in depending on the time are built. Deceleration of the processes with time in the solutions for fractional derivatives which is characteristic for such medium has been established.
The results of experimental measurements of the temperature dependence of the
effective thermal conductivity of various granite samples obtained by the
absolute stationary method in the temperature and pressure ranges of 273-
523 K and 0.1-400 MPa, respectively, are analyzed. The power-law character
of the temperature dependence of the effective thermal conductivity for all
measured granite samples at atmospheric pressure is established. We have
shown that pressure significantly affects the power law of the temperature
dependence of the effective thermal conductivity of granite samples. A
low-parameter description of the temperature-pressure behavior of thermal
conductivity is proposed. A correlation is established between its
components.
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