Abstract
The thermal conductivity models of Fourier, Cattaneo-Vernotte, Maxwell-Cattaneo-Luikov and models with fractional time derivatives of temperature and heat flux are considered. An algorithm for the numerical solution of the generalized problem of one-dimensional heat conduction is constructed. The algorithm comprises all the models listed above applying boundary conditions of the third kind and difference analogs of differential operators of the second order of accuracy in coordinate and time. The parameters (Biot number, time of thermal relaxation and thermal damping, indicators of fractional derivatives) that describe experimental transient processes are determined using the listed models applied for both in the center and on the surface of a low heat-conducting body.
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