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1 Journal of Applied Mathematics and Computational Mechanics

1 2018

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Application of numerical methods for solving the non-Fourier equations. A review of our own and collaborators’ works

Majchrzak E., Mochnacki B.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 2

43--50

Thermal processes occuring in the solid bodies are, as a rule, described by the well-known Fourier equation (or the system of these equations) supplemented by the appropriate boundary and initial conditions. Such a mathematical model is sufficiently exact to describe the heat transfer processes in the macro scale for the typical materials. It turned out that the energy equation based on the Fourier law has the limitations and it should not be used in the case of the microscale heat transfer and also in the case of materials with a special inner structure (e.g. biological tissue). The better approximation of the real thermal processes assure the modifications of the energy equation, in particular the models in which the so-called lag times are introduced. The article presented is devoted to the numerical aspects of solving these types of equations (in the scope of the microscale heat transfer). The results published by the other authors can be found in the references posted in the works cited below.