Keywords: heat conduction, temperature waves, numerical simulation, cylinder, sphere, solid body.

This paper is concerned with a numerical investigation of the temperature waves in cavities of rectangular, cylindrical and spherical forms with heat conduction. The different dependences of heat conductivity on temperature are studied. Timeperiodic boundary conditions have been applied for all problems. Analytical solutions for these problems are usually very complex if they exist at all, since the heat conductivity is function of temperature. Numerical methods are simple and effective way to find solution for this problem.

We have obtained a nonzero averaged heat flux for a period on the surface of the cavity and inside it even if periodic boundary conditions are equal. It is possible with using pure heat conductivity if the domain where temperature wave propagation consists of two parts with different dependences on heat conductivity. If the one part of the domain has an increasing heat conductivity with temperature and the second part has a decreasing heat conductivity with temperature then a positive averaged heat flux for period from the first part of the domain to the second is obtained.

This phenomenon may be combined with thermoelectric effect to design inexpensive energy sources. The boundary conditions can be implemented using periodic temperature variations of the atmosphere or the secondary energy of technological processes. It is possible to construct an energy source in different ways using the temperature waves, for example, connecting two parallel plates, two cylinders or two spheres with increasing and decreasing heat conductivities with temperature. Then a working thermoelectric transducer will be obtained.

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