Analytical exact solutions of heat conduction problems for anisotropic multi-layered media. (English) Zbl 1057.80003

The authors consider the steady heat conduction through a two-dimensional multi-layered media with the layers running parallel to one direction. It is supposed that the problem is linear i.e. the thermo-physical coefficients are constant. The boundary conditions are of the first and second kind (the temperature or the heat flux at the upper surface of the body are prescribed and for the both cases the temperature at the bottom is zero). By using a specific linear transformation of the Cartesian coordinates the general unisotropic differential equations of a multi-layered problem are transformed into an equivalent multi-layered body with isotropic characteristics. The exact solution of this problem is obtained by means of Fourier transformation technique. Numerous examples are solved by computer analysis.


80A20 Heat and mass transfer, heat flow (MSC2010)
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