Heat Transfer in a Half-Space with Transversal Anisotropy Under the Action of a Lumped Heat Source

The authors have obtained a novel analytical solution to the problem of the theory of heat conduction in an anisotropic half-space with an anisotropy of the transversal type when the anisotropy takes place in planes formed by two coordinate axes, whereas in the direction of the third coordinate axis guided deep into the body, the material is isotropic. The solution was obtained by two applications of the variablewise Fourier transformation in the anisotropy plane and of the specially developed method of substitution in the direction of the third coordinate. The obtained results point to the drift of the heat fluxes and temperature fields toward the principal axis with a larger coefficient of the thermal-conductivity tensor, with this coefficient being the larger the higher the degree of anisotropy in the indicated direction. It has been established that isothermal surfaces have the shapes of elliptic paraboloids.