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Introduction. Although several problems of heat flow in composite cylinders have been studied, all the cases considered treat the heat flow in the radial direction only [1,2,3]. The case of combined radial and axial heat flow in composite cylinders presents an interesting boundary value problem which has also considerable significance in the theory of vibrations and propagation of electromagnetic waves [4,5,6]. In this paper, we consider a case of combined radial and axial heat flow in the unsteady state in finite cylinders composed of two coaxial parts of different materials. The temperature distribution in the cylinder at any instant under the assumed boundary and initial conditions has been obtained by the use of the Laplace transformation.The procedure is illustrated by a numerical calculation in a particular case.The Problem. Composite cylinder made of two different materials, the inner cylinder 0 < r < a and the outer cylinder a < r 0 (see Fig. 1).

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The dynamic problem of the deformation of a homogeneous, perfectly elastic and isotropic half space due to harmonically time-dependent tractions over the boundary of an embedded spherical cavity is discussed. The solution is developed completely and rigorously by a method of successive approximations. Lamb’s solution for a point source in a half-space is derived as a limit case of the general solution. The problem is suggested by its applications in the theory of underground explosions and in seismology.

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