Abstract

We consider the boundary-value problem of stationary heat conduction in a three-dimensional domain formed by a layer and a half-space with a cavity bounded by a smooth closed surface. On the contact boundary of the layer and half-space, conditions of ideal thermal contact are satisfied, and on the other boundary of the layer, a heat flow is given. Convective heat exchange with a medium of zero temperature occurs over the surface of the cavity. Using a constructed Green matrix for the corresponding layered domain, we reduce the boundary-value problem to a Fredholm integral equation of the second kind with an unknown function on the surface of the cavity. The numerical solution is performed using sincquadratures, Gauss–Legendre quadrature formulas, and the projection method with spherical basis functions. Results of numerical experiments are presented.

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