Abstract
With the use of the Laguerre and Hankel integral transforms, the solution of a two-dimensional initial-boundary-value heat conduction problem for a two-layer slab under mixed boundary conditions is constructed: one of the surfaces is heated by a heat flux distributed axisymmetrically in a circle of radius R and is cooled by the Newton law outside this circle. The solution of the problem is reduced to a sequence of infinite quasi-regular systems of algebraic equations. The results of numerical analysis of the temperature field in the two-layer slab made from an aluminum alloy and ceramicsare presented depending on the relative geometric properties of the components and cooling intensity.
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