V.I. Havrysh, R.B. Tushnytskyy, V.Ya. Krayovskyy, Ye.V. Levus

Èlektron. model. 2017, 39(2):91-102


The paper deals with an axially symmetric boundary value problem of heat conduction for isotropic piecewise-homogeneous layer with a through cylinder-shaped inclusion heated at one of its boundary surfaces by concentrated heat flow. Having expressed the heat conductivity factor for the whole system as an indivisible entity with a help of a unit function, we obtained the heat conduction equation with discontinuous and singular coefficients for the considered structure. Having made piecewise-linear approximation of temperature at the lateral surface of the inclusion and at the surfaces of conjugation of the layer’s elements, and then having applied Hankel’s transformation, and analytical-numerical solution of the problem is obtained. The temperature field in a “layer-inclusion” (the material of layer is silicon, the material of the inclusion is silver) structure has been calculated and analyzed.


temperature, isotropic piecewise-homogeneous layer, heat conduction, through foreign inclusion, perfect thermal contact, heat flow.


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