Axially symmetric problems of stationary heat conduction and thermoelasticity for a body with thermally active or thermally insulated disk inclusion (crack)

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We present solutions of axially symmetric problems of stationary heat conduction and thermoelasticity for a body with a thin thermally active disk inclusion (where the temperature or heat flow is given) and also with a thermally insulated inclusion. The heat conduction problems are reduced to integral equations, and exact solutions are obtained in the case where their right-hand sides are polynomials of arbitrary degree. We determine the components of the stress tensor and displacement vector as well as, in the case of cracks, the stress intensity factors.