The task of thermal conductivity for a bimaterial with a system of partially heat permeable cracks and a heat source

The work is devoted to the stationary task of thermal conductivity about crack interaction in a bimaterial subjected to a heat source. It was assumed that the cracks are heat permeable though the heat permeability is different for internal cracks and for an interface crack. The methods of complex potentials and the method of superposition are used for the construction of equations to the problem. In case when the length of the interface crack is much lager than the characteristic length of the internal crack the singular integral equations are solved by small parameter method. The asymptotic analytical formulas for coefficient intensity of thermal flow at the crack tips are derived. The influence of the crack locations and their orientations on the coefficients of thermal intensity at the interface crack tips are investigated for different thermal conductivity coefficients of the crack surfaces and for different location of the heat source.