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This paper is devoted to the acoustic mismatch model and diffusion mismatch model of Kapitza thermal resistance. We consider that diffusion in the transition layer can be represented by variable composition and finite thickness instead of previous assumptions of a “black box” approximation. The effect of heat flow on the interface is reviewed in the acoustic mismatch model where energy is transferred between two different materials and the critical incident angles are taken into account. Finally we provide calculations of the Kapitza resistance for several interfaces (Metal-Sapphire and Metal-Silicon).

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