Solutions are developed for the conductive heat flow in the xy plane where there is a uniform flow at infinite values of y, and where y = 0 represents the interface between two materials. This interface consists of an arbitrary pattern of perfectly conducting strips and non-conducting gaps. It is assumed that thermoelastic effects are negligible. The solution takes the form of an equation with one unknown parameter per gap, and these unknowns can be found by a simple solution process involving numerical integration. The effective resistance of the interface can then be determined by a simple numerical integration.
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