The problem of two dissimilar semi-infinite solids at different initial temperatures brought into contact has a well-known simple analytical solution. In the present work, this problem is re-examined with the additional simultaneous complications of both contact resistance and surface heat generation. While contact resistance is always present to some degree due to surface asperities or oxidation layers, heat generation at the contact interface can also occur in certain situations. These situations can occur in applications such as ultrasonic welding or arise in situations involving electromagnetic radiation passing through an optically transparent medium, but dissipating as heat at an interface with an opaque material that is in contact with the transparent material. In this paper, an analytical solution to the unsteady conduction problem is developed that accounts for both contact resistance and interfacial heat generation. The solution confirms that the initially warmer object rapidly decreases in temperature in the vicinity of the interface as heat flows into the cooler object and the heat generated at the interface preferentially flows to the cooler material. After a short time, however, the temperatures of both materials at the interface increase in temperature above even the initial temperature of the initially hotter material. An experiment was performed that verified the analytical solution.

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