Theory of Heat Conduction for Two Region Problems Using Green's Functions
This paper derives equations which describe transient temperature distributions in adjacent regions which share a common boundary. These regions consist of materials with distinct, constant physical properties. The theory is developed for two types of boundary contact. The first formula is developed for perfect contact where there is continuity of both temperature and flux. The second formula allows for a thermal resistance at the boundary which retains continuity of flux, but causes a temperature drop across the boundary. As an example, the two-region theory is applied to quadrants 1 and 2 which are separated by an infinitely thin resistive layer on the y-axis and are heated along the x-axis. This problem was solved by a direct approach in a previous paper and the two-region Green’s function approach gives the same results.
Keywords Two Regions Heat Conduction Unsteady State Laplace Transform
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