1-D Green's Functions For Heat Conduction Between Semi-infinite Slabs With Perfect and Imperfect Boundary Contact
This document presents two derivations for 1-D Green's functions for semi-infinite slabs in contact along the boundary x=0. The case of imperfect contact with a heat transfer coefficient h is derived and the case of perfect contact is obtained by taking h to infinity. The two dimensional case with source point (x',y') is reduced to the one dimensional case by applying a constant source in the y' direction. Because the two-dimensional source solutions have complex representations, we get 1-D complex representations also. However, these complex, 1-D forms can also be reduced to all real, closed forms which agree with a direct attack using the 1-D equations.
The case of perfect insulation on x=0 is also computed by taking h to zero. The result is 'the method of images' solution in the source region and zero in the other region.
The convolution for a continuous (constant) source in time is carried out to produce a point source solution with continuous heat generation.
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