This paper presents the derivation of the Green's function for composite cylinders 0<r<a and r>a in perfect contact on the surface r=a. Because the source function can be in either region, there are two pairs of functions which define the Green's function. Each pair is the solution to a two-region conduction problem with zero initial temperatures and continuity of temperature and flux on the cylinder r=a. These pairs are used in conjunction with a general formula to get the solution to other problems where the cylinders are in perfect contact, but may have non-zero initial conditions and/or possibly a distribution of internal heat sources. The Green's function approach and a direct approach agree when applied to three problems with known solutions. A fourth problem illustrates a complication where the Laplace transform of the general solution is more useful.
Keywords Two Regions Heat Conduction Unsteady State Laplace Transform
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Researchers should cite this work as follows:
- heat conduction
- two regions heat conduction
- unsteady state Laplace transform
- Green\'s function