A procedure to obtain accurate solutions for many transient conduction problems in complex geometries using a Galerkin-based integral (GBI) method is presented. The nonhomogeneous boundary conditions are accommodated by the Green’s function solution technique. A Green’s function obtained by the GBI method exhibits excellent large-time accuracy. It is shown that the time partitioning of the Green’s function yields accurate small-time and large-time solutions. In one example, a hollow cylinder with convective inner surface and prescribed heat flux at the outer surface is considered. Only a few terms for both large-time and small-time solutions are sufficient to produce results with excellent accuracy. The methodology used for homogeneous solids is modified for application to complex heterogeneous solids.
Green’s Function Partitioning in Galerkin-Based Integral Solution of the Diffusion Equation
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Haji-Sheikh, A., and Beck, J. V. (February 1, 1990). "Green’s Function Partitioning in Galerkin-Based Integral Solution of the Diffusion Equation." ASME. J. Heat Transfer. February 1990; 112(1): 28–34. https://doi.org/10.1115/1.2910360
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