Abstract
An analytical solution is presented for nonhomogeneous, one-dimensional, transient heat conduction problems in composite regions, such as multilayer slabs, cylinders and spheres, with arbitrary convection boundary conditions on both outer surfaces. The method of solution is based on separation of variables and on orthogonal expansion of functions over multilayer regions. Similar analytical procedures are available in the literature for a variety of combinations of boundary conditions, but not including the ones considered here, although such cases are encountered in practice very often. The effect of layer thermal properties on density of eigenvalues and accuracy of solution is also examined.
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