In this paper, we present an analytical double-series solution for the time-dependent asymmetric heat conduction in a multilayer annulus. In general, analytical solutions in multidimensional Cartesian or cylindrical coordinates suffer from existence of imaginary eigenvalues and thus may lead to numerical difficulties in computing analytical solution. In contrast, the proposed analytical solution in polar coordinates (2D cylindrical) is “free” from such imaginary eigenvalues. Real eigenvalues are obtained by virtue of precluded explicit dependence of transverse (radial) eigenvalues on those in the other direction.
Analytical Solution to Transient Asymmetric Heat Conduction in a Multilayer Annulus
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Jain, P. K., Singh, S., and Rizwan-uddin (October 20, 2008). "Analytical Solution to Transient Asymmetric Heat Conduction in a Multilayer Annulus." ASME. J. Heat Transfer. January 2009; 131(1): 011304. https://doi.org/10.1115/1.2977553
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