Analytical solution to transient asymmetric heat conduction in a multilayer annulus

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 (r,z) 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.