Numerical Solution of Periodic Heat Transfer in an Anisotropic Cylinder Subject to Asymmetric Temperature Distribution

Abstract

This paper details the numerical solution of the heat conduction problem in a two-dimensional anisotropic cylinder subject to asymmetric and periodic temperature distribution on the outer wall. The dimensional analysis of the problem reveals that the heat conduction is a function of five non-dimensional parameters. The parameters are: non-dimensional frequency (α), cylinder outer to inner radius ratio (R2), Biot number (Bi), orthotropicity factor (K22), and anisotropicity factor (K22). The study details the effect of each parameter on the maximum radial heat conduction to the cylinder inner and outer walls, qj and q2 respectively, as well as the phase shift between qt and q2. Depending on the combination of the parameters, the magnitude and/or phase of heat conduction in an anisotropic cylinder can be significantly different from those of an orthotropic and isotropic cylinder subject to the same externally imposed temperature distribution.