Analytical Solution of Heat Conduction in a Multi-Layer Orthotropic Cylinder Subject to Periodic and Asymmetric Heat Flux

Abstract

The problem of heat conduction in a multi-layer two-dimensional orthotropic cylinder subject to asymmetric and periodic heat flux on the outer wall was solved analytically. The dimensional analysis of the problem revealed that the heat conduction through the cylinder is a function of the Biot number (Bi) and four non-dimensional parameters per layer. These layer-dependant parameters include: frequency ratio (α*m), thickness ratio (x*m), radial conduction ratio (K*rm), and tangential conduction ratio (K*tm). The derivation is valid for an arbitrary number of layers. The number of possible combinations increases dramatically with the number of layers. Thus as an example, the results for a cylinder composed from three layers, are presented and discussed. The results showed that the magnitude of heat conduction in a multi-layer orthotropic cylinder can be significantly different from those of an isotropic cylinder subject to the same externally imposed heat flux. The solution could be extended to an arbitrary varying imposed heat flux through the use of Fourier series and the principle of superposition. The solution also includes the analytical periodic temperature distribution across the cylinder. This could be used to study the effect of thermal stress fatigue in each layer and at the interface of adjacent layers.