Thermal insulation behavior of a multi-layer orthotropic cylinder

The problem of heat conduction in a multi-layer, two-dimensional, orthotropic cylinder subject to asymmetric and periodic temperature distribution on the outer wall is solved analytically. Dimensional analysis of the problem shows that heat conduction through the cylinder is a function of the Biot number (Bi) and the following four non-dimensional parameters in each layer: frequency ratio (α*n), thickness ratio (x*n) and radial (K*r,n) and tangential (K*t,n) conduction ratios. The derivation is valid for an arbitrary number of layers and has been used to study the effect of layer order on inter-layer and overall heat transfer. A cylinder composed of two layers is discussed as an example.