The problem of heat conduction in a two-dimensional orthotropic cylinder subject to asymmetric and periodic heat flux distribution imposed on the outer wall was solved analytically. The dimensional analysis of the problem revealed that the heat conduction was a function of four nondimensional parameters: Blot number (Bi), the ratio of the cylinder outer radius to the inner radius (R-2), nondimensional frequency (alpha), and orthotropicity factor (K-t). The results show that the insulation characteristics of a cylinder made from orthotropic material can be significantly better than that of a cylinder made from isotropic material subject to the same thermal conditions. The case of a graphite fiber epoxy was used to demonstrate the effectiveness of orthotropic materials under periodic and asymmetric thermal loading.