---

In this study, 2D Asymmetric heat transfer in multi-layer composite cylinder is investigated, analytically. The boundary conditions are the most linear general boundary conditions which can cover all the heat transfer mechanisms consists of convection, conduction and radiation. The fibers are wounded around the cylinder. The angle of fibers and composite materials can be changed layer by layer. The governing equation of orthotropic conduction has been extracted and temperature distribution series have been obtained using the separation of variables method. In order to find the unknown series’ coefficients, three independent set of equations have been constructed by applying the boundary conditions inside/outside of cylinder and temperature/heat flux continuity between the layers. These set of equations have been solved using the orthogonal function relations and Thomas algorithm to find the recursive relation for unknown coefficients. The effect of design parameter, fiber angle and layers’ materials, have been investigated via two functional examples.