The Green's function method for solving axial conduction effects of moving media on its steady-state temperature field was introduced. The mathematical expression describing steady-state temperature fields under first and second classes of non-homogeneous boundary conditions was derived using eigenvalues and eigenvalue functions to obtain the Green's function solutions. It was confirmed that the steady-state heat transfer problems can be solved under the non-homogeneous boundary conditions by employing Green's function method. The heat transfer of the moving media between two parallel plates and within a circular tube was calculated under uniform heat flux conditions for semi-infinite and finite lengths and the analytical dimensionless temperature solutions were obtained. The relationship between the axial conduction effects of moving media and the Pe and x/H was also analyzed. The results show that: the larger Pe means the smaller dimensionless temperature for both cases of uniform heat flux conditions of semi-infinite and limited lengths; more intense temperature changes in the absence of surface heat flux and more mild temperature changes for the case of uniform wall heat flux of semi-infinite length are observed; in the case of limited length under uniform heat flux condition

significant differences compared with the case of uniform heating in semi-infinite region and more dramatic temperature changes in the whole computational domain are observed.