An analytical solution and experimental investigation concerning the problem of turbulent heat transfer in an annulus are made with simultaneously devoloping velocity and temperature distribution under the condition of a constant wall heat flux. For the theoretical study several groups of differential and integral equations are derived and solved by using a finite difference technique. From the asymptotic solutions some turbulent heat transfer relations are obtained. In the experiments the inner diameter of the channel is 12.34mm and the outer diameter is 19.00mm. The inner wall of the channel is provided with constant heat flux and the outer wall heat-insulated. The range of the parameters Re= (2-13.5) × 104; Pe=128-854. It is found that the asymptotic solutions agree very well with the experimental data obtained by the authors and others.