A method is proposed for the determination of the velocity distribution of the local heat transfer and friction factor for fully developed turbulent flows of fluids of constant properties through ducts of arbitrary cross section with a prescribed heat flux distribution at the wall. The method can be divided into three parts. The first part concerns the distribution of the velocity near the wall. The velocity profile on a line normal to the wall is represented by equations of the same type as those used for the circular geometry, with the reduced velocity u+ as a function of the reduced distance n+ to the wall. Only the friction velocity u* varies. When the distribution of the local friction velocity is known, the velocity profile in each point is known. This approach is supposed to be valid as long as the local radius curvature of the wall is not too small compared to the average hydraulic diameter. The second part concerns the velocity distribution in the core. In this region it is assumed that the flow can be represented by a gradient-diffusion type of equation.