By means of a linear perturbation theory, the influences of density, viscosity, thermal conductivity, and specific heat capacity, all varying with temperature, are taken into account. The wall heat flux is assumed to be constant at the inner and outer wall, with an arbitrary ratio between these two. Even for variable properties the problem can be reduced to solving a set of ordinary differential equations with three parameters: heat flux ratio, diameter ratio, and Prandtl number. Skin friction and heat transfer results are given for specific numbers of the parameters, including the limiting cases of pipe and channel flows.