The shear flow in a tube and a slit at a fully developed flow and temperature distribution for a non-linear viscous medium has been analysed of which the constitutive equation is described by a generalized Carreau model. The influence of of the transition parameter a on shear rate, velocity and temperature profile has been investigated. First, it is essential to find a solution to determine the reduced momentum and the energy balance with suitable inequalities in the form of intervals in which the solution must be contained. The intervals are sharply limited, in general that means that they cannot be improved, Within these limits, the solutions show a very different rheological behaviour depending on the quantity of a dimesionless flow rate Q.