Abstarct: Flow and heat transfer between two coaxial cylinders, one or both rotating, with an axial flow of fluid superimposed, which makes a combination of rotating and axial regimes, is of great importance, scientifically and technically. Such flows have a wide range of applications in mechanical systems such as bearings, asynchronous motors with axial ventilation, rotating heat exchangers, drilling of oil wells, etc. In this study, it is tried to investigate a laminar flow of water which first enters a pipe ( inner cylinder ) and then enters an annulus with hot rotating outer wall, by modelling the conditions of an Industrial System ( water cooled rollers used in steel industries ). Also the variation of temperature and rate of heat transfer through the flow were explored. Thermo fluid survey of such a system, with minimum changes respect to main industrial system and it’s boundary conditions, is one of the new investigative aspects of this study. First and second chapters are assigned to the review of previous investigations and also introduction of this study and dominant equations. In third chapter an analytical method is proposed for solving the heat transfer equation in hydrodynamically developed – thermal developing area of flow. The major part which is done by numerical methods, is presented in the form of a comprehensive model in fourth chapter and the results are in fifth chapter. The results show that rotation of outer wall of the annulus has insignificant effect on convective heat transfer, in low rotational speeds. In addition the influence of this rotation on axial velocity profile is little which this effect is more considerable in entrance region of annulus.