IfT_s >T_f , the fluid temperature approaches asymptotically and the temperature profile at a distance x is shown in fig.4.3. However, a thermal boundary may be defined (similar to velocity boundary) as the distance from the surface to the point where the temperature is within 1% of the free stream fluid temperature (T_f ). Outside the thermal boundary layer the fluid is assumed to be a heat sink at a uniform temperature ofT_f . The thermal boundary layer is generally not coincident with the velocity boundary layer, although it is certainly dependant on it. That is, the velocity, boundary layer thickness, the variation of velocity, whether the flow is laminar or turbulent etc are all the factors which determine the temperature variation in the thermal boundary layer. The thermal boundary layer and velocity boundary layer are related by the Prandtl number, is called the momentum diffusivity and  is called the thermal diffusivity; is less than unity, the momentum boundary layer (or velocity boundary layer) remains within the thermal boundary layer. If P_r >1, the boundary layers will be reversed as shown in the fig.4.4. The thermal boundary layer and velocity boundary layer coincides at P_r =1.

Fig.4.4: The relation of two boundary layers at different Pr numbers

The above boundary layer theory will be helpful to understand the heat transfer in the process. Through the boundary layers heat transfer is covered in a separate chapter, but the detailed derivation and development of all the relationships having engineering importance for the prediction of forced convection heat transfer coefficient is beyond the scope of the course. The reader may consult any standard fluid mechanics and heat transfer books for detailed knowledge.

The purpose of this chapter is to present a collection of the most useful of the existing relations for the most frequently encountered cases of forced convection. Some of these relations will be having theoretical bases, and some will be empirical dimensionless correlations of experimental data. In some situations, more than one relation will be given.