Similarity in Convective Heat Transfer

Consideration will now be given to what is basically the same question that was earlier dealt with by using dimensionless analysis. The problem is, essentially, that of determining under what conditions the flow and temperature distributions about 

If the velocity fields in the two flows are similar then the velocity components at these two points will be such that  

Attention will first be given to the determination of conditions under which the velocity fields are similar, the temperature field being dealt with later. The following dimensionless coordinate system is introduced  

The velocity components are also expressed in dimensionless form using the following  

The pressure is nondimensionalized using the dynamic pressure based on U as follows  

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