4.4.1 Reynolds analogy
Reynolds has taken the following assumptions to find the analogy between heat and momentum transport.
1. Gradients of the dimensionless parameters at the wall are equal.
2. The diffusivity terms are equal. That is
Thus if we use the above assumptions along with the eq.4.32 and 4.33,
Thus if we use the above assumptions along with the eq.4.32 and 4.33,
Equation 4.34 is known as Reynolds’s analogy.
The above relation may also be written in terms of the Darcy’s friction factor (fD) instead of fanning friction factor (fD = 4f)
Where Stanton number (St) is defined as,
The advantage of the analogy lies in that the h may not be available for certain geometries/situations however, for which f value may be available as it is easier to perform momentum transport experiments and then to calculate the f. Thus by using the eq.4.34 the h may be found out without involving into the exhaustive and difficult heat transfer experiments.