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 (f_{D} = 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.
4.4.2 The ChiltonColburn analogy
The Reynolds analogy does not always give satisfactory results. Thus, Chilton and Colburn experimentally modified the Reynolds’ analogy. The empirically modified Reynolds’ analogy is known as ChiltonColburn analogy and is given by eq.4.35,
(4.35 a)
or
(4.35 b)
It can be noted that for unit Prandtl number the ChiltonColburn analogy becomes Reynolds analogy.
4.4.3 The Pradntl analogy
In the turbulent core the transport is mainly by eddies and near the wall, that is laminar sublayer, the transport is by molecular diffusion. Therefore, Prandtl modified the above two analogies using universal velocity profile while driving the analogy (eq. 4.36).
(4.36)
4.4.4 The Van Karman analogy
Though Prandtl considered the laminar and turbulent laminar sublayers but did not consider the buffer zone. Thus, Van Karman included the buffer zone into the Prandtl analogy to further improve the analogy.
(4.37)
Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
58 videos70 docs85 tests
