Page 121 - Modelling in Transport Phenomena A Conceptual Approach

4.5. FLOW IN CIRCULAR PIPES 101

in which all properties except p, are evaluated at the mean bulk temperature.
Equation (4.5-25) is valid for
13 5 Re 5 2030

0.48 5 Pr 5 16,700
0.0044 5 p/pw 5 9.75
The analytical solution5 to this problem is only possible for very long tubes, i.e.,
LID + 00. In this case the Nusselt number remains constant at the value of 3.66.

4.5.2.2 Turbulent flow correlations
The following correlations approximate the physical situation quite well for the
cases of constant wall temperature and constant wall heat flux:
Dittus-Boelter correlation

Dittus and Boelter (1930) proposed the following correlation in which all physical
properties are evaluated at the mean bulk temperature:

I Nu = 0.023 Prn 1 (4.5-26)

where
0.4 for heating
n={ 0.3 for cooling
The Dittus-Boelter correlation is valid when
0.7 5 Pr 5 160

Re 2 10,000
LID 2 10
Sieder-'Pate correlation

Sieder and Tate (1936) correlation is
I
I Nu = 0.027Re4d5 PI-'/^ (p,~'p,)~.'~ (4.5-27)

in which all properties except pw are evaluated at the mean bulk temperature.
Equation (4.5-27) is valid for

0.7 5 Pr 5 16,700
Re 2 10,000
LID 2 10

5See Section 9.3.1.2 in Chapter 9.