Page 122 - Modelling in Transport Phenomena A Conceptual Approach

102 CHAPTER 4. EVALUATION OF TRANSFER COEFFICIENTS

Whitaker correlation

The equation proposed by Whitaker (1972) is
(P/Pw)0*14 1
I Nu = 0.015 Ret83 (4.528)

in which the Prandtl number dependence is based on the work of Fkiend and
Metzner (1958), and the functional dependence of p/pw is from the work of Sieder
and Tate (1936). All physical properties except pw are evaluated at the mean bulk
temperature. The Whitaker correlation is valid for

2,300 5 Re 5 1 x lo5

0.48 5 Pr 5 592

0.44 5 p/p, 5 2.5

4.5.2.3 Calculation of the heat transfer rate

Once the average heat transfer coefficient is calculated from correlations by using
Eqs. (4.5-25)-(4.528)) then the rate of energy transferred is calculated as

where AT,,, logarithmic mean temperature difference, is defined by

(4.530)

The derivation of Eq. (4.5-29) is given in Section 9.3 in Chapter 9.

Example 4.15 Steam condensing on the outer surface of a thin-walled circular
tube of 65 mm diameter maintains Q uniform surface temperature of 100 "C. Oil
flows through the tube at an average velocity of 1 m/ s. Determine the length of the
tube in order to increase oil temperature from 40 "C to 60 "C. Physical properties
of the oil are as follows:

p = 12.4 x kg/ m. s
s
At 50 "C : v = 4.28 x m2/
{ Pr = 143
At 100 "C : /.I = 9.3 x kg/ rn. s