Page 109 - Modelling in Transport Phenomena A Conceptual Approach

4.4. FLOW NORMAL TO A SINGLE CYLINDER 89

4.4.2 Heat Xkansfer Correlations

As stated in Section 4.3.2, the analytical solution for steady-state conduction from
a sphere to a stagnant medium gives Nu = 2. Therefore, the correlations for
heat transfer in spherical geometry require that Nu + 2 as Re -+ 0. In the case
of a single cylinder, however, no solution for the case of steady-state conduction
exists. Hence, it is required that Nu + 0 as Re -+ 0. The following heat transfer
correlations are available in this case:

Whitaker correlation

Whitaker (1972) proposed a correlation in the form

I NU = (0.4 Re2 + 0.06 Rey ) (p,/pw)1’4 1 (4.46)

in which all properties except p,,, are evaluated at T,. Equation (4.46) is valid
for
1.0 5 Reo _< 1.0 X lo5
0.67 5 Pr 5 300
0.25 5 p,/p, 5 5.2

Zhukauskas correlation

The correlation proposed by Zhukauskas (1972) is given by
I NU = C Reg Pr” (Pr, / Pr,)lI4 I (4.47)

where
n= { 0.37 if Pr 5 10
0.36 if Pr > 0
and the values oA C and m axe given in Table 4.3. All properties except Pr, shou 1
be evaluated at T, in Eq. (4.47).

Table 4.3 Constants of Eq. (4.47) for the circular cylinder in cross flow.

ReD C m
1 - 40 0.75 0.4
40 - 1000 0.51 0.5
1 x 103 - 2 x 105 0.26 0.6
2 x lo5 - 1 x lo6 0.076 0.7