Page 432 - Bird R.B. Transport phenomena

414 Chapter 13 Temperature Distributions in Turbulent Flow

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A Deissler & Eian (1952) Pr = 0.73
* Allen & Eckert (1964) Pr = 8.0
и Malina & Sparrow (1964) 3 < Pr < 75
« J A Friend & Metzner (1958) 55 < Pr < 590
о Harriott & Hamilton (1965) 452 < Sc < 97,600

3x10 -5
3 x 10" 5

Fig. 13.4-2. Comparison of the expression in Eq. 13.4-20 for the wall heat flux in fully developed turbulent
flow with the experimental data of R. G. Deissler and С S. Eian, NACA Tech. Note #2629 (1952); R. W. Allen
and E. R. G. Eckert, J. Heat Transfer, Trans. ASME, Ser. C, 86,301-310 (1964); J. A. Malina and E. M. Sparrow,
Chem. Eng. Sci, 19,953-962 (1964); W. L. Friend and A. B. Metzner, AIChE Journal 4,393-402 (1958); P. Har-
riott and R. M. Hamilton, Chem. Eng. Sci., 20,1073-1078 (1965). The data of Harriott and Hamilton are for the
analogous mass transfer experiment, for which Eq. 13.4-20 also applies.

Extensive calculations based on Eq. 13.4-19 were performed by Sandall, Hanna, and
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Mazet. These authors took the turbulent Prandtl number to be unity. They divided the
region of integration into two parts, one near the wall and the other for the turbulent
core. In the "wall region" they used the modified van Driest equation of Eq. 5.4-7 for the
mixing length, and in the "core region" they used a logarithmic velocity distribution.
Their final result 3 is given as
q D Re PrVf/2
0 (13.4-20)
k(T 0 - T ) 12.48 Pr 2/ 3 - 7.853 Pr 1/ 3 + 3.613 In Pr + 5.8 + 2.78 In Qg
b
In obtaining this result, Eq. 6.1-4a has been used.
Equation 13.4-20 agrees with the available data on heat transfer (and mass transfer)
within 3.6 and 8.1% over the range 0.73 < Pr < 590, depending on the sets of data stud-
ied. The analogous mass transfer expression, containing Sc = ii/p% AB instead of Pr, was
reported 3 to agree with the mass transfer data within 8% over the range 452 < Sc <
97600. The agreement of the theory with the heat transfer and mass transfer data, shown
in Fig. 13.4-2, is quite convincing.

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О. С Sandall, O. T. Hanna, and P. R. Mazet, Canad. J. Chem. Eng., 58,443-447 (1980). See also О. Т.
Hanna and О. С Sandall, AIChE journal, 18, 527-533 (1972).