Page 650 - Bird R.B. Transport phenomena

630 Chapter 20 Concentration Distributions with More Than One Independent Variable

r—— — — m • — , '
Mass transfer - = 2 — ^ <
out of stream /0.72 / л /^072 л =, / 2
/
77/ / > 0.72
0.8
7
K = 0
f
0.6 // / /ч J / transfer > "^ Mass transfer
о mass
//
/ /
0.4 I/ / // into strea m
0.2f // X /
Y. — —

0.8 1.6 2.4 3.2 4.0 4.8 5.6 6.4 7.2 8.0

Fig. 20.2-3. Velocity, temperature, and composition profiles in the laminar boundary layer on a
flat plate with mass transfer at the wall [H. S. Mickley, R. C. Ross, A. L. Squyers, and W. E. Stew-
art, NACA Technical Note 3208 (1954).]

The gradients of the velocity, temperature, and composition at the wall are obtainable
from the derivative of Eq. 20.2-43:
, Л, Ю 1
П'(0,Л,Ю = (20.2-44)
rj = O " expf-Л f*f(lj, K)dvjdr
o 1
Some values computed from this formula by numerical integration are then given in Table
20.2-1.

Table 20.2-1 Dimensionless Gradients of Velocity, Temperature, and Composition in Laminar Flow Along a Flat Plate"

К Л = 0.1 Л = 0.2 Л = 0.4 Л = 0.6 Л = 0.7 Л = 0.8 Л = 1.0 Л = 1.4 Л = 2.0 Л = 5.0
-3.0 0.4491 0.7681 1.3722 1.9648 2.2600 2.5550 3.1451 4.3273 6.1064 15.0567
-2.0 0.3664 0.5956 1.0114 1.4100 1.6070 1.8032 2.1945 2.9764 4.1524 10.0863
-1.0 0.2846 0.4282 0.6658 0.8799 0.9829 1.0842 1.2836 1.6754 2.2568 5.1747
-0.5 0.2427 0.3452 0.4999 0.6291 0.6890 0.7468 0.8579 1.0688 1.3707 2.8194
-0.2 0.2165 0.2948 0.4024 0.4849 0.5213 0.5555 0.6190 0.7333 0.8861 1.5346
0.0 0.1980 0.2604 0.3380 0.3917 0.4139 0.4340 0.4696 0.5281 0.5972 0.8156
0.2 0.1783 0.2246 0.2736 0.3011 0.3108 0.3187 0.3305 0.3439 0.3496 0.3015
0.5 0.1441 0.1657 0.1751 0.1701 0.1656 0.1603 0.1485 0.1240 0.09096 0.01467
0.75 0.1032 0.1023 0.0840 0.0638 0.0549 0.0471 0.0340 0.0172 0.00571 0.0000152
0.87574^ 0 0 0 0 0 0 0 0 0 0
" Taken from the following sources: E. Elzy and R. M. Sisson, Engineering Experiment Station Bulletin No. 40, Oregon State University,
Corvallis, Or. (1967); H. L. Evans, Int. }. Heat and Mass Transfer, 3, 321-339 (1961); W. E. Stewart and R. Prober, Int. ]. Heat and Mass
Transfer, 5,1149-1163 (1962) and 6, 872 (1963). More complete results, and reviews of earlier work, are given in these references.
'' The value К = 0.87574 is the largest positive mass transfer rate attainable in this geometry with steady laminar flow. See
H. W. Emmons and D. С Leigh, Interim Technical Report No. 9, Combustion Aerodynamics Laboratory, Harvard University (1953).