Page 651 - Bird R.B. Transport phenomena

§20.2 Steady-State Transport in Binary Boundary Layers 631

The molecular fluxes of momentum, energy, and mass at the wall are then given by the
dimensionless expressions

/ ° ^ = П'(0,1, K)l-^- (20.2-45)

П Ч Р Г Ю
° ' ' ' ' (20.2-46)
(T -T ) P r V 2v ~ x
c\'O * x/
JAO n'(0,Sc,lO V
- <o ) SC \j2v x (20.2-47)
AK x
with the tabulated values of П'(0, Л, К). Thus the fluxes can be computed directly when К
is known. These expressions are obtained from the flux expressions of Newton, Fourier,
and Fick, and the profiles as given in Eq. 20.2-43. The energy flux q 0 here corresponds to
the conduction term -kVT of Eq. 19.3-3; the diffusive flux j A 0 is obtained by using Eq. 20.2-47
above.
The fluid properties p, /x, C , p k, and 4t AB have been treated as constants in this develop-
ment. However, Eqs. 20.2-45 to 47 have been found to agree closely with the corresponding
variable-property calculations, " provided that К is generalized as follows,
8 10

and that p, /л, C pf k, and ЯЬ are evaluated at the "reference conditions'' T f = \(T 0 + T ) and
АВ
x
a>A( = ] I(<*>AO + Ч400).
In many situations, one of the following dimensionless quantities
V
{ПА
R. = ° + "f - ~ 0 ) (20.2-49)
Ho
(n + n )(a> - o) J (<o - o) J(n + n )
A0 m A0 A A0 A A0 B0
: ~ (zU.z-Ы;
JAO "AO ~ ^
is known or readily computed. These flux ratios, R, are independent of x under the present
boundary conditions and are related to Л and К as follows,
- тщ!ю -
R (202 52)

according to Eqs. 20.2-45 to 51. From Eq. 20.2-52 we see that the dimensionless interfacial
mass flux К can be tabulated as a function of R and Л, by use of the results in Table 20.2-1.
Then К can be found by interpolation if the numerical values of R and Л are given for one of
the three profiles (i.e., if we can specify R , v or R T and Pr, or R and Sc.) Convenient plots of
M
these relations are given in Figures 22.8-6 and 7.
As a simple illustration, suppose that the flat plate is porous and is saturated with liquid
A, which vaporizes into a gaseous stream of A and B. Suppose also that gas В is noncondens-
able and insoluble in liquid A, and that <о and а> are given. Then R can be calculated from
А0 Аж lo

For calculations of momentum and energy transfer in gas flows with К = 0, see E. R. G. Eckert,
s
Trans. A.S.M.E., 78,1273-1283 (1956).
9 For calculations of momentum and mass transfer in binary and multicomponent gas mixtures, see
W. E. Stewart and R. Prober, bid. Eng. Chem. Fundamentals, 3, 224-235 (1964); improved reference
conditions are provided by Т. С Young and W. E. Stewart, ibid., 25, 276-482 (1986), as noted in §22.9.
in For other methods of applying Eq. 20.2-47 to variable-property fluids, see О. Т. Hanna, AIChE
Journal, 8, 278-279 (1962); 11, 706-712 (1965).