Page 173 - Industrial Ventilation Design Guidebook
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•4.3 HEAT AND MASS TRANSFER I 3 5
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A U z ___——-
X
FIGURE 4.37 Boundary layer flow.
where u 0 is the velocity outside the boundary layer or formally, c As = C A(Z = 0);
c Ao is the concentration of component A outside the boundary layer,
T s = T(z = 0), and T 0 is the temperature outside the boundary layer. The dimen-
sion L is the characteristic length. All dimensionless variables range between 0 and 1..
For example, u x(x, z) = u 0w x(^(x), 17(2)). Using the chain rule,
Treating the other terms in a similar manner, the linear momentum equation
in a dimensionless form is obtained:
where Re = (u 0L)/v is the Reynolds number.
The dimensionless form of the continuity equation (4.278) (u y = 0) in
two-dimensional boundary layer flow is
- -3 — -1
For the two equations (4.285) and (4.286) and two unknown vari-
ables w x(^, TJ), w z(^,, 17), boundary conditions are 17 = 0; w x = 0, 17 = »=;
w x = 1, w z = 0. The boundary condition w z(rj — 0) is not given in a mass
transfer case, as it depends on the vaporization.
The dimensionless form of Eq. (4.282) is
where Pr = (/xCp)/A is the Prandtl number and /u, is the dynamic viscosity, giving
