Page 174 - Industrial Ventilation Design Guidebook
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1 36 CHAPTER 4 PHYSICAL FUNDAMENTALS
Boundary conditions for the dimensionless temperature are
From Eqs. (4.285)-(4.286) and (4.287)-(4.288),
Equation (4.289) is an approximation in the mass transfer case, as the bound-
ary conditions cannot always set w z(z = 0) = 0. For the case j A = -; B , we
nearly have w z(z — 0) = 0, and the analogy equation is based on this situa-
tion.
The dimensionless form of Eq. (4.281) is
where Sc = v/D' AB is the Schmidt number. We thus have
Boundary conditions for the dimensionless concentration are
Equation (4.287) is in exactly the same form as Eq. (4.290), and the boundary
conditions (4.288) and (4.291) are also similar.
If the solution to Eq. (4.289) is known, it is also valid for (4.290)-(4.291);
hence
The function F is then the same in Eqs. (4.289) and (4.292). This is not strictly
correct, however; see the comments after Eq. (4.289).
We can apply this result to determine the analogy between mass and heat
2
transfer factors. Mass flow density j A (mol/m s) can be given as
The mass transfer factor k' c is used because Eqs. (4.289) and (4.292) demand
the boundary condition w z(rj = 0) = 0, which represents the case j A — ~j E.
Strictly speaking, a new mass transfer factor should be defined that represents
the situation M Aj A = -M Bj B or w z = 0.
Using the dimensionless quantities Z A and 17, Eqs. (4.284c) and (4.284f),
Eq. (4.293) can be written as
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