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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