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Tham khảo tài liệu 'a heat transfer textbook - third edition episode 3 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 11.6 Mass transfer at low rates 639 Figure 11.13 Mass diffusion into a semi-infinite stationary medium. with mi mift for t 0 all x mi miu for x 0 t 0 mi - mit0 for x o t 0 This math problem is identical to that for transient heat conduction into a semi-infinite region Section 5.6 and its solution is completely analogous to eqn. 5.50 mi - mi u mi 0 - mi u The reader can solve all sorts of unsteady mass diffusion problems by direct analogy to the methods of Chapters 4 and 5 when the concentration of the diffusing species is low. At higher concentrations of the diffusing species however counterdiffusion velocities can be induced as in Example 11.8. Counterdiffusion maybe significant in concentrated metallic alloys as for example during annealing of a butt-welded junction between two dissimilar metals. In those situations eqn. 11.72 is sometimes modified to use a concentration-dependent spatially varying interdiffusion coefficient see 11.6 . 640 An introduction to mass transfer 11.6 Figure 11.14 Concentration boundary layer on a flat plate. Convective mass transfer at low rates Convective mass transfer is analogous to convective heat transfer when two conditions apply 1. The mass flux normal to the surface nis must be essentially equal to the diffusional mass flux ji s from the surface. In general this requires that the concentration of the diffusing species mi be low.9 2. The diffusional mass flux must be low enough that it does not affect the imposed velocity field. The first condition ensures that mass flow from the wall is diffusional as is the heat flow in a convective heat transfer problem. The second condition ensures that the flow field will be the same as for the heat transfer problem. As a concrete example consider a laminar flat-plate boundary layer in which species i is transferred from the wall to the free stream as shown in Fig. 11.14. Free stream values at the edge of the b.l. are labeled with the subscript e and values at the wall the s-surface are .
