By Hill Jr C.G.
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Extra info for An introduction to chemical engineering kinetics & reactor design
In case of simultaneous mass and heat transfer processes, for example when cooling of flue gases containing water vapours for utilization of their heat, or in case of packed bed cooling towers, the piston flow model can be written as follows: The basic equation of mass transfer (evaporation and condensation): Ghdxh /dh = Kcae (CG -CG*); The basic equation of heat fransfer: (170) 55 w0. pa. cp(dta/h) = Kae (tG -1^ ; (171) Balance of the heat transfer through the interfacial area: L. a0 (tG - fJ + r & (dxt/dh) ; (172) Material balance through the interfacial area: (173) where Wg and the concentration of the evaporated or condensed component are given by: w0 ^(hO+xJ/po, xJ.
1. Molecular diffusion at interface The first step in calculating the mass of the transferred substances G per unit of time, using equation (132), (133), (136) and (137), is to obtain the partial mass transfer coefficients ki and fe. There are two possibilities to transfer the substances from the bulk of the fluid to the interface, diffusion and convective mass transfer. Independently of the convection effect the great diffusion effect on the mass transfer processes always exists. According to the first Fick's law of diffusion the molar diffusion flux NA (mol/m2s) of the component A in a two-component system (A and B) is proportional to the concentration gradient of this component dCu/dx .
149) at the boundary conditions (150) to (153) the following equation is obtained: (154) where G is the mass of the transferred substance per unit of interfece in mol/m2, or kg An2 and F- the mass transfer area in m2. From Eq. (150) it is easy to see that with increasing of time the mass transfer rate decreases. The average mass flux N^av can be obtained by integration of Eq. (154) taking into account the distribution of the elements by time of exposure. (155) Hereupon, the partial mass transfer coefficient for the liquid phase can be obtained as: (156) where/is a function depending on the distribution of the contact time.