.4.5 DEFINITION OF THE MASs TRANSFER COEFFICIENT Solution of mass transfer probl
ID: 1027612 • Letter: #
Question
.4.5 DEFINITION OF THE MASs TRANSFER COEFFICIENT Solution of mass transfer problems is oftentimes facilitated by defining the mass transfer coeffi cient, k. The mass transfer coefficient can be thought of as the proportionality constant that relates the molar flux of the solute U) to the overall concentration driving force, i.e., j,-kh Crm The mass transfer coefficient is often given in terms of the dimensionless group, known as the Sherwood number (Sh). The Sherwood number is the convection to that by diffusion and is defined as Sh kmUD, where L is a characteristic length. For example, for convective mass transfer within a cylindrical tube, the characteristic length is the tube diameter. ratio of the transport rate of the solute by We can write, in general, Equation 5.13, which defines the mass transfer coefficient in terms of the flux of solute at the surface of an object, using Fick's first law: ac High Low (5.13) For the problem just considered in Figure 5.1. CHigh-C, and C1-0. Comparing Equation 5.13 with Equation 5.10, we see that the mass transfer coefficient is then given by (5.14) From Equation 5.14, we also see that the mass transfer coefficient is directly proportional to the .ky solute diffusivity and inversely proportional to the concentration boundary layer thickness, ie., D/8c. For the unsteady diffusion problem shown in Figure 5.1, the mass transfer coefficient, however is not constan t, but decreases as the concentration boundary layer thickness increases over timeExplanation / Answer
Fick's law says, flux of any property is directly proportional to its concentration gradient. For e.g. flux of mass,m, is proportional to dm/dx. Here proportionality constant D comes in to game with negative symbol implying initial value of property is decreasing.
This D is given by
jm = -D dm/dx
D = lambda2 / 2tau
where lambda is mean free path and tau is collision time.
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