HomeworkSolutions_C14

HomeworkSolutions_C14 - Homework Set # 14: Unsteady-state...

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Homework Set # 14: Unsteady-state transfer of species Problem #1: Recall the example of the unsteady state evaporation of component A contained in a test tube in the lecture note (or see Example 20.1-1, 2 nd edition). Extend this example to account for interphase transfer of both species A and B. Show how to obtain Eqs. 20.1-23 to -25. Answer: Equations 20.1.1,2 and 3 are still valid if both species are crossing the interface. In Eq. 20.1-3 we now eliminate c by using Eq. (D) of Table 17.8-2 (evaluated at the interface) to get () ( ) 00 * 0 0 0 1 11 Az Bz AA z zz Az A Az Bz A NN r xx u Nx z x r z = = ++ ∂∂ == −+ + When (or the ratio r = goes to zero), this equation simplifies to Eq 20.1-4. 0 0 Bz N = 0 0 / Az Bz N N Equation 20.1-5 is then replaced by ( ) 2 2 0 0 1 A AB z A r A x D tx r = ⎛⎞ + −= ⎜⎟ ∂− + ⎝⎠ x z We now introduce the dimensionless variables Π (defined in Eq. 20.1-23) and Z (defined just below Eq. 20.1-8); note that when ( ) 0, 1 A x X = Π=− . Then the combination of variables method gives (cf. 20.1-9) the ordinary differential equation.
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This note was uploaded on 09/01/2011 for the course PGE 312 taught by Professor Peters during the Fall '08 term at University of Texas.

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HomeworkSolutions_C14 - Homework Set # 14: Unsteady-state...

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