HomeworkSolutions_C14

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

This preview shows pages 1–2. Sign up to view the full content.

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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online