Final-2012.pdf - SECTION: NAME: CBE 320 Transport Phenomena...

SECTION: NAME:
CBE 320 May 15, 2012
Transport Phenomena Final Exam
Part A: Short Answer
1. (5 pts.) What are the dimensions of the following quantities?
a. J
star
A
b. N
A
c. D
AB
d. k
x
(mass transfer coefficient)
e. c
A
2. (5 pts.) A magnetohydrodynamic pump can drive a fluid by exerting a body force K ∇ H
2
([=] force/volume)
on the fluid, where K is a material parameter, and H is the magnetic field strength. Assuming the fluid is
incompressible and Newtonian with constant ρ and μ , write down the equation of motion for this situation in
differential form. Recall that the Navier-Stokes equation is
ρ
D v
Dt
= -∇ p + μ ∇
2
v + ρ g
1

3. (5 pts.) In a certain problem, the diffusivity is related to the mass transfer rate by
D
AB
=
N
Az
|
z = z
1
RT Δ z
p ln( p
B 2
/p
B 1
)
Calculate D
AB
in units of m
2
/s for the following parameter values: N
Az
|
z = z
1
= 7 . 26 × 10
- 9
g-mole/cm
2
· s,
R = 8 . 31451 J/mole · K, T = 273 K, Δ z = 17 . 1 cm, p = 755 mm Hg, p
B 2
= 755 mm Hg, and p
B 1
=
722 mm Hg. The following information may be useful:
1 m = 100 cm
760 mm Hg = 1 atm
1 atm = 101 . 325 kPa
1 Pa = 1 N/m
2
1 J = 1 N · m
1 mole = 1 g-mole
4. (5 pts.) Write down the Stefan-Boltzmann law. Define each quantity and give their SI (i.e., MKSA) units.
2

5. (5 pts.) Gas A dissolves in a beaker of stagnant liquid B , and reacts with B to form C ( R
A
= - k
primeprimeprime
1
c
A
). Sketch
plots of c
A
as a function of z for both small and large k
primeprimeprime
1
. Here, z is the distance below the liquid/gas interface.
6. (5 pts.) A material ( A ) is diffusing (no convection) into a porous cylinder (radius R , length L ) from a flowing
fluid ( B ). The concentration of species A within the fluid is c
A
( r, θ, z, t ) , and the diffusivity within the fluid
is D
AB
. Using this information, write an integral expression for the total rate of transport of species A from
the fluid into the cylinder (moles A /time). You may assume that A is dilute so that the total concentration is
constant, and that transport at the cylinder ends may be neglected.
3