Final-2013.pdf - SECTION: NAME: CBE 320 Transport Phenomena...

SECTION: NAME:
CBE 320 December 16, 2013
Transport Phenomena Final Exam
Part A: Short Answer
1. (5 pts.) What are the SI units of the following:
a. N
A
b. j
A
c. D
AB
d. k
x
e. c
A
2. (5 pts.) Write down the Stefan-Boltzmann law for gray (nonblack) bodies. Define each quantity and
give their SI (i.e., MKSA) units.
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3. (10 pts.) Consider a non-isothermal flow problem for mixtures with length, velocity and temperature
scales lscript
0
, v
0
and T
1
- T
0
, respectively. Recall the following definitions of some basic dimensionless
groups:
Re =
lscript
0
v
0
ρ
μ
Pr =
ˆ
C
p
μ
k
Sc =
μ
ρ D
AB
Br =
μv 2
0
k ( T
1
- T
0
)
Gr =
gβ ( T
1
- T
0
) lscript 3
0
ν
2
Gr
ω
=
gζ ( ω
A 1
- ω
A 0
) lscript 3
0
ν
2
Express each of the following dimensionless groups as a ratio of forces or phenomena (e.g., Re =
inertial forces / viscous forces).
a. ReSc
b. RePr
c. Gr
ω
/ Re 2
d. Br
e. GrPr
2

4. (5 pts.) Forced-convection energy transport from a sphere is described the following correlation for
the mean Nusselt number:
Nu
m
= 2 + 0 . 6 Re
1 / 2
Pr
1 / 3
.
What is the appropriate correlation for the dimensionless mean mass transfer coefficient for forced-
convection mass transfer from a sphere?
5. (5 pts.) A mass balance for species A in a mixture is written below.
ρ
Dω
A
Dt
= ρ D
AB
∇
2
ω
A
+ r
A
.
Simplify this expression for a stagnant liquid mixture.
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6. (5 pts.) Fluid between two parallel disks (radius R ) is set in motion because the top disk is rotated at
angular velocity Ω . Write an integral expression for the torque exerted by the fluid on bottom disk in
terms of the appropriate stress tensor components.
7. (5 pts.) Explain in words (use expressions too if you wish) why k
x, loc
for mass transfer from a solid
sphere increases as the flow becomes more turbulent.
8. (5 pts.) Consider turbulent flow of an incompressible Newtonian fluid (density ρ , viscosity μ ) in a
circular tube (radius R , length L ). Provide the definition of the quantity ( v n
z
) in terms of integral(s)
over the appropriate quantities.
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