finals18.pdf - SECTION: NAME: CBE 320 Transport Phenomena...

SECTION: NAME:
CBE 320 May 10, 2018
Transport Phenomena Final Exam
Part A: Short Answer
1. (5 pts.) What are the SI units of the following quantities?
a. n
A
b. J
⋆
A
c. ρ
A
d. D
AB
/ν
e. k
c
(mass transfer coefficient)
2. (5 pts.) Write the Stefan-Boltzmann law. Provide a definition for each term.
1

3. (5 pts.) Consider a pure fluid of A molecules at room temperature, in which the density does not vary with time
or position. Do the A molecules diffuse? Explain.
4. (5 pts.) The local Nusselt for forced convection along a flat plate can be expressed
Nu
loc
≡
h
loc
x
k
= 0 . 332 Re
1 / 2
x
Pr
1 / 3
where Re
x
= xv
∞
ρ/μ , with x the distance from the leading edge of the plate. What is the correlation for the
local Sherwood number, Sh
loc
≡ k
x, loc
x/c D
AB
?
5. (5 pts.) Data for | τ
yx
| as a function of | dv
x
/dy | for a Newtonian fluid in simple shear flow are given in the
figure below. Estimate the viscosity μ of this fluid.
| dv
x
/ dy | (1/s)
0 5 10 15 20
0.0
0.5
1.0
1.5
2.0
t
yx
(Pa)
v y
x
( )
2

6. (5 pts.) Gas A dissolves sparingly in stagnant liquid B in a beaker. As it diffuses, A undergoes an irreversible,
first-order homogeneous reaction, A + B → AB . The top of the liquid in the beaker is defined as z = 0 , the
bottom of the beaker is at z = L , and the cross-sectional of the beaker is S . Given the concentration profile
c
A
( z ) , and using the fact that there is no convection, write an expression for the net rate of consumption of A
in terms of the concentration profile.
7. (5 pts.) The mass transport of species A in a binary mixture of A and B can be written (for constant ρ , D
AB
,
and dilute in A )
Dc
A
Dt
= D
AB
∇
2
c
A
+ R
A
.
Simplify this expression for a stagnant liquid solution.
8. (5 pts.) A fluid flows past a post with rectangular cross-section ( 0 < x < a , 0 < y < b ). Write an integral for
the x component of the force exerted by the fluid on the top surface ( z = constant surface).
x
y
z
3

9. (5 pts.) A three-layer composite slab consists of a metal (material “01”) with thermal conductivity k
01
, a ceramic
(material “12”) with thermal conductivity k
12
, and another metal (material “23”) with thermal conductivity k
23
,
as illustrated in the figure below. The temperature at x
0
is T
0
, and the temperature at x
3
is T
3
( < T
0
) . The
relative magnitudes of the thermal conductivities are k
12
< k
01
< k
23
. On the diagram below, sketch the
steady-state temperature profile T ( x ) for x
0
< x < x
3
( T
0
and T
3
are already indicated on the diagram).
k
01
k
12
k
23
T
x
x
0
x
1
x
2
x
3
T
0
T
3
10. (5 pts.) The amount of money in your checking account depends on how much you deposit, how much you