finalf17.pdf - SECTION: NAME: CBE 320 Introductory...

SECTION: NAME:
CBE 320 December 19, 2017
Introductory Transport Phenomena Final Exam
Part A: Short Answer
1. (5 pts.) Give the SI units for the following quantities:
a.
ν
D
AB
b. n
A
c. k
′′′
1
(i.e., in R
A
= − k
′′′
1
c
A
)
d. k ∇ T
e. h (heat transfer coefficient)
2. (5 pts.) Write the Planck distribution law. Provide a definition for each term.
1

3. (5 pts.) A mass balance for species A in a mixture is written in one form below. Label each term,
describing its physical significance.
∂ρ
A
∂t
= − ( ∇ · ρ
A
v ) − ( ∇ · j
A
) + r
A
.
4. (5 pts.) When an electric field is applied to a fluid containing ions, the ion species i experiences an
additional contribution to the molar flux given by E q
i
c
i
ω
i
( E is the electric field, q
i
is the charge on
species i , c
i
is the molar concentration of species i , and ω
i
is the mobility of species i ). Write down
an expression for the modified Fick’s Law, describing the total molar flux of species i relative to fixed
coordinates. Assume that everything else in the fluid constitutes species “ B ”.
2

5. (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.
6. (5 pts.) The mean Nusselt number for forced convection past a sphere is given by
Nu
m
=
h
m
D
k
= 2 + 0 . 60
parenleftBigg
Dv
∞
ρ
μ
parenrightBigg
1 / 2
parenleftBigg
hatwide
C
p
μ
k
parenrightBigg
1 / 3
. (1)