CHE 378: Heat and Mass Transfer Spring 2008 Homework 6 Due: Friday, February 22, 2008 at the beginning of lecture
1. Middleman 2.1 2. Middleman 2.11 Clarification: The units of K given in the problem
CHE 378: Heat and Mass Transfer Spring 2008 Homework 7 Due: Friday, February 29, 2008 at the beginning of lecture
1. Middleman 2.23 2. Middleman 3.28 3. Middleman 3.35 4. Middleman 3.36 5. Middleman 3
CHE 378: Heat and Mass Transfer Spring 2008 Homework 11 Due: Friday, April 18, 2008 at the beginning of lecture
1. Middleman 6.54 2. In a textbook on unit operations, the following statement was made:
CHE 378: Heat and Mass Transfer Spring 2008 Homework 2 Due: Friday, January 25, 2008 at the beginning of lecture
1. A spherical shell with inner radius r1 and outer radius r2 has surface temperatures
CHE 378: Heat and Mass Transfer Spring 2008 Homework 1 Due: Friday, January 18, 2008 at the beginning of lecture
1. An aluminum pan whose thermal conductivity is 237 W/(m*C) has a flat bottom with dia
CHE 378: Heat and Mass Transfer Spring 2008 Homework 4 Due: Friday, February 8, 2008 at the beginning of lecture
1. A rear window defroster in an automobile consists of uniformly distributed highresis
One-Dimensional Transient Heat Conduction
(bounded solids)
planar slab
A n cos n exp n2 X Fo
An
n 1
x/L
4sin n
2 n sin 2 n
T Ta
To Ta
n tan n Bi
Bi
X Fo t / L
2
hL
k
Jn x
cylinder
A n J o n exp
The time that a given slice of the film is in contact with the
soluble wall, or the contact time tc, is well-described by
A) L/<vx>
C) L2/DAB
B) L2/
D) (L/g)1/2
tc
L
vx
The time that component A take
Mechanisms of Heat Transfer
Thermodynamics allows us to determine the internal energy change and net
heat transferred for a given process, or the steady-state net rate of heat transfer.
Additional inf
Steady-State Heat Conduction With Internal Energy Generation
one-dimensional
In various cases, heat conduction occurs in a medium within which internal energy is also generated
by some process. Exampl
Diffusion of Naphthalene in a Narrow Tube (Ex. 2.1.1)
L
solid A
xA1
z=0
z
A
cross-sectional area S
B
stream of A,B (ideal gas)
xA2 < xA1
constant T,P
B: nitrogen
(insoluble in A)
A: naphthalene
There
Mass Transfer Controlled by External Diffusion and Convection
R
v
kc
cA,surf
cA,
free stream velocity
pure liquid or solid sphere of A
with given vapor pressure
As the liquid/solid evaporates, A will
Two tanks of equal volumes are kept at the same T and P, one filled with just N 2
(gas) and the other filled with just CO2 (gas). At some point, the line connecting
the two tanks is opened, and both s
Sustained Release Hollow Fiber System (2.3 M)
cA,out 0
Rout
gas mixture A,B
rapidly moving stream with no A
CA,in
Rin
A represents some active chemical agent (e.g., insecticide) that has
been encapsul
Fundamentals of Mass Transfer
Mass transfer: the transport or movement of matter from one location to another
(the material of interest is described by a net velocity)
one of several key differences w
Consider the laminar boundary layer that develops over a flat plate
free stream
v
vx
v = 0.99v
x: v < v
velocity boundary layer
y
v
x
The velocity profile is described by
the following set of equation
At this time, T To beyond this distance,
and so the system has not yet sensed
the presence of a heat flux at the surface.
To
t1
T
Lets consider the T response of a
semi-infinite medium (with Bi > 1).
Diffusion Across a Thin Barrier Separating Two Fluids
steady-state, one-dimensional, dilute limit
L
well-mixed fluid mixture with
species A of small concentration
well-mixed fluid mixture with
species
Diffusion with a Homogeneous Chemical Reaction
(steady-state, one-dimensional)
gas A
(well-mixed)
pA or cA,g
z=0
z
z
z + z
liquid B
Gas A with constant pressure (or concentration) dissolves in liquid
cylinder
dV 2rdr 2R 2 d
1
d
0
1
d
T
1
TdV
dV
2 d
0
0
1 A1J o 1 exp 12 X Fo
sphere
dV 4r 2dr 4R 3 2d
2A1
long time
Q tot VC P T To
1
d
VC P To Ta 1
2
BiJ o 1
2
exp
X Fo
1
2
1
0
1
2
d
1
3
Transient Heat Transfer by Conduction
For a non-steady-state process, the temperature in a conducting material will, in general, be
a function of position and time. Due to the objects finite thermal c
In many situations, we are less interested in the concentration at a particular location
within the object, and more interested in the amount of material that has been added
or removed at a given time
Diffusion with Reaction at a Boundary
glass
gel
corrosive solution (well-mixed)
co
surface reaction
occurs on the
glass/gel interface
(1st order kinetics)
Z(t)
z=0
Reactant diffuses through gel and ir
Diffusion and Reaction Inside a Sphere
rapid stream moving past
sphere with cA
(steady-state, one-dimensional)
No convective mass transfer limitations near interface : kc .
R
Inside sphere, A is consu
PURDUE UNIVERSITY
SCHOOL OF CHEMICAL ENGINEERING
CHE37800: Heat and Mass Transfer
Spring 2015
Problem set #7
Due: 3/11/15
[1] Consider Example 2.1.4 in Middleman. Assume that even though the system is
PURDUE UNIVERSITY
SCHOOL OF CHEMICAL ENGINEERING
CHE37800: Heat and Mass Transfer
Spring 2015
Problem set #10
Due: 4/15/15
[1] Problem 6.4 (M) (See Appendix C for estimates of the properties of the ai
PURDUE UNIVERSITY
SCHOOL OF CHEMICAL ENGINEERING
CHE 37800: Heat and Mass Transfer
Spring 2015
Problem set #5
Due: 2/18/15
[1] Problem 11.14 (M)
[2] Problem 11.15 (M)
[3] Problem 11.25 (M)
[4] Problem
PURDUE UNIVERSITY
SCHOOL OF CHEMICAL ENGINEERING
CHE 37800: Heat and Mass Transfer
Spring 2015
Problem set #3
Due: 2/04/15
[1] Integrated circuits (IC) are encapsulated in a rectangular case made of c
PURDUE UNIVERSITY
SCHOOL OF CHEMICAL ENGINEERING
CHE 37800: Heat and Mass Transfer
Spring 2015
Problem set #1
Due: 1/21/15
o
[1] You are provided with an uncovered pot that contains 0.50 kg of water a