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Michigan State University
DEPARTMENT OF CHEMICAL ENGINEERING AND MATERIALS SCIENCE
CHE 210: Modeling and Analysis of Transport Phenomena
Fall 2007
Quiz 3: Solution
1. (20 pts.) Oxygen is stored in a spherical wellinsulated container surrounded by a thick
evacuated annular jacket filled with particulate insulation.
The radius of the container is
r
0
and
the outer radius of the insulation jacket is
r
1
.
The temperatures at
r
0
and
r
1
are
T
0
and
T
1
,
respectively, with
T
0
<
T
1
.
The thermal conductivity is constant
and, for the purposes of this
analysis, you may assume that the spherical container itself has negligible thickness.
a. (17 pts.)
Use a shell balance to derive the equation for the temperature distribution across the
insulation.
b. (3 pts.)
Derive an expression for the steadystate rate of heat transfer from the atmosphere to
the insulation
.
Solution
:
a.
The shell balance gives:
()
( )
22
44
0
rr
r
rq
ππ
+Δ
−
=
Dividing by
Δ
r
and taking the limit as
r
Æ
0, we get
2
11
0 0
0;
Boundary conditions:
at
;
at
r
d
r
q
TT rrTT rr
dr
==
=
=
=
We integrate this equation once to get:
rq C
q
r C
−
=⇒=
Noting that
q = – k(dT/dr)
, we get:
111
2
r
CCC
qd
T
d
r
T
C
rk
r
k
r
−
⇒
=
+
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This note was uploaded on 05/21/2008 for the course CHE 210 taught by Professor Robertofoli during the Fall '07 term at Michigan State University.
 Fall '07
 RobertOfoli
 Chemical Engineering, Materials Science, pH

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