Homework 1 – due Friday, 8/27
1. In class 1, we discussed a spherical, stainless steel (AISI 302) canister that was used to store reacting
chemicals that provide for a uniform heat flux,
q”
, to its inner surface. If the canister is suddenly
submerged in a liquid bath of temperature
T
∞
< T
i,
where
T
i
is the initial temperature of the canister
wall. Assume negligible temperature gradients in the canister wall.
Values:
T
∞
= 350 K
T
i
= 500 K
h
= 500
r
o
= 0.4 m
r
i
= 0.3 m
a) develop an equation for the variation of the wall temperature with time. What is the initial rate
of change of the wall temperature if
q
” = 10
5
W/m
2
?
b) what is the steadystate temperature of the wall?
c) Compute and plot the steadystate temperature as a function of
h
for the range 100 <
h
<
10,000 W/m
2
K. Is there a value of
h
below which operation would be unacceptable?
Hint: remember which processes are volumetric and which involve surface area.
a)
(
)
(
)
(
)
dt
dT
c
r
r
T
T
r
h
r
q
p
i
o
o
i
3
3
2
2
1
3
4
)
(
4
4
"
−
=
−
−
∞
π
ρ
π
π
(
)
(
)
(
)
dt
dT
c
r
r
T
T
r
h
r
q
p
i
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 '10
 FALCONER,J
 Thermodynamics, 8 cm, 90 %, 20 cm, 65 W, negligible temperature gradients

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