Thermal & Fluids Engineering I. Spring 2006.
Homework #3 Solution.
WebCT post date: 02/09/2006
31
An arctic explorer builds a temporary shelter from windpack snow.
The shelter is roughly
hemispherical with an inside radius of 1.5 meters. After completing the shelter, the explorer crawls
inside and closes off the entrance with a block of snow.
Assume the shelter is now air tight and
loses negligible heat by conduction through the walls.
If the air temperature when the explorer
completes the shelter is 10
o
C, how long will it take before the air temperature inside reaches
10
o
C?
Assume the explorer does not freeze to death or suffocate, but sits patiently waiting for the
temperature to rise.
The explorer generates body heat at a rate of 300 kJ/h.
Approach:
Use the first law to find the change in temperature.
Assumptions:
1. The air behaves like an ideal gas under these
conditions.
2. The shelter is perfectly insulated and airtight.
3. The specific heat of the air is constant.
Solution:
Let the system be the air inside the shelter.
From the first law
v
Q
U
mc
T
= Δ
=
Δ
The mass of air can be determined from the ideal gas law
( )
( )
( )
( )( )
3
3
1
4
101kPa
π 1.5 m
28.97kg kmol
2
3
9.46kg
8.314kJ kmol K
10 + 273 K
PVM
m
RT
=
=
=
⋅

The only heat added to the air is body heat. The walls are assumed to be thick and highly insulating. The
rate of heat transfer is related to the total heat transferred by
v
Q
Q t
mc
T
=
Δ =
Δ
d
Solving for elapsed time
( )
( )
( ) ( )
( )
2
1
9.46kg
0.717kJ kg K 10
10 K
300kJ h
v
mc T
T
t
Q
t

Δ =
⋅
 
Δ =
d
where
c
v
may be found in Table A8. Evaluating
0.45h
27min
t
Δ =
=
Answer
Comments:
In actuality, there must be some air entering and leaving the shelter or the explorer would be unable to
breathe; therefore, the rise in temperature may not be as rapid as calculated.
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Page 2
311
On a cold winter day, the interior walls of a room are at 55
o
F.
A man standing in the room loses
heat to the walls by thermal radiation.
The man’s surface area in 16 ft
2
, his clothing has an
emissivity of 0.93 and his surface temperature is 70
o
F.
He generates 300 Btu/h of body heat.
What percentage of the man’s body heat is transferred by radiation to the walls?
Approach:
Use
( )
4
4
s
surr
Q
A T
T
ε σ
=

d
to determine radiation heat transfer
from the man and compare this to his body heat.
Assumptions:
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 Spring '06
 Tascuic
 Heat, Heat Transfer, Tsurr, Fluids Engineering I., Engineering I. Spring

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