Homework 5
1. (15 pts) In Class 9 we looked at an infinite cylinder with a convection coefficient h = 1000 W/m
2
K.
Let’s say the centerline temperature must be increased from T
i
= 300 K to T = 750 K. Plot the centerline
temperature distribution vs. time for
h
= 100, 500 and 1000 W/m
2
K. In each case, stop the calculation
when
T
= 500 K. (10 pts) How long does it take to reach a centerline temperature of 500 K for each
convection coefficient.(3 pts) Can any of these be treated as lumped capacitance?
θ*
o
= T(0,t)  T
∞
/T
i
 T
∞
= C
1
exp(ζ
1
2
*Fo)
T = C
1
exp(ζ
1
2
*Fo)( T
i
 T
∞
) + T
∞
With h = 100, it can be treated as lumped capacitance.
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2. (20 pts) One way to determine thermal conductivity of a solid is to embed a thermocouple in a thick
slab and measuring the response to a change in temperature. Consider a material with a density of 950 kg/
m3 and a
c
= 1100 J/kgK. The material is heated to a uniform temperature of 100
o
C and the cooled by
passing air at 25
o
C over one surface.
If a thermocouple is embedded a distance of 10 mm below the
surface,
the
h
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 Fall '10
 DEGRAZIA
 Heat, Heat Transfer, pts, TI, thermal boundary layer

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