Problems 629
18.8. As explained in earlier chapters, fins, or extended sur-
faces, commonly are used in a variety of engineering
applications to enhance cooling. Common examples
include a motorcycle engine head, a lawn mower
engine head, heat sinks used in electronic equipment,
and finned tube heat exchangers in room heating and
cooling applications. For long fins, the temperature dis-
tribution along the fin is given by:where
hheat transfer coefficient (W/m
(^2) #
K)
pperimeter of the fin 2(ab) ( m)
Across-sectional area of the fin (a*b) ( m
2
)
kthermal conductivity of the fin material
(W/m #K)
m
B
hp
kA
TTambient 1 TbaseTambient 2 e
mx
18.9. Use the graphical method discussed in this chapter to
obtain the solution to the following set of linear of
equations.
18.10. Use the graphical method discussed in this chapter to
obtain the solution to the following set of linear of
equations.
18.11. Without using your calculator, answer the following
question. If 6
4
is approximately equal to 1300, then
what is the approximate value of 6
8
?
18.12. Without using your calculator, answer the following
questions. If log 8 0.9, then what are the values of
log 64, log 80, log 8000, and log 6400?
18.13. Plot the functions,yx,y 10
x
, andylogx. Vary
thexvalue from 1 to 3. Is the functionylogxa
mirror image ofy 10
x
with respect toyx, and if
so, why? Explain.
18.14. Using a sound meter, the following measurements were
made for the following sources: Rock band at a concert
(100 10
6
mPa), a Jack hammer (2 10
6
mPa), and a
whisper (2000 mPa). Convert these readings to dB values.
18.15. A jet plane taking off creates a noise with a magnitude
of approximately 125 dB. What is the magnitude of
the pressure disturbance (in mPa)?
18.16. Identify the size and the type of the given matrices.
Denote whether the matrix is a square, a column,
a diagonal, a row, or a unit (identity).
a. b. c.
d. e. £
100
010
001
31 yy §
2
y
3
4
c
40
08
≥ d
x
x
2
x
3
x
4
£ ¥
320
245
056
§
x 1 x 2 10
2 x 1 3 x 2 5
4 xy 1
x 3 y 14
x
a
b
Base
Problem 18.8
What are the dependent and independent variables?
Next, consider aluminum fins of a rectangular pro-
file shown in the accompanying figure, which are used
to remove heat from a surface whose temperature is
100 C. The temperature of the ambient air is 20 C.
Plot the temperature distribution along the fin using
the following data:k 180 W/m # K, h
15 W/m
(^2) #
K,a0.05 m, andb0.015 m. Varyx
from zero to 0.015 m. What is the temperature of the
tip of the fin? Plot the temperature of the tip as a func-
tion ofk. Vary thekvalue from 180 to 350 W/m #K.
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