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Unformatted text preview: ME 114 Homework Set 4 Fall 2008 S hown have; The fin array ofProbiem‘STl‘Heis commonly found
in compact heat exchangers, whose function is to
provide a large surface area per unit volume in
transferring heat from one ﬂuid to another. In such
applications, it is desirable to minimize the thermal
resistance Rh 0 of the ﬁn array. Consider a unit heat
exchanger core that is 1 m long in the direction of
air flow and l m wide in a direction normal to both
the air ﬂow and the fin surfaces. The length of the
fin passages between adjoining parallel plates is
L = 8 mm. while the fin thermal conductivity and
convection coefficient are k = 200 W/m ' K (alu
minum) and h = 150 W/rn2  K, respectively. If the fin thickness and pitch are‘t = 1 mm and
S = 4 mm, respectively, what is the value of
RM? Hint: There is a We of '
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Caﬂcitil‘am 51+ at [ME 0‘! Slams/mtﬁ‘jr A as Steel balls 12 mm in diameter are annealed by
heating to 1150 K and then slowly cooling to 400
K in an air environment for which T3, = 325 K and
h = 20 W/m2  K. Assuming the properties of the
steel to be k = 40 W/m  K. p = 7800 kg/m3, and
c = 600 J/kg ' K, estimate the time required for the cooling process. Mtg 6+ V21 (1 {Gigi/1‘ . After a long, hard week on the books, you and your
friend are ready to relax. You take a steak 50 mm
thick from the freezer. How long do you have to let
the good times roll before the steak has thawed?
Assume that the steak is initially at —6°C, that it
thaws when the midplane temperature reaches 4°C,
and that the room temperature is 23°C with a con
vection heat transfer coefficient of 10 W/m2  K.
Treat the steak as a slab having the properties of
liquid water at 0°C. Neglect the heat of fusion as
sociated with the melting phase change. Assam/16 Convection CM be?“ Due October 2 et'clgg‘ ' Cylindrical steel rods (A131 1010). 50 mm in diam eter, are heat treated by drawing them through an
oven 5 m long in which air is maintained at 750°C.
The rods enter at 50°C and achieve a centerline .
temperature of 600°C before leaving. For a con
vection coefficient of 125 W/m2  K, estimate the
speed at which the rods must be drawn through the oven. A row of 3—ftlong and Lin—diameter used uranium D.
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each other w1th a centertocenter distance of 8 in at a 15 ft from the ground surface at a location where
tribunal conductivityof the soil is 0.6 Btu/h  ft  °F. If the
“Ge temperature of the rods and the ground are 350“F and spectively, determine the rate of heat transfer from the
_'OdS to the atmosphere through the soil. The soil temperature in the upper layers of the earth
varies with the variations in the atmospheric conditions. Before
a cold front moves in, the earth at a location is initially at a uni
form temperature of 10°C. Then the area is subjected to a tem
perature of  10°C and high winds that resulted in a convection
heat transfer coefﬁcient of 40 W/m2 ‘ °C on the earth’s surface
for a period of 10 h. Taking the properties of the soil at that lo
cation to be k = 0.9 W/m  °C and a = 1.6 X 10'5 mils, deter
mine the soil temperature at distances 0, 10, 20, and 50 cm
from the earth’s surface at the end of this 10h period. Winds,
~10°C ...
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 Rhee,Jinny

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