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Unformatted text preview: PROBLEM 1.11
KNOWN: Dimensions and thermal conductivity of a chip. Power dissipated on one surface. FIND: Temperature drop across the chip. SCHEMATIC: ,k—mSLtbsfra re Chip, k=150W/M°K ASSUMPTIONS: (1) Steadystate conditions, (2) Constant properties, (3) Uniform heat
dissipation, (4) Negligible heat loss from back and sides, (5) Onedimensional conduction in
chip. ANALYSIS: All of the electrical power dissipated at the back surface of the chip is
transferred by conduction through the chip. Hence, from Fourier’s law, mm a
01'
AT: t~P2 : 0.001mx4w 2
kW 150 W/mK(0.005 m)
AT 3 1.1“ C. < COMMENTS: For ﬁxed P, the temperatme drop across the chip decreases with increasing k
and W, as well as with decreasing t. PROBLEM 1.23 KNOWN: Width, input p0wer and efﬁciency of a transmission. Temperature and convection
coefﬁcient associated with air ﬂow over the casing. FIND: Surface temperature of casing. SCHEMATIC:
a, = 30°C
h; = 200 W/mZK q
‘—"'l>
Po = “Pi
T ______,
P5150 “P w=o.3m ASSUMPTIONS: (I) Steady state, (2) Uniform convection coefﬁcient and surface temperatme, (3)
Negligible radiation. ANALYSIS: From Newton’s law of cooling,
q : 11As (Ts ‘11»): 6hW2 (Ts ‘10)
Where the output power is n P, and the heat rate is
q = 1"} “”Po = P; (1—17): lSthX746W /th0.07 = 7833 W Hence, q = 30°c+————7§§§W—W =102.5°C < 6 law2 6x200 W/mZKX(0.3m)2 Tssz+ COMMENTS: There will, in fact, be considerable variability of the local convection coefﬁcient
over the transmission case and the prescribed value represents an average over the surface. PROBLEM 1.44 KNOWN: Radial distribution of heat dissipation in a cylindrical container of radioactive
wastes. Surface convection conditions. q FIND: Total energy generation rate and surface temperature.
SCHEMATIC: ASSUMPTIONS: (l) Steady—state conditions, (2) Negligible temperature drop across thin
container wall. ANALYSIS: The rate of energy generation is  . _ I 2
Eg = Jqu=q0 00 [l—(r/ro) ]27rrLdr
Eg = 27:qu (r3 Iz—rg 14) or per unit length,  2
Efﬂqor‘). <
2 Performing an energy balance for a control surface about the container yields, at an instant, E’—E’ =0 g out and substituting for the convection heat rate per unit length, . 2
”gr" = h(27rr0)(TS 40°)
TS = Tm + q°r° ‘ < 4h COMMENTS: The temperature within the radioactive wastes increases with decreasing r from TS at r0 to a maximum value at the centerline. ...
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 Fall '08
 Rothamer
 Heat Transfer

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