The Diamond Ring Solution. The processing chip on the computer that controls the navigation equipment on your spacecraft is overheating. Unless you fix the problem, the chip will be damaged and the navigation system will shut down. You open the panel and find that the small copper disk that was supposed to bridge the gap between the smooth top of the chip and the cooling plate is missing, leaving a 2.2 mm gap between them. In this configuration, the heat cannot escape the chip at the required rate. You notice by the thin smudge of thermal grease (a highly thermally conductive material used to promote good thermal contact between surfaces) that the missing copper disk was 2.2 mm thick and had a diameter of 1.3 cm. You know that the chip is designed to run below 75 °C, and the copper cooling plate is held at a constant 5.0 °C. (a) What was the rate of heat flow from the chip to the copper plate when the original copper disk was in place and the chip was at its maximum operating temperature? b) The only material that you have available

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Chapter8: Natural Convection
Section: Chapter Questions
Problem 8.26P
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The Diamond Ring Solution. The processing
chip on the computer that controls the
navigation equipment on your spacecraft is
overheating. Unless you fix the problem, the
chip will be damaged and the navigation
system will shut down. You open the panel
and find that the small copper disk that was
supposed to bridge the gap between the
smooth top of the chip and the cooling plate
is missing, leaving a 2.2 mm gap between
them. In this configuration, the heat cannot
escape the chip at the required rate. You
notice by the thin smudge of thermal grease
(a highly thermally conductive material used
to promote good thermal contact between
surfaces) that the missing copper disk was
2.2 mm thick and had a diameter of 1.3 cm.
You know that the chip is designed to run
below 75 °C, and the copper cooling plate is
held at a constant 5.0 °C.
(a) What was the rate of heat flow from the
chip to the copper plate when the original
copper disk was in place and the chip was at
its maximum operating temperature?
The only material that you have available
Transcribed Image Text:The Diamond Ring Solution. The processing chip on the computer that controls the navigation equipment on your spacecraft is overheating. Unless you fix the problem, the chip will be damaged and the navigation system will shut down. You open the panel and find that the small copper disk that was supposed to bridge the gap between the smooth top of the chip and the cooling plate is missing, leaving a 2.2 mm gap between them. In this configuration, the heat cannot escape the chip at the required rate. You notice by the thin smudge of thermal grease (a highly thermally conductive material used to promote good thermal contact between surfaces) that the missing copper disk was 2.2 mm thick and had a diameter of 1.3 cm. You know that the chip is designed to run below 75 °C, and the copper cooling plate is held at a constant 5.0 °C. (a) What was the rate of heat flow from the chip to the copper plate when the original copper disk was in place and the chip was at its maximum operating temperature? The only material that you have available
on board to bridge the gap between the chip
and copper plate is lead. If the cross-
sectional area of the lead piece you plan to
wedge into the gap is 1.7 cm², what is the
rate of heat flow from the chip to the copper
plate? Does it match the value calculated in
part (a)?
(c) While brainstorming for other possible
solutions to your problem, you happen to
glance down at the engagement ring on your
finger: a large, glittering diamond. The top
and bottom surfaces are flat and nearly
rectangular (L = 0.90 cm and W = 0.50 cm),
and the thickness looks to be about 2.2 mm,
just right to bridge the gap. You pry the
diamond out of its holder and press it into
the gap. What is the rate of heat flow now?
Good enough?
(a) Number
(b) Number i
&
i
Number
i
Units
Units
Units
<>
<>
<>
Transcribed Image Text:on board to bridge the gap between the chip and copper plate is lead. If the cross- sectional area of the lead piece you plan to wedge into the gap is 1.7 cm², what is the rate of heat flow from the chip to the copper plate? Does it match the value calculated in part (a)? (c) While brainstorming for other possible solutions to your problem, you happen to glance down at the engagement ring on your finger: a large, glittering diamond. The top and bottom surfaces are flat and nearly rectangular (L = 0.90 cm and W = 0.50 cm), and the thickness looks to be about 2.2 mm, just right to bridge the gap. You pry the diamond out of its holder and press it into the gap. What is the rate of heat flow now? Good enough? (a) Number (b) Number i & i Number i Units Units Units <> <> <>
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