Homework 4 solutions problem 1

Homework 4 solutions problem 1 - rate? R f = θ b /16 q f...

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Homework 4 – problem 1 1. In class 6 we talked about the importance of heat dissipation from chips and how fins can increase this dissipation. However this heat dissipation is limited by the maximum operating temperature of the chip, usually about 75 o C. One solution is to create a 4 X 4 array of copper fins metallurgically joined to the outer surface of a square chip that is 12.7 mm on a side. a) Assuming 1-D steady-state conditions with negligible contact resistance between the pins and the chip, sketch and label the equivalent thermal circuit. What is the resistance? b) Make the same assumptions as before, however include a contact resistance of 10 -4 m 2 -K/W and sketch, label and calculate the resistance. c) What is the maximum heat rate for both of these situations? d) What is the percentage enhancement of heat transfer of the fins? e) If you use the infinite fin approximate (why can’t you), what happens to the fin heat transfer
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Unformatted text preview: rate? R f = θ b /16 q f Look on p. 144 to find q f for Case A. (The θ b ’s cancel out). Same R f . The maximum heat rate q c = 16q f + q b + q i Now to figure out some of our constants: From p. 144: The heat rate from the chip top is by convection: The heat rate from the board is also by convection: We use A c =( 0.0127 m) 2 because we’re looking at the bottom of the board. q i = 0.29 W q c = 16(2.703) + 7.32 + 0.03 = 50.9 W W/out the fins, q c = 1000 W/m 2-K (0.0127 m) 2 55 o C + 0.29 = 9.16 W. 50.9/9/16 = 555 % enhancement. When we add a contact resistance, the q i changes insignificantly: = 0.29 W as well. Same heat transfer rate. The infinite fin assumption is only for L > 2.65/m. In this case, = .032 won’t work. If we use it, the actual heat transfer rate will be overestimated since q f = M = 3.17W and our q f = 2.7 W....
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This note was uploaded on 08/13/2011 for the course CHEM 3210 taught by Professor Degrazia during the Fall '10 term at Colorado.

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Homework 4 solutions problem 1 - rate? R f = θ b /16 q f...

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