MECH344 - Heat and Mass Transfer
Ryan Sullenberger Februrary 16th, 2009
7.1 An air - cooled heat sink used on a computer circuit board has to dissipate 0.8 W of power to the surrounding air at 20 °C.The microchip being cooled by the heat sink cannot exceed 80 °C. a) If the heat transfer coefficient is 35 W/m²·K, and the microchip (and attached heat sink) have base dimensions 12 mm x 8 mm (on the surface at which they are attached), show that this device does need a heat sink. In[133]:=
Eg := 0.8
In[134]:=
h := 35
In[135]:=
Abase := H0.012 * 0.008L
In[136]:=
Tinf := 20
In[137]:=
Solve@Eg h * Abase * HT - TinfL, TD
Out[137]=
88T ® 258.095<<
The temperature obviously exceeds 80 deg. C, \ a heatsink is definitely required, or this microchip is toast. b) If the heat sink fins are of length 3.8 mm and thickness 0.25 mm, and have a thermal conductivity of 222 W/m·K, how many fins does the heat sink need to have to adequately dissipate the heat? ClearAll@nD Lc := 0.0038 + 0.00025 2 w := 0.012 t := 0.00025 Af := 2 * w * Lc Ab := H0.012 * 0.008 - n * t * 0.012L At := n * Af + Ab Ηf := 0.98 h := 35
Solve for how many fins are needed to keep temperature at 80 deg C : Af SolveB0.8 h * At * 1 - n * 88n ® 3.19038<<
At
* H1 - Ηf L H80 - 20L, nF
Solve for the temperature of the CPU if the number of fins is doubled : n := 2 * 3.190384488248253`
2
mech344-feb15.nb
Af SolveB0.8 h * At * 1 - n * At
88T ® 54.3249<<
* H1 - Ηf L HT - 20L, TF
Because we rounded, solve for the exact temperature of the CPU using 5 fins : n := 3.190384488248253` Af SolveB0.8 h * At * 1 - n * At
88T ® 80.<<
* H1 - Ηf L HT - 20L, TF
c) If the number of fins from part (b) was doubled, how much more effective would the heat sink be?(i.e., would doubling the number of fins be a good idea?) Prove your answer by calculating the values, that is, the ratio of the overall efficiencies and surface temperatures between the two situations. Calculate efficiencies : Η0 @n_D := 1 - n *
Af At
* H1 - Ηf L
Η0 @3.190384488248253` D 0.984467 Η0 @2 * 3.190384488248253` D 0.968934 Η0 @3.190384488248253` D Η0 @2 * 3.190384488248253` D 1.01603
T1 over T2 : 80.0 54.32494279176202` 1.47262
By doubling the number of fins, the fin efficiency dropped by 0.02. However, it is clear that the temperature of the CPU (microchip) also dropped by a substancial amount, 25.68 degrees Celcius. Considering that the problem stated that the microchips temperature was O.K. to idle at 80 deg. C, doubling the amount of fins is not entirely needed unless the microchip requires to operate in high performance situations. It is known that microchips and CPUs perform more effectively at lower temperatures. The relatively low loss of efficiency could be worth the temperature drop in many scenarios. Recently a group of students in Las Vegas, Nevada broke the world record for overclocking an AMD64 Phenom II quad-core processor to 6.5 Ghz, using liquid helium as the cooling agent. The system was able to perform a cold boot around ~ 20 deg. K, and they smashed the 3DMark05 world record.