3.151   Because of the large number of devices in today’s PC chips, finned heat sinks are often used to maintain the chip at an acceptable operating temperature. Two fin designs are to be evaluated, both of which have base (unfinned) area dimensions of 53 mm X 57 mm. The fins are of square cross section and fabricated from an extruded aluminum alloy with a thermal conductivity of 175 W/m · K. Cooling air may be supplied at 25°C, and the maximum allowable chip temperature is 75°C. Other features of the design and operating conditions are tabulated.

 

 

Heat sink Top View

 

Fin Dimensions

 

 

Convection

 

Cross Section     Length       Number of     Coefcient

Design   w x w (mm)        L (mm)  Fins in Array  (W/m2 · K)

A              3 X 3                30               6 X 9              125

w                                                                                                         B              1 X 1                  7             14 X 17             375

Square fins                                                                                                       

57 mm

 

Lf                             S

Lb

 

Heat sink Interface,

R"t,c Chip, qc, Tc

53 mm

 

 

 

 

 

 

 

 

 

3 mm ´ 3 mm cross section

 

 

 

 

 

 

 

Tb = 75°C

 

Consider a square chip of width Wc = 16 mm and conditions for which cooling is provided by a dielec- tric liquid with Too = 25°C and h = 1500 W/m2 · K. The heat sink is fabricated from copper (k = 400 W/m · K), and its characteristic dimensions are w = 0.25 mm, S = 0.50 mm, Lƒ = 6 mm, and Lb = 3 mm. The pre- scribed values of w and S represent minima imposed by manufacturing constraints and the need to maintain adequate flow in the passages between fins.

(a)    If  a  metallurgical  joint  provides  a  contact  resis- tance  of  Rt",c  = 5  X 10-6  m2 · K/W  and  the  maxi- mum allowable chip temperature is 85°C, what is the  maximum  allowable  chip  power  dissipation qc?   Assume   all   of   the   heat   to   be   transferred through the heat sink.

It may be possible to increase the heat dissipation by  increasing  w,  subject  to  the  constraint   that

 

54 pins, 9 ´ 6 array (Design A)

 

Determine which fin arrangement is superior. In your analysis, calculate the heat rate, efficiency, and effec- tiveness of a single fin, as well as the total heat rate and overall efficiency of the array. Since real estate inside the computer enclosure is important, compare the total heat rate per unit volume for the two designs.