3.83      An isothermal silicon chip of width W = 20 mm on a side is soldered to an aluminum  heat  sink  (k  = 180 W/m · K) of equivalent width. The heat sink has a base thickness of Lb = 3 mm and an array of rectangu- lar fins, each of length Lf = 15 mm. Airflow at Too = 20°C is maintained through channels formed by the fins and a cover plate, and for a convection coefficient of h = 100 W/m2 · K, a minimum fin spacing of

1.8 mm is dictated by limitations on the flow pressure drop.  The  solder  joint  has  a  thermal  resistance  of R"t, c = 2 X 10-6  m2 · K/W.

 

Chip, Tc, qc

Solder, Rt",c

 

(a)   Consider limitations for which the array  has N = 11 fins, in which case values of the fin thickness t = 0.182 mm and pitch S = 1.982 mm are obtained from the requirements that W = (N - 1)S + t and S - t = 1.8 mm. If the maximum allowable chip temperature is Tc = 85°C, what is the corresponding value of the chip power qc? An adiabatic fin tip con- dition may be assumed, and airflow along the outer surfaces of the heat sink may be assumed to provide a convection coefficient equivalent to that associated with airflow through the channels.

(b)   With (S - t) and h fixed at 1.8 mm and 100 W/m2 · K, respectively, explore the effect of increas- ing the fin thickness by reducing the number of fins. With N = 11 and S - t fixed at 1.8 mm, but relaxation of the constraint on the pressure drop, explore the effect of increasing the airflow, and hence the convection coefficient.