Question

1. As more and more components are placed on a single integrated circuit (chip), the amount of heat that is dis­sipated continues to increase. However, this increase is limited by the maximum allowable chip operating temperature, which is approximately 75°C. To maxi­mize heat dissipation. it is proposed that a 4 × 4 array of copper pin fins of length 12.7 mm and diameter 1.5mm be metallurgically joined to the outer surface of a square chip that is 12.7 mm on a side. What is the decrease of the chip temperature due to using the fins and determine the maximum allowable chip power in each case (assume the fins tips are insulated and neglect the chip thickness, T$\infty$_i = 40 °C and h_i = 60 W/m² K, T$\infty$_o = 20 °C and ho = 150 W/m² k, k_b=20 W/m.k   

Sideview Pin fins, D, Top view Chip, c. T Chip Lb Air W= 12.7 mm → Board, k

Answer 1

DP= 1-5mm 20c o o o 0 Lp 127mm h 150 o o O O 12:7mm For given geometry of fin 37,203 · Maximum Allomable temperature at base of fins 75 Hence For insulated tip boundary condition Tb-TooCosh mL χ = L = 12,-7x10-3 m At T-20 Cosh (o) 75-20 Cosh (37 203 x 127x1o3) 69.384℃ T= Decrease of chip temperature 75-69.384 = 5.6154℃ Heat transfer through fin Heat transfer from each fin hPKAc T-To) x tan h(m) 289x1y4x000152 (75-20) x tanh (37203x 00127) -V 150X.mx o o○ら 0.460 W .: -Heat transfer from 16 fins = 16 x 0460 = 7.36 W Heat transfer from the annular space between ins [0.01272-16xTax o. 00152J x(75-20) =150x 4 1,097 W Total heat transfer tHeat transfer from fin t Heat trangfer from annular space t Heat transfer from board can't compute as data not = 7.364 1.097= 8.457 w Makimum a lowable chip poner 8457w. provided