You are a packaging engincer for a silicon vallcy high-tech company. You arc cur

Question

You are a packaging engincer for a silicon vallcy high-tech company. You arc currently leading thc cffort to design a thermal abatement mthod to dissipate the power from a 1 cm × 1 cm chip using an amy of square fins, A base design for a 4x4 array is shown below in Fig. I, where the fin array extends to the edge of the chip. The width of cach fin is equal to the gap between fins. Note that for purposes of calculating the fin array efficiency for each row, the row includes the gap in front of it as shown in the figure. The fin array sits on a base of 1 mm thickness as shown in Fig. 2. A contact resistance of 10- mKW cxists between the chip and the base. The length of the fins is fixcd at 0.5 cm. Inlet airflow Row I or Row 2 W chip Row 3 Row 4 Lb Chip Figure 1. Top view of 4x4 fin array arrangement, including row number Figure 2. Side view of 4x4 fin array arrangement. Note that the fin array above is arranged into 4 rows, where Row 1 faces the inlet airflow. Because of the effects of flow blockage, the heat transfer cocfficient is different for cach row and may be defined as: 500 W/m·K Row l: h! Rows 2 N: hi = 0Bly-r where j is the row number. Therefore, Row 2 has a heat transfer cocfficient of 08x500 W/m'K. Row 3 is 0.8x500 WmK. and so on. Note that this corrclation holds regardless of the number of rows N . The following parameters are held constant in the design: chip = l cm = 0.5 cm 1. [10 points] Calculate the fin width win Tm = 25°C I mun k = 230 W/mK h.-500 WhK hj=0.8h-1. j > 1 2. Note that it varies with row sinee the heat [10 points] Calculate the fin effieiency ny for each row. transfer coefficient varies for cach row. Discuss why you see the variation of with row. 3. [10 points] Calculate the overall array cflicicncy no for cach row. Again, it varies with row sincec h varics with row 4. [20 points] Callate the chip temperature Tchip assuming that the chip is at a constant temperature. 5. [10 points] The fin array is generated by cutting a solid bloek of Aluminum that costs 50 cents. Determine the cost of producing a heat sink with this basc Each cut costs 5 cents to manufacture. case configuration.

Explanation / Answer

M = (2h/kT)1/2

Lc = 0.5 cm

So for first row h1 = 500                               m1 = 0.1207

            Second row h2 = 0.8*500                m2 = 0.1080

            Third row h3 = 0.64*500                 m3 = 0.0966

             Forth row h4 = 0.512*500              m4 = 0.0864

nf1 = 0.9999 (m2k)-

nf2 = 0.9999 (m2k)-

nf3 = 0.9999 (m2k)-

nf4 = 0.9999 (m2k)-

q = hA(T-T0)

q = 10 W

A = Area = (0.01)2

T0 = 298 K

So, T = 498 K

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