Question 2

You are to design a finned heat sink for a computer mother board, which comprises of vertically

mounted rectangular parallel plates on a porous base, as shown in figure 2. The height of each

fin is 40 mm, and the temperature of the fins are constant at 80 °C. The heat from the fins

induces an air flow (due to free convection) from the surroundings through the porous base

and through the parallel plates, where they exit at the top. The surrounding temperature is

constant at 20 °C. The base is square, with a width of 50 mm.

Neglect

heat

transfer

Air flow (via

free convection)

Fins

Neglect

heat

transfer

50 mm

Porous base

Neglect

heat

transfer

Figure 2: Free convection in between parallel plates.

40 mm

Neglecting the heat transfer from the bottom of the base, and through the extreme left and

right side of the fins, i.e., the only heat transfer is due to the convection in between the parallel

plates (as shown in figure 2), calculate the minimum number of fins (plates) required if the

required heat transfer rate is 18 W. [10 marks]

You may assume that the thickness of the fins is negligible.