Cooling Fin

PART VII

Here we explore the effect of shape on the cooling fin. We cut a notch in the top-right hand corner of the fin, and repeat the conditions of PART IV.

Modifying the shape of the cooling fin presents some serious challenges. First, how can we "cut a notch" in a cooling fin that is modeled as a system of equations? We assumed that cutting a notch means setting the interior points and boundary conditions to zero. However, doing so yields an ill-conditioned matrix with more zeros than coefficients to solve for. Therefore, the results presented here may not be correct.

In order to aid in understanding the effect of "cutting a notch" in the cooling fin, we present a diagram of a 4x4 cooling fin, and it's associated system of equations.

First, we show the effect of cutting a notch for the standard 5 Watt input.

Assuming that our procedure for cutting a notch is correct, then the result is higher performance. The cooling fin dissipates the same power at a lower temperature with a notch cut in it, as compared to PART II.

Next, we find the maximum power that the fin can dissipate with the constraint of a maximum temperature of \(80^{\circ}C\).

Here we really see the benefit of a notch in the fin. The cooling fin can dissipate more than twice the power as in PART IV.

Source code here