# Thermal Analysis

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Basic thermal analysis was conducted on the heat sink plate of the lighting module. The system was modeled as a circular fin (with the fin area corrected for the fact that the plate is in fact not a complete disk. To find the efficiency of the fin, the following equation was used:

Where r1 and r2c are the inner (LED) and corrected outer radii, K and I represent modified Bessel Function of the first and second kind, and C2 and m may be defined as follows:

Where h is the convective coefficient of the environment surrounding the fin, k is the conductive coefficient of the steel plate, and t is the thickness of the plate. After obtaining the efficiency, the resistance and delta-T were found using the following simple equations:

Calculations employed conservative values for the necessary variables so as to not understate any potential problem with the heat buildup. With a full heat flux of 3W going into the plate, the following data was obtained.

As can be seen, the temperature of the LED would be over the prescribed temperature of 150C. After some consideration, it was determined that the calculations should be repeated for 2.5W which could be set as the new maximum LED input.In addition to lowering the end power to 2.5W, it was also necessary to increase the thickness of the plate from .0625" to 0.125". This was the only way in which it was feasible to get a heat sink efficiency over 90%. Even with these changes, the thermal analysis shows that there may be a problem with the current design. It will therefore be crucial to test the actual heat of the LED and heat sink. A Test Plan has been written to describe the procedure for this test.

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