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I am using Luminus COB with the rating given as Maximum power 65W and typical power 29W.
At 800mA the power I would get is 29W while at 1600mA it is 65W.

When I connect it to a power supply of 1400mA, the COB worked for 6-7 hours and later it started flickering and was burned out for some reason. The heat sink was for 100W.

However I connected an aluminium plate over the heat sink to fit the COB holder and made sure of the plate and heat sink making proper connection without leaving voids.

What can be the reason behind the COB burning out quickly?

The Current or the aluminum plate?

Link for data sheet of LED
http://www.luminus.com/products/Luminus_XnovaCXM18-GEN1_Datasheet.pdf

http://www.mouser.com/ds/2/260/LPC-60-SPEC-806139.pdf

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The reason for it burning out is that at the current with which you were driving it, your heatsink was inadequate.

Heatsink design is an important part of any circuit that must have heat removed from it in order to function properly. In the case of your LED, the goal is to not exceed the stated maximum junction temperature of the device, which your datasheet will reference as probably around 140°C. The LED will also have a stated junction to case thermal resistance near 0.56 °C/W. You must use these parameters along with your maximum ambient operating temperature to specify a heatsink that removes enough heat from the device so as to not exceed the maximum junction temperature.

A given heatsink will have its own thermal resistance characteristic. This thermal resistance, added to the device thermal resistance represents the total thermal resistance from junction to air. Multiply this times the power your LED is drawing and add the ambient temperature and you have the junction temperature.

At 1.4 A and a voltage drop of 37 volts, your LED was dissipating ~ 57 watts. If your ambient temperature is 25 °C, your heatsink should have a thermal resistance of no more than 1.0 °C/W to keep the junction below 80% of its rated maximum. Your existing design is probably greater than 1.5 °C/W.

A reasonable heatsink design will also include a very thin layer of thermal transfer compound to fill the micro voids between the device and the heatsink.

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