# I Converstion of radiant flux (watts) to temperature (C)

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1. Sep 25, 2014

### Joel DB

Hey all,
I'm having some unique challenges on an optical system I've created, where I'm arraying several LEDs under 1 optic/reflector. We're beginning to see major degradation of the metallic coating that is applied to the part, and I'm tyring to quanitfy the temperature (converted from radiant flux incident on the reflector surface) at the surface of the reflector. I need to know what temperatures we're seeing inside the optic so I can recommend a coating specifiation for a vendor.

Seems the internet is flooded with things, or I could rewind back to some physics textbooks, but trying the forum first, in case there are any good suggestions.

JD

2. Dec 18, 2016

### Gan_HOPE326

In the most basic case of only radiative emission I'd say you could simply consider the Stefan-Boltzmann law:

$$J=\sigma T^4$$

where J is your incoming flux by unit of surface and $\sigma$ is a known physical constant. Of course this assumes black body behaviour and no other forms of heat dispersion. If you assume a grey body (namely that your optic reflects and absorbs equal percentages of radiation at all wavelengths) nothing really changes because if J is the flux you already know is coming then both sides of the equation get multiplied by the emissivity $\epsilon$. If instead you add another 'sink' of heat, like some conduction mechanism with thermal resistance R, then you have

$$\epsilon J = \epsilon \sigma T^4 + \frac{(T-T_{room})}{R}$$

and that further lowers your equilibrium temperature.