# Problems with thermal radiation simulation of gray surfaces

Question asked by Mark Egan on Jul 21, 2016

Solidworks seems to offer the capability to analyze thermal radiation between gray surfaces. Ie, surfaces that have emissivities less than 1. There does not seem to be the capability (at least in SW 2016) to input different emmissivities for each surface in a radiative load - you are only allowed to set one single emissivity value. That's less than optimal and not very realistic but ok, I get it - this is a limited and somewhat new module. I can make do with one emissivity value between surfaces for a first cut analysis before moving to thermal desktop or similar. However, there seems to be a problem which is quite serious in my view if I'm correct: SW is NOT calculating radiation between two gray surfaces, but rather between one gray surface and a blackbody (emissivity/absorption = 1) which can be verified with hand calculations using fundamental equations. This is a fundamentally different type of solution to that being advertised by the load menu (see images below).

Doing a bit of digging into the SW help files, we come across this, which gives a correct equation for heat transfer between a gray body and a black body, but then gives an incorrect equation for heat transfer between two gray bodies. A high school student can see that the emissivities in the fractions cancel and we're left with a purely geometric factor. This is obviously incorrect. The whole point is accounting for the emissivities of the two surfaces being analyzed.

This is concerning if this equation is what is being used to calculate gray body interactions in the SW software. The radiation load gives two options, in effect advertising two sets of solutions: blackbody radiation transfer, and gray body radiation transfer where the surfaces have the same emissivity. The first solves correctly, the latter does not. It is solving for graybody to blackbody. This should be corrected by either correctly advertising it as such, or better yet expand the capabilities to actually include options to analyze multiple gray surfaces (ideally with differing emissivities).

Does my assessment have any inaccuracies? Have others verified this problem?