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Consider a cylindrical metal rod of a certain diameter and length and a rectangular plastic plate of certain dimensions. The rod is suspended in air above the plate at a certain distance from the plate. The rod heats itself to a certain temperature above the ambient temperature and thus starts radiating its heat. The thermal radiation from the rod should heat the plate below.

Now my question is, is there a formula I can use to calculate the temperature rise in the plate caused due to thermal radiation from the rod?

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  • $\begingroup$ Isn't it obvious that the closer the rod is to the plate the hotter the plate will get? Also that the rod should have its largest area parallel to the plate? $\endgroup$
    – sammy gerbil
    Commented Apr 6, 2020 at 15:09
  • $\begingroup$ @sammygerbil Sorry I had made a mistake in the question. I've edited it now. I'm actually trying to ask how to calculate the temperature rise. $\endgroup$
    – Somanna
    Commented Apr 6, 2020 at 15:13

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Given the emissivity of the rod and the plate and the geometry of their configuration, you could probably determine the power flux between the two.

But it's a big step to go from that to the temperature of the plate, because it will be in equilibrium with the rest of the environment, probably via both radiation and convection. So the radiative temperature of the environment, temperature-driven convection, other air movers will all influence the final temperature of the plate. Small changes in some parameters (like whether the plate is horizontal or vertical) can have substantial effects on the final temperature. Normally this prediction would be done from an empirical model, not from thermodynamic first principles.

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