How well do you understand radiant heat transfer?

A problem for the physics minded among you:
Given:
• Two parallel plates, separated by a distance of 20 meters.
• The first plate is continuously heated to maintain a temperature of 350 k
• The second plate is continuously cooled to maintain a temperature of 300 k
• The space between the plates is at atmospheric pressure, 20% oxygen, 80% nitrogen
• Under all conditions, total pressure is constant at 1 bar.

Assume that the plates are sufficiently large that all energy transfer is between the plates only and the plates are black body radiators/absorbers. UPDATE And assume the only mechanism for heat transfer between the plates is radiant transfer. And assume there is no absorption of radiant energy by oxygen or nitrogen. And for the pedantic amoung you, please realize that in engineering there is a field of study called heat transfer. We don’t call it “enthalpy transfer” because it deals with thermal energy only and enthalpy can be transferred by other mechanisms.
Anyway.
Find:
The (UPDATE steady state) temperature of the intervening gas, the energy input to the first plate and the energy removed from the second plate under the following conditions.
1% of the original atmosphere is displaced by CO2
2% of the original atmosphere is displaced by CO2
5% of the original atmosphere is displaced by CO2
10% of the original atmosphere is displaced by CO2
20% of the original atmosphere is displaced by CO2
50% of the original atmosphere is displaced by CO2

Plot the results.

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About John Eggert

A minerals processing engineer in Canada. A cynic by nature, but open to being convinced!
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4 Responses to How well do you understand radiant heat transfer?

  1. Andyj says:

    John, you keep failing yourself.
    What C02. Do you mean standard air with n% C02?
    What about expansion of the gas. Is this the question?
    Same issue when you posed stuff on WUWT. You never once mentioned the lapse rate and gas pressure. The great driver to ground temperature, on all planets with an atmosphere.

  2. John Eggert says:

    Andy:

    You seem angry. That is OK. I get angry about these things too. I don’t think we are as far apart as you think. Now. On to your specific questions.

    Not sure how I am failing.

    “What CO2?” CO2 is something one can buy, purify or make.
    “Do you mean standard air with n% C02?” I mean exactly what I said. that is
    • The space between the plates is at atmospheric pressure, 20% oxygen, 80% nitrogen
    • Under all conditions, total pressure is constant at 1 bar

    Given that “under all conditions, total pressure is constant”, expansion is not relevant to the problem posed.

    What does lapse rate have to do with a constant pressure question?

    This is a very difficult question. One needs education equivilant to introductory university physics, advanced heat transfer and access to some approximation of solutions to radiative transfer equations. But it is a clear question for anyone versed in the field.

    Again, thanks for your interest.

    Cheers

    JE

  3. John,

    I created a radiative transfer model which you can see at Visualizing Atmospheric Radiation – Part Two and the code at Part Five.

    I remembered this example here and quickly butchered up the code to make 2 plates 20 meters apart with fixed temperature (rather than an atmosphere with very different conditions).

    I have calculated a few things.
    With no CO2 of course the energy supplied to plate 1 (the hotter plate) at 350K is 392 W/m^2 – this doesn’t need an RTE model.

    At 1% – energy supplied to plate 1= 364 W/m2
    2% – 359
    5% – 351
    10% – 344
    20% – 334
    50% – 316

    At 1%, the temperatures stablize at (5, 15, 25, 35, 45m): 340 334 327 321 313
    50% the temperatures stablize at (5, 15, 25, 35, 45m): 340 334 328 322 315

    I have spectra as well for these different conditions.

    Does this match up with what you have calculated?

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