Black, isothermal boundary walls

An isothermal gas at temperature TG is enclosed by isothermal walls at a temperature Tw Tg. As a simplification the walls will be idealised as black bodies reflection does not need to be considered. A heat flow QGW from the gas to the colder walls is transferred by radiative exchange. If the gas is to maintain its 

The radiation flow emitted by the gas generates a mean irradiance 

aG is the absorptivity of the gas for the radiation emitted by a black body at temperature Tw. As the gas is not a grey radiator, aG is not the same as eG, except for the limiting case where Tw = TG. H.C. Hottel and R.B. Egbert [5.58], see also [5.48], determined aG for C02 and H20 from absorption measurements, and related them to the emissivity from 5.6.3, as shown in the following equations  

The emissivities are taken from Fig. 5.74 to 5.76, for a wall temperature Tw and the product (pGsm) reduced by a factor of (TW/TG). For pressures p above 1 bar, the pressure corrections mentioned in section 5.6.3 have to be brought into play 

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If the bodies participating in radiative exchange cannot be assumed to be black bodies, then the reflected radiation flows also have to be considered. In hollow enclosures, multiple reflection combined with partial absorption of the incident radiation takes place. A general solution for radiative exchange problems without simplifying assumptions is only possible in exceptional cases. If the boundary walls of the hollow enclosure are divided into isothermal zones, like in 5.5.2, then a relatively simple solution is obtained, if these zones behave like grey Lambert radiators. Each zone is characterised purely by its hemispherical total emissivity si — whilst at = is valid for its absorptivity, and for the reflectivity... 

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