Grey isothermal boundary walls

If the gas filled enclosure is surrounded by grey walls with emissivity w = w(Tw), then the energy reflected by the walls also has to be considered. Rough, oxidised and dirty walls have emissivities that are only slightly smaller than one. In this case, which often applies in furnaces, the reflected radiation proportion is of little importance. The heat flow QGW transferred from the gas to the walls is smaller, by a factor that lies between w and 1, than the heat flow calculated according to (5.206) for black walls. At sufficiently large values of w, around w 0.8, the approximation recommended by H.C. Hottel and A.F. Sarohm [5.48] of 

In the consideration of the radiation reflected by the walls, the exchange of radiation can be calculated just like in section 5.5.3. According to (5.143), the heat released by the walls to the outside 

The radiosity Hw includes, according to (5.142), the emissive power Mw = wcrT((, of the wall area and the reflected fraction of the irradiance Ew  

A more exact calculation of the radiative exchange, in which the absorption of the reflected radiation in the gas space has been extensively modelled, has been presented by K. Elgeti [5.64]. Another method for the consideration of the spectral absorption bands can be found in [5.37], section 17-7. 

Example 5.15 A cylindrical combustion chamber with diameter D = 0.40 m and length L = 0.95 m contains a combustion gas at temperature Tq = 2000 K and pressure p = 1.1 bar. The partial pressures of CO2 and H2O are pco2 = O.lObar and pu2o = 0.20bar respectively. The walls of the chamber are at Tw = 900 K and their emissivity is w = 0.75. Determine the heat flow transferred from the gas to the chamber casing. 

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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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