Radiative exchange between grey Lambert radiators

3 Radiative exchange between grey Lambert radiators 

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 

We will now investigate radiative exchange between the isothermal walls (zones) of the enclosure illustrated in Fig. 5.57. The temperature of some of the zones is known, for others the heat flow supplied from or released to the outside is given. The heat flows of the zones with known temperatures and the temperature of each zone with stipulated heat flow are what we are seeking. There are as many unknown quantities (temperatures or heat flows) as there are zones. 

The energy balance equations for all the zones need to be established to solve this radiative exchange problem. This is done using the net-radiation method introduced by G. Poljak [5.49], This yields a system of linear equations that, when solved, deliver the unknown temperatures and heat flows. With simple 

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