The zone method:: A new explicit matrix relation to calculate the total exchange areas in anisotropically scattering medium bounded by anisotropically reflecting walls

A new explicit matrix relation for the calculation of the total exchange areas (TEA) in emitting, absorbing and anisotropically scattering semi-transparent medium bounded by emitting, absorbing and anisotropically reflecting walls has been established. It has been used to directly determine the TEA as a function of radiative properties and geometry of the medium and its boundaries. Computation calls for direct exchange areas (DEA) and indirect exchange areas (IEA). A new definition of these exchange areas reduces their integration order and provides practical energy balance relations for their computation in the case of complex geometry elements. The new formulation is applied in the case of an emitting, absorbing and linearly anisotropic scattering semi-transparent slab bounded by black surfaces. This method is also applicable to nongray medium using the weighted sum of gray gases model.