Radiation Through an Isothermal and Diffuse Scattering Medium

4 Radiation Through an Isothermal and Diffuse Scattering Medium 

Thermal radiation through an isothermal and diffuse scattering medium represents one of the simplest cases of radiation in a particulate medium. This problem was treated by Love and Grosh (1965). 

For an isothermal medium at temperature Tp, the monochromatic radiant emission from particles 4 is a function of Tp and X only and is independent of Z. In addition, we may assume that the solutions of Eqs. (4.81) and (4.82) are of the form 

Substitution of Eq. (4.83) into Eqs. (4.81) and (4.82) leads to 2n linear algebraic equations in x and Jt(i+n) with parameter y. The matrix of the coefficients yields 2n eigenvalues yt as well as 2n sets of eigenvectors x, and x(i+ ) for each eigenvalue. Here, k is an iterative index. The solutions can be expressed as 

The determination of Z s depends on the boundary conditions defined. With the assumption of diffuse walls, the intensities at the wall may be written as 

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