Mathematics
Scientific paper
May 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984jqsrt..31..423g&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer (ISSN 0022-4073), vol. 31, May 1984, p. 423-438.
Mathematics
2
Boundary Conditions, Diffuse Radiation, Eigenvalues, Energy Dissipation, Radiative Transfer, Relaxation Method (Mathematics), Temperature Distribution, Differential Equations, Fredholm Equations, Integral Equations
Scientific paper
The problem of the dissipation of temperature perturbations in a finite homogeneous atmosphere is solved for the situation in which the temperature at one boundary is maintained constant (that is, the temperature perturbation is zero for all times) while energy can be freely radiated to space through the other boundary. Exact solutions are shown for the exponential-sum fit to the kernel of the basic integral equation. These solutions constitute the set of radiative eigenfunctions. Also, approximate solutions in terms of the radiative eigenfunctions in the diffusion approximation (one exponential term in the expansion of the kernel) are obtained. These, in turn, are used in the solution of an initial value problem. The constant temperature boundary condition simulates the interface between two regions in one of which the relaxation processes are much more rapid than the purely radiative relaxation of the other.
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