Problem of radiative transfer

A SIMPLE TREATMENT OF THE PROBLEM OF RADIATIVE TRANSFER IN SUPERNOVA-LIKE ENVELOPES... 

Other areas of radiative transfer have been driven by increased capability of analysis due to the great strides in computer capability. Just a few years ago, two-dimensional problems of radiative transfer in enclosures with a participating medium were at the edge of computational capability. Now, these are routine, and many three-dimensional cases have been analyzed. Because of the need in applications such as utility steam generator design to analyze three-dimensional geometries with up to tens of thousands of surface and volume computational elements, much research is now focused on further increases in computational speed. Massively parallel computers may well provide the required computational capability for such problems. 

Geometric Optics Results with Emission. When the temperature of a semitransparent layer is large, emission of radiation becomes significant, and the problem of radiative transfer becomes more complex. The change in refractive index at each interface causes total internal reflection of radiation in the medium with higher refractive index at the boundary. This effect must be treated in the RTE at the boundary of the medium, and diffuse boundary conditions are no longer correct for the exact solution of this type of problem. Various approaches have been attempted. 

The determination of the distribution of the LVRPA requires the use of some type of radiative transfer model. In the case of transparent pollutants, it can be considered that Cl depends on Ti02 concentration (Qatai) only, and not on the concentration of the pollutant, since it is the former component which absorbs and scatters radiation. This allows imcoupling the radiation problem from the degradation kinetics when Equation (13) is solved that is, one can first evaluate and then, independently of the value of the pollutant concentration, integrate F2(Cl) over the reactor volume. Once this quantity has been calculated, its numerical value is taken as a constant in Equation (13), which can now be solved to obtain the evolution of Cp av... 

The equation of radiative transfer is an energy balance except for this concept, its physical content is slight. The phy.sical problems of interest enter through the extinction coefficient and the source function. Many papers and monographs have been written on its solution... 

Summary. In conclusion, some suggestions are made on how to model the problem of radiative heat transfer in porous media. First, we must choose between a direct simulation and a continuum treatment. Wherever possible, continuum treatment should be used because of the lower cost of computation. However, the volume-averaged radiative properties may not be available in which case continuum treatment cannot be used. Except for the Monte Carlo techniques for large particles, direct simulation techniques have not been developed to solve but the simplest of problems. However, direct simulation techniques should be used in case the number of particles is too small to justify the use of a continuum treatment and as a tool to verify dependent scattering models. 

As shown, the quadratic integrals Q and R of Rybicki for unpolarized radiation and the quadratic integrals Sq and of Siewert and McCormick for polarized radiation are closely related. These integrals of radiative transfer provide us with a convenient tool for solving some elementary inverse problems. Numerical experiments have shown that for these problems the single-scattering albedo can be derived with great accuracy even when the measurements are not so accurate. The determination of other characteristics of the medium is much more complicated. 

This chapter is divided into three parts. In Section 10.2, we discuss the interesting problem of heat transfer in novel materials called nanofluids, which are suspensions of nanoparticles in liquids. Here, the central question is to understand the heat transfer across the interface between a nanoparticle and the surrounding base fluid. We believe that understanding heat transfer across the interface provides crucial insights into the observed enhanced thermal conductivities of nanoparticle suspensions in polar liquids (Choi 2009). We provide an overview of the computation of thermal conductivity for inhomogeneous systems using MD simulations, followed by a discussion on the heat transfer due to radiative heating. 

Atmospheric and oceanic scientists often use the word parameterization to describe this formalism. In our jargon, the goal is to parameterize the collective effects of small-scale processes on large-scale processes. Because small-scale processes are sundry, the parameterization problem is multifaceted. Typically, small-scale processes are broken down into distinct classes of problems—clouds, radiative transfer, hydrometeor interactions, surface interactions, small-scale turbulence, chemistry, and so on—processes that can be thought of as the atoms. Although one may be interested only in the net effect of all of these processes, atomization facilitates idealization and subsequent study. 

Given the thermal absorption coefficient and the boundary conditions on the heating, it is possible to determine the constants of temperature (To and T ) and phase ( ) in Eq. (21). The inverse problem is faced by the radio astronomer, namely to determine the thermal absorption coefficient from measurements of the thermal emission. This is done in the following manner. The temperature distribution given by Eq. (21) is used in the equation of radiative transfer... 

Independently of whether the radiation field is generated internally or is imposed externally, the study of how it interacts with the atmosphere is embodied in the theory of radiative transfer. Many authors have dealt with this theory in various contexts. Monographs include those by Kouiganoff (1952), Woolley Stibbs (1953), Goody (1964), and Goody Yung (1989). A standard text is by Chandrasekhar (1950), which treats the subject as a branch of mathematical physics. The emphasis is on scattered sunlight in planetary atmospheres and on various problems of astrophysical interest. 

While a proper solution of the radiative transfer problem in media at B Bqed — 4.4 x 1013 G has necessarily to wait for a description in terms of the Stokes parameters, the search for the proton cyclotron feature in the spectra of AXPs and SGRs begun. Up to now no evidence for the proton line has been found in the thermal components of SGRs and AXPs, although these... 

An adequate answer to these questions must be based on the detailed study of the processes of formation and growth of dust particles in these environments. However, dust formation cannot be considered as an isolated problem because due to their huge absorption cross sections even a small contamination of the atmospheres by circumstellar dust may have a significant influence on the radiative transfer and (via energy- and momentum-coupling) on the thermodynamic and hydrodynamic structure of the dust forming shell. 

Toor, J. S. and Boni, A. A., "A Model Combustor Heat Transfer Problem-Radiative Transfer Between Surfaces With Nongray Gases and Soot," Heat Transfer 1974, Vol. 1, Proc. of 5th International Heat Transfer Conference, Tokyo, Japan, 1974. 

F. R. Steward, Radiative Heat Transfer Associated with Fire Problems, Part IV of Heat Transfer in Fires thermophysics, social aspects, economic impact, P. L, Blackshear, ed., Scripta Book Co., New York Wiley, 1974, 273-486. 

The bed-to-wall heat-transfer coefiicient in a fluidized bed at high temperatures is larger than at room temperature (Y19). Questions have been raised about the effect of radiative heat transfer at high temperatures (B12, Y19), and more studies are necessary on this problem. 

The difference between the fourth power of the temperature of the emitter and that of the body which receives the radiation, is characteristic of radiative exchange. This temperature dependence is found in numerous radiative heat transfer problems involving grey radiators. 

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