Max A Heaslet

Radiative transport and wall temperature slip in an absorbing planar medium

Abstract Radiative heat transfer through a nonisothermal absorbing and emitting grey gas between heated walls is studied. Specific attention is directed toward the evaluation of temperature near the walls and of the precise evaluation of energy flux by means of methods and tabulated functions studied by Chandrasekhar and Ambartsumian. The precision achieved permits an assessment of the accuracy of existing approximate methods and of the errors incurred in numerical solutions of the governing equations.

PREDICTIONS OF THE STRUCTURE OF RADIATION-RESISTED SHOCK WAVES

The continuum, inviscid‐flow equations of gas dynamics are used to predict the effect of thermal radiation on the internal structure of a shock wave. Numerical solutions of the governing equations show that considerable variation in the nature of the temperature and velocity profiles occurs, depending on the magnitude of the over‐all velocity change and the relative strengths of the radiative and convective energy fluxes. A unique feature of the work is the demonstration that, for a range of parametric values, discontinuities necessarily arise in the temperature and velocity profiles. The results include: (a) numerical integration of the basic equations for a representative range of parameters; (b) an analytic study of the equations by means of expansion procedures; (c) a study of the uniqueness of the solutions; (d) proof that previously published investigations cannot be generally applicable since they are restricted to continuous solutions; (e) prediction within a strong shock of a temperature maximum ...

Theoretical predictions of radiative transfer in a homogenous cylindrical medium

Abstract Analytical and numerical methods of predicting radiative transfer are developed particularly for a homogeneous medium with constant extinction coefficient in a circularly symmetric, cylindrical region. Efficient formulations of the influence functions in the governing integral equation and the flux integral are given. Applications of the results include an integral method of calculating flux losses associated with radial distributions of internal sources of energy release, and predictions based on the use of simplified methods of approximation. Planar and spherical regions are also considered since comparisons between approximate and precise predictions then become possible. Cases of physical interest include both conservative and noncervative radiative transfer; for example, thermal radiation in the continuum regime as well as spectral line emission from an isothermal plasma with two-level impurity ions.

Application of invariance principles to a radiative transfer problem in a homogeneous spherical medium

Abstract The problem of steady-state, radiative transport through a finite, spherically symmetric and uniformly generating medium is considered. The governing equations are applicable to the study of thermal radiation in a heat generating grey gas as well as to the idealization proposed by Cuperman, Engelmann, and Oxenius to study radiation loss in a homogeneous, isothermal spherical plasma due to an optically thick spectral line associated with the de-excitation energy of two-level impurity ions. The analysis is related directly to the study of a one-dimensional problem in a slab of finite optical thickness. This equivalence then permits the direct application of results based on the invariance principles of Ambartsumian and Chandrasekhar. In particular, exact expressions are derived for the source function at the spherical boundary and the radiative flux loss. These results are expressed in terms of tabulated moments of Chandrasekhars X and Y functions.

Theoretical predictions of spectral line formation by noncoherent scattering.

Abstract The formation of spectral lines by noncoherent scattering with a frequency-independent source function is predicted theoretically for a plane-parallel medium of finite optical thickness. The problem is reduced, as in earlier investigations of monochromatic scattering, to one of determining two standard functions X and Y or, in the case of a semi-infinite medium, a single function H . Analytic approximations of these functions are discussed and representative numerical calculations are included. Particular attention is devoted to Doppler broadening. Comparisons of both analytic and tabular results are made with purely numerical studies of particular cases.

Radiative source-function predictions for finite and semi-infinite non-conservative atmospheres.

The probabilistic method of Sobolev and Cases method of normal mode expansion are combined to predict source-function distributions for radiative transfer in non-conservative, planeparallel atmospheres. The solutions obtained for semi-infinite atmospheres are exact and can be expressed in terms of functions and parameters associated with the non-conservative Milne problem. The predictions for finite atmospheres are approximate and are constructed from the semi-infinite solutions. Tabular values of the requisite functions and parameters are provided to facilitate rapid numerical evaluation of the solutions. Although the finite solutions corresponds to the zeroth-order (optically thick) approximation by Cases method, an assessment of the accuracy indicates that the results are useful for optical thicknesses as small as one or even less. The close connection between the results obtained and the method of point-direction gain of Van de Hulst is discussed.

Radiative transport in an absorbing planar medium II. Predictions of radiative source functions

Source function solution for radiative heat transfer through nonisothermal absorbing and emitting gray gas

Radiation flux from a slab or sphere

Green formula and moment functions, predicting rate of radiative energy loss from boundaries of absorbing-emitting slab or sphere

Radiative heat-transfer calculations for infinite shells with circular-arc sections, including effects of an external source field

Abstract Diffuse radiation from infinite shells with circular-arc cross-sections is analyzed for cases involving external source fields of either diffuse or parallel radiation. The governing integral equations are derived under conditions corresponding to a modified grey-body analysis, and the inversions given in closed form. Specific applications provide local heat transfer corresponding to constant shell temperature, local temperature corresponding to constant heat transfer, and predictions of equilibrium temperatures when the shell is a thermal shield. Comparisons are made with similar calculations for hemispherical shields.

Cylindrical sections with uniform diffuse-radiation characteristics

Abstract Calculations are made that determine the cross-sectional shapes of cylindrical or twodimensional cavities that exhibit uniform radiation characteristics when the interior surface is a diffuse emitter. Immediate applications arise for concave cylindrical radiators or grooves on the surface of an opaque material when temperature is held fixed and uniform emission or heat flux is desired. Geometric interrelations between these and similar results for axially symmetric concavities are determined.