Radiation Heat Transfer in a Spherical Enclosure Containing a Participating, Heat-Generating Gas

Abstract

An analysis is made of the thermal radiation in an absorbing-emitting nonisothermal gas confined in a hollow spherical enclosure or in the space between two concentric spheres. The gas is gray and contains a volume heat source, while the bounding walls are black and isothermal. The conservation of energy principle yields an integral equation which has been solved for a wide range of geometric and radiative conditions. It is found that as the absorption coefficient increases in a fixed geometry, the gas temperature decreases and becomes more nonuniform. On the other hand, as the enclosure size increases, the gas temperature increases and becomes more nonuniform. An approximate analysis using a conduction-type transfer law has been carried out, and the results are compared with the integral equation solutions.

The effects of radiative heat transfer during the melting process of a high temperature phase change material confined in a spherical shell

“…In their model the scattering of radiation within the medium was considered and the influence of the differential approximation technique on the wall heat fluxes was presented. Ryhming [15], Viskanta and Crosbie [16] and Jia et al [17] extended the analysis of Sparrow et al [11] to include a uniform but different temperature at the bounded surfaces. It should be mentioned that in the results reported by Ryhming [15] three values of inner to outer wall temperature ratios T 1 /T 2 = 2, 5 and 25 were reported.…”

“…A simplified analytical method, based on a diffusion approximation, for calculating radiation heat transfer in the aforementioned system has been presented by Konakov [10]. Sparrow et al [11] have discussed the contribution of the absorption coefficient and the size of the container on the medium temperature distribution. In the model, an absorbing-emitting, gray gas was assumed as a participating medium while uniform and equal temperatures have been imposed at the shell surfaces.…”

Radiation From Nonisothermal Gases to the Stagnation Point of a Hypersonic Blunt Body

“…[9] numerically. The temperature and mass absorption coefficient as a function of location may be varied in any fashion.…”

“…The amount of radiation emitted by this elementary volume per unit time is (9)(10)(11) 4KaT*-2Trr 2 sm<l)d(i)dr [3] The energy leaving the elementary volume in a solid angle dcois 2Xo-7 74 r 2 sin</> d<t>drdu [4] As a result of absorption, the amount of energy which arrives at dA at a distance I from the elementary volume is dQ = 2KaT 4 r 2 sm(l)d<f)drdu exp(-C" Kdl) [5] where the absorption coefficient K is not constant but a function of location. The solid angle dw corresponding to an elementary area dA at the stagnation point is…”