Molecular Gas Band Radiation in Cylinders

Abstract

The radiative heat flux in a molecular gas within a cylinder is formulated in terms of an axial band absorptance. The axial band absorptance function is used to reduce the two angular, one spatial, and one spectral integrals encountered to one angular and one spatial integral such as is encountered in radiative transfer problems with spherical symmetry. A closed form is obtained for the axial band absorptance for the exponential-winged band model. Illustrative results are presented for a cylindrical gas volume with trapezoidal, parabolic, or Gaussian temperature profile. Mean beam length, absorptivity, and emissivity of a cylinder of gas are obtained as a function of the optical depth at the band head.

Nongray Particulate Radiation in an Isothermal Cylindrical Medium

“…A simple physical interpretation of its behavior is obtained by noting that when T w = OK the radial flux is only a consequence of medium emission: q"(k) = F(q, k)aT e 4 . Under optically thin conditions, energy emitted within the cylinder 0 < r' < r escapes from it without being absorbed.…”

“…1.000 1.000 1.000 1 Exact solution 2 Modified gray solution 3 Solution using D n (x) = a n e~b" x and Wien's distribution (corrected) 4 Values obtained by interpolation between 0.9 and 1.1 results where T g = BCr 0 T g /C 2 = 3.91 q (24)…”

“…The second approximate solution investigated here accounts exactly for the nongray properties of the particles and instead performs the geometric integrations in an approximate way. The functions D n (x) appearing in equation 2are approximated as D n (x) =* a n e~b" x after the manner of [3,4]. In addition, Wien's distribution, It>\ w -2Ci\~b exp (-C2/XT), is used to approximate the Planck function.…”

“…The equations describing the radiative heat transfer in an infinitely long cylindrical medium are well known [1,2]. Using the radial radiative flux formulation of [2], several investigators have studied radiative transfer in nongray gaseous media having discrete absorption bands [3][4][5][6][7][8][9][10]. In [3][4][5] radiation was taken to be the only mode of energy transfer while in [6][7][8][9][10] combined modes were considered.…”

Models for Infrared Atmospheric Radiation

“…In recent years, however, attempts have been made to incorporate the angular integration of the equation of radiative transfer by introducing the so-called axial or slab band absorptance models [93,99,100,106]. By use of these models, in certain cases, the spectral as well as angular integration in the radiative flux equations can be avoided.…”