A Novel, Noniterative Inverse Boundary Design Regularized Solution Technique Using the Backward Monte Carlo Method

In this paper, the inverse radiation boundary problem is solved using a simplified backward Monte Carlo method (MCM) for cases in which radiation is the dominant mode of heat transfer (i.e., radiative equilibrium). For an N-surface enclosure, N2 radiative transfer factors are required to carry out the radiant exchange calculations. In this paper, it is shown that when the enclosure is comprised of some adiabatic surfaces (as is nearly always the case in radiative furnaces), this number can be reduced considerably. This reduction in the required number of distribution factors causes a clear simplification in the formulation of the inverse problem and a substantial reduction in the computational time. After presenting the formulation for the inverse problem, standard test cases are solved to demonstrate the efficiency and the accuracy of the proposed method.

Radiative Characteristic of Spherical Cavities With Specular Reflectivity Component

An exact analytical method is presented for determination of emissive as well as absorptive performance of spherical cavities having diffuse-specular reflective walls. The method presented utilizes a novel coordinate transformation technique, which provides convenient means for setting up the governing radiant exchange integral equations. These equations are then solved by the usual iterative method devized for the Fredholm integral equation of the second kind. The suggested coordinate transformation is also utilized for determination of directional absorptivity of a fully specular spherical cavity when collimated radiation enters through its mouth from a specified direction. Results show that for a spherical cavity the dependence of the apparent emissivity on the degree of specularity is high when the emissivity of the cavity wall is low, but this dependence decreases as the emissivity of the cavity wall increases. Also there are situations, unlike cases of cylindrical and conical cavities, for which the purely diffuse spherical cavity is a more efficient emitter than the purely specular cavity having an identical geometry and wall emissivity. Moreover, it is shown that the apparent directional absorptivity of specular spherical cavities having small openings becomes highly fluctuating as the direction of the incident radiation changes

Reordering the Absorption Coefficient Within the Wide Band for Predicting Gaseous Radiant Exchange

The “exact” calculation of the radiant transfer in gaseous enclosures has remained impractical for design; the highly complex nature of the absorption spectrum of the gases has meant that an inordinately large computational effort is required to effect an exact answer. In this paper we show how the complex absorption distribution for an isothermal gas can be replaced by a set of smooth curves. This procedure can be visualized as one of actually reordering the full complex absorption distribution within each vibration-rotation band, and then replacing it by a smooth curve. Such a smooth curve can then be readily approximated by a stepwise function, and radiant exchange calculations can be carried out at each step and then summed over all the steps to get the total exchange. This paper explains how the reordered curve can be obtained and gives some sample plots of the reordered absorption coefficient curve. Fitted functions for the rearranged curves have been provided, and some solutions to the radiant exchange problems are given and compared to line-by-line solutions. About 50 to 200 steps in the stepwise curve are found to be adequate in order to obtain an answer within a few percent of the exact answer.