Geometric Factors for Radiative Heat Transfer Through an Absorbing Medium in Cartesian Co-ordinates

1960 ◽  
Vol 82 (4) ◽  
pp. 360-368 ◽  
Author(s):  
A. K. Oppenheim ◽  
J. T. Bevans
Keyword(s):  
Radiative Heat ◽  
Unit Area ◽  
Diffuse Radiation ◽  
Radiation Beam ◽  
Actual Distribution ◽  
Absorbing Medium ◽  
One Dimensional ◽  
Geometric Factors ◽  
Absorption Law ◽  
Dimensional Integral

Heat flux conveyed by diffuse radiation from surface A1 and A2 through an absorbing medium is expressed by the relation Q1−2=J1 ∫A1×A2f(l12)(cosθ1cosθ2/πl122)dA1dA2 where J1 is the radiosity of A1 (sum of the emitted, reflected, and transmitted flux per unit area), l12 is the radiation beam (the distance between surface elements dA1 and dA2), θ1 and θ2 are the angles between the radiation beam and the normals to the surface elements, and f(l12) is the function describing the absorption law. The foregoing four-dimensional integral is transformed into a sum of one-dimensional integrals for the cases of opposite-parallel and adjoining-perpendicular rectangles. The results are suitable for numerical integration with any total absorption law obtained from the actual distribution of monochromatic absorptivities over the whole spectrum.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

Wavelets in the Solution of Nongray Radiative Heat Transfer Equation

1998 ◽  
Vol 120 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Y. Bayazitoglu ◽  
B. Y. Wang
Keyword(s):  
Transfer Equation ◽  
Solution Method ◽  
Radiative Heat ◽  
Radiative Transfer Equation ◽  
Basis Functions ◽  
Wavelet Basis ◽  
System Of Equations ◽  
Heat Transfer Equation ◽  
One Dimensional ◽  
The One

The wavelet basis functions are introduced into the radiative transfer equation in the frequency domain. The intensity of radiation is expanded in terms of Daubechies’ wrapped-around wavelet functions. It is shown that the wavelet basis approach to modeling nongrayness can be incorporated into any solution method for the equation of transfer. In this paper the resulting system of equations is solved for the one-dimensional radiative equilibrium problem using the P-N approximation.

scholarly journals The on-axis magnetic well and Mercier's criterion for arbitrary stellarator geometries

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
P. Kim ◽  
R. Jorge ◽  
W. Dorland
Keyword(s):  
Magnetic Field ◽  
Original Work ◽  
Three Dimensional ◽  
Radial Distance ◽  
Analytical Form ◽  
One Dimensional ◽  
Modern Notation ◽  
Magnetic Well ◽  
First Time ◽  
Dimensional Integral

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities for arbitrary three-dimensional magnetic field geometries is derived. For this purpose, a near-axis expansion based on a direct coordinate approach is used by expressing the toroidal magnetic flux in terms of powers of the radial distance to the magnetic axis. For the first time, the magnetic well and Mercier's criterion are then written as a one-dimensional integral with respect to the axis arclength. When compared with the original work of Mercier, the derivation here is presented using modern notation and in a more streamlined manner that highlights essential steps. Finally, these expressions are verified numerically using several quasisymmetric and non-quasisymmetric stellarator configurations including Wendelstein 7-X.

Handling of Collimated Irradiation on a Plane-Parallel Participating Medium

2000 ◽  
Author(s):  
Christian Proulx ◽  
Daniel R. Rousse ◽  
Rodolphe Vaillon ◽  
Jean-François Sacadura
Keyword(s):  
Heat Flux ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Radiative Heat Flux ◽  
Scattering Media ◽  
One Dimensional ◽  
Plane Parallel ◽  
Collimated Beam ◽  
Good Agreement

Abstract This article presents selected results of a study comparing two procedures for the treatment of collimated irradiation impinging on one boundary of a participating one-dimensional plane-parallel medium. These procedures are implemented in a CVFEM used to calculate the radiative heat flux and source. Both isotropically and anisotropically scattering media are considered. The results presented show that both procedures provide results in good agreement with those obtained using a Monte Carlo method, when the collimated beam impinges normally.

Line-by-Line Random-Number Database for Monte Carlo Simulations of Radiation in Combustion System

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Tao Ren ◽  
Michael F. Modest
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Heat ◽  
Random Number ◽  
Test Cases ◽  
Combustion System ◽  
Absorption Coefficients ◽  
One Dimensional ◽  
The Monte Carlo Method

With today's computational capabilities, it has become possible to conduct line-by-line (LBL) accurate radiative heat transfer calculations in spectrally highly nongray combustion systems using the Monte Carlo method. In these calculations, wavenumbers carried by photon bundles must be determined in a statistically meaningful way. The wavenumbers for the emitting photons are found from a database, which tabulates wavenumber–random number relations for each species. In order to cover most conditions found in industrial practices, a database tabulating these relations for CO2, H2O, CO, CH4, C2H4, and soot is constructed to determine emission wavenumbers and absorption coefficients for mixtures at temperatures up to 3000 K and total pressures up to 80 bar. The accuracy of the database is tested by reconstructing absorption coefficient spectra from the tabulated database. One-dimensional test cases are used to validate the database against analytical LBL solutions. Sample calculations are also conducted for a luminous flame and a gas turbine combustion burner. The database is available from the author's website upon request.

scholarly journals A Fast-Converging Scheme for the Electromagnetic Scattering from a Thin Dielectric Disk

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1451
Author(s):  
Mario Lucido ◽  
Mykhaylo V. Balaban ◽  
Sergii Dukhopelnykov ◽  
Alexander I. Nosich
Keyword(s):  
Integral Equations ◽  
Electromagnetic Scattering ◽  
Disk Surface ◽  
Hankel Transform ◽  
Transform Domain ◽  
One Dimensional ◽  
Analytical Technique ◽  
Generalized Boundary Conditions ◽  
Dielectric Disk ◽  
Dimensional Integral

In this paper, the analysis of the electromagnetic scattering from a thin dielectric disk is formulated as two sets of one-dimensional integral equations in the vector Hankel transform domain by taking advantage of the revolution symmetry of the problem and by imposing the generalized boundary conditions on the disk surface. The problem is further simplified by means of Helmholtz decomposition, which allows to introduce new scalar unknows in the spectral domain. Galerkin method with complete sets of orthogonal eigenfunctions of the static parts of the integral operators, reconstructing the physical behavior of the fields, as expansion bases, is applied to discretize the integral equations. The obtained matrix equations are Fredholm second-kind equations whose coefficients are efficiently numerically evaluated by means of a suitable analytical technique. Numerical results and comparisons with the commercial software CST Microwave Studio are provided showing the accuracy and efficiency of the proposed technique.

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