Two-flux and Green"s function method for transient radiative transfer in a semitransparent layer by Robert Siegel

Cover of: Two-flux and Green

Published by National Aeronautics and Space Administration, National Technical Information Service, distributor in [Washington, D.C, Springfield, Va .

Written in English

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Subjects:

  • Conductive heat transfer.,
  • Convective heat transfer.,
  • Radiative transfer.,
  • Cooling.,
  • Temperature distribution.,
  • Transient heating.,
  • Absorptivity.

Edition Notes

Book details

Other titlesTwo flux and Green"s function method for transient radiative transfer in a semitransparent layer
StatementRobert Siegel.
SeriesNASA-TM -- 111700, NASA technical memorandum -- 111700..
ContributionsUnited States. National Aeronautics and Space Administration.
The Physical Object
FormatMicroform
Pagination1 v.
ID Numbers
Open LibraryOL17124862M

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Effect of scattering on temperature distributions in The two-flux method was used to obtain transient solu- a layer initially at uniform temperature after exposure to lions for a plane layer including internal reflections and scat- radiation on one side and convective cooling on the other by: Two-flux and Green's function method for transient radiative transfer in a semitransparent layer.

[Robert Siegel; United States. National Aeronautics and Space Administration.]. The two-flux method was used to obtain transient solutions for a plane layer including internal reflections and scattering. The layer was initially at uniform temperature, and was heated or cooled by external radiation and convection.

The two-flux equations were examined as a means for evaluating the radiative flux gradient in the transient energy equation. A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation.

Each boundary of the layer is exposed to a hot or cold radiative environment Cited by: 9. A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation.

Each boundary of the layer is exposed to a hot or cold radiative environment Author: Robert Siegel. and convection. The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation.

An advantage of the two-flux method is that isotropic scattering is included without added complexity. The layer refractive indices are larger than one. Discrete ordinates solution of coupled conductive radiative heat transfer in a two-layer slab with Fresnel interfaces subject to diffuse and obliquely collimated irradiation Journal of Quantitative Spectroscopy and Radiative Transfer, Vol.

84, No. 4Cited by: The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity.

The layer refractive indices are larger than by: The two-flux radiative transfer equations are solved by deriving a Green's function. This yields the local radiative heat source needed to numerically solve the transient energy equation. An advantage of the two-flux method is that isotropic scattering is included without added complexity.

The layer refractive indices are larger than : Robert Siegel. This work considers transient radiative and conductive heat transfer in a semitransparent layer of ceramic, submitted to several thermal and radiative boundary conditions.

Siegel, R.,“Two-Flux and Green’s Function Method for Transient Radiative Transfer in a Semitransparent Layer,” Proceedings of the 1 st International Symposium on Radiative Transfer, Kus¸adasi, Turkey, Radiative Transfer I, Begeil House, New York, pp. –Cited by: Two-flux and Green's function method for transient radiative transfer in a semitransparent layer [microf Prediction of the thermal environment and thermal response of simple panels exposed to radiant heat [mic Two-flux Green's function analysis for transient spectral radiation in a composite [microform] / R.

Siegel. Transient coupled radiative and conductive heat transfer in a three-layer absorbing and isotropically scattering composite with semitransparent specular interfaces and surfaces is investigated.

The transient energy equation is solved by the full implicit control-volume method in combination with spectral band by: method, and transient solutions were obtained for optical thicknesses of a plane layer up to 8. For optical thicknesses up to 50, a Green's function method was developed (ref.

Transient two-flux solutions were compared with exact numerical solutions of the radiative transfer equations from reference 4, and very good agreement was obtained.

This. The transient coupled radiative and conductive heat transfer in a semitransparent composite under the complex boundary conditions is investigated by the ray tracing method in combination with Hottel’s zonal method and the control-volume method.

The composite is composed of two plane layers of nonscattering semitransparent media with the different thermophysical properties in each : Ping-Yang Wang, He-Ping Tan, Xin-Lin Xia. A Green's function solution is derived for the two-flux radiative transfer equations, and this solution is coupled with the transient energy equation.

The refractive indices of the layers are. Transient combined conduction and radiation with anisotropic scattering. Jen-Hui Tsai and Cited by: full radiative transfer problem had to be solved anew in each iteration because the lower boundary condi-tion had changed. In this paper, we use the Green’s function method to derive an analytical solution for the radiance over a surface with arbitrary reflective properties.

The concept of the Green’s function, developed in neutron. A Green`s function solution is derived for the two-flux radiative transfer equations, and this solution is coupled with the transient energy equation. The refractive indices of the layers are larger than one, and the analysis includes internal reflections at the boundaries and.

In combination with ray tracing method, spectral band model and the Hottel and Sarofim's zonal method, the radiative transfer coefficients (RTCs) of the multi-layer composite are deduced.

The RTCs are used to calculate the radiative heat source term in the transient energy control equation, which is solved by the fully implicit discrete control Cited by: Loureiro FF, Mansur WJ () A new family of time integration methods for heat conduction problems using numerical green’s function.

Comput Mech – zbMATH MathSciNet Google Scholar Chapter 1 Basics of radiation transfer theory Planck function: blackbody radiation The source function S is the value that the intensity acquires in a homogeneous medium when τ # 1.

From thermodynamics we know that this radiation field must be a thermal and this radiation goes through a layer File Size: 70KB. two-flux and green's function method for transient radiative transfer in a semitransparent layer transient radiative transfer sunil kumar, kunal mitra doi: /ichmtradtransfproc $ inverse problems of radiative transfer in absorbing, emitting and scattering media m.

ozisik, j. bokar. What makes radiative transfer hard, and how to solve it - An introduction If we would, at all times and at all locations, know the valuesof j ν and α ν,thenwhat we have learned in Chapter 3 would be enough to understand the topic of radiative transfer.

Of course, some technical details still. The lattice Boltzmann method (LBM) is extended to solve transient radiative transfer in one-dimensional slab containing scattering media subjected to a collimated short laser irradiation.

By using a fully implicit backward differencing scheme to discretize the transient term in the radiative transfer equation, a new type of lattice structure is devised. The Equation of Radiative Transfer The method used in this study to solve the equation of radiative transfer is the successive orders of scattering technique.

It was chosen for two main reasons; 1) it is physically intuitive, especially as the physics remains clear through the mathematical formalism, and hence relatively easy to code; and 2) it.

ANALYTICAL HEAT TRANSFER Mihir Sen Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN May 3,   Heat conductivity in a wall is a traditional problem, and there are different numerical methods to solve it, such as finite difference method, 1,2 harmonic method, 3,4 response coefficient method, 5 –7 Laplace’s method, 8,9 and Z-transfer function.

10,11 But in some way, they are not easy to use because calculating time is strongly limited by time step and mesh size, regular temperature Cited by: 2. 10 ⋅ Solution of the Equation of Radiative Transfer Figure shows the geometry for a plane-parallel slab. Note that there are inward (µ0) directed streams of radiation.

The boundary conditions necessary for the solution are specified at τν = 0, and τν = τ0. Since the equation of transfer is a first order linear equation, only oneFile Size: KB.

Solving Transient Conduction And Radiation Using Finite Volume Method 83 transfer, the finite volume method (FVM) is extensively used to compute the radiative information. This method is a variant of the DOM. It does not suffer from the false-scattering as in DOM and the ray-effect is also less pronounced as compared to other Size: 1MB.

The Radiative Transfer Equation Ross Bannister, January/April Derivation of the radiative transfer equation As a pencil of radiation traverses a layer of the atmosphere, the radiance is modified in three ways (acting to either increase (+) or decrease (-) the radiation).

• Size: 19KB. Methods for solving the radiative transfer equation with multiple scattering. Part 4: Monte Carlo method. Radiative transfer methods for inhomogeneous clouds. Objectives: 1. Monte Carlo method. Examples of radiative transfer methods for inhomogeneous clouds: 1D with a cloud fraction, independent column approximation (ICA), and SHDOM.

Day 2 Lecture 2 Basics about radiative transfer - Bruno Carli 3 DRAGON ADVANCED TRAINING COURSE IN ATMOSPHERE REMOTE SENSING Radiative Transfer Equation The specific intensity of radiation is the energy flux per unit time, unit frequency, unit solid angle and unit area normal to the direction of Size: KB.

Two-flux and Green's function method for transient radiative transfer Robert Siegel Transient heat transfer in a semitransparent radiating layer with boun Robert Siegel1 book Richard H.

Comfort, 1 book Kuan-Chen Fu, 1 book Aaron Barnes, 1 book S. Anghaie, 1 book. Radiative Transfer In Spheres 2 model is valid for transfer problems in central symmetry whenever the radiation field is a compe-tition of both the centripetal and the centrifugal flow of energy in homogeneous and heterogene-ous media.

The solution of these diffusion equations is delightfully simple and accurate. Zeeman line transfer: the Feautrier method Lambda operator method for Zeeman line transfer Solution of the transfer equation for polarized radiation Polarization approximate lambda iteration (PALI) methods Exercises References Chapter 13 Multi-dimensional radiative transfer Introduction   This study contains the derivation of an infinite space Green’s function of the time-dependent radiative transfer equation in an anisotropically scattering medium based on analytical approaches.

The final solutions are analytical regarding the time variable and given by a superposition of real and complex exponential by: Radiative Transfer overhead, then from () the flux density of solar radiation at the top of the Earth’s atmosphere is where!" is the arc of solid angle subtended by the sun in the sky.

Because!" is very small, we can ignore the variations in cos#in the integration. With this so-called parallel beam approximation,the inte-File Size: KB.

P-N model, diffuse approximation, and two-flux method have been discussed. Tan and Hsu [9] developed an integral equation formulation for transient radiative transfer. Guo and Kumar [10] extended the radiation element method to consider the transient radiative transfer.

Mitra et al. [11]File Size: KB. Radiative Transfer 98 () – Modified method of characteristics in transient radiation transfer Kamal M. Katika, Laurent Pilon Mechanical and Aerospace Engineering Department, Henri Samueli School of Engineering and Applied Science, University of California, Westwood Plaza, RoomLos Angeles - Los Angeles, CAUSA.

- 1 - On the Derivation of Vector Radiative Transfer Equation for Polarized Radiative Transport in Graded Index Media J.M. Zhaoa, J.Y. Tanb, L.H. Liua* a School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street, HarbinPeople’s Republic of ChinaCited by: 8.dynamics (CFD) [13] problems and then extended to two-dimensional radiative transfer problem by Chai et al.

[14, 15]. They found very promising results for different 2D problems. Coelho et al. [16] used this method with the FVM and the DOM to predict radiative heat transfer in enclosures containing obstacles of very small thickness (baffles).Details.

The equation of radiative transfer is given by, where is the specific intensity (red line), is the gas density, is the opacity or absorption coefficient, and is the emission coefficient. The equation describes how incident radiation is affected along a path define the source function as well as the optical depth.

and can rewrite the equation of radiative transfer in terms.

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