Modified Zonal Method for Thin Solid Semi-Transparent Media With Reflective Boundary

2007 ◽  
Author(s):  
Georges M. El-Hitti ◽  
Maroun Nemer ◽  
Khalil El Khoury ◽  
Denis Coldic
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transient Operation ◽  
Scattering Media ◽  
Zonal Method ◽  
Total Heat Transfer ◽  
Transfer Factors ◽  
Transparent Media ◽  
The Matrix ◽  
Time Required

In this paper a detailed description of a modified zonal method used for the prediction of transient operation in glass treatment furnaces is presented. This method calculates the radiative transfer factors for scenes containing both diffusive surfaces and absorbing-emitting/non-scattering media with high indices of refraction all embedded in a totally transparent atmosphere. The method used combines the flux plans approximation for calculation of the view factors, the plating algorithm originally developed by Edwards for calculation of the total heat transfer factors, and finally, Emery’s equations for deduction of the surface-volume and volume-volume heat transfer factors. The matrix of radiative transfer is then simplified by eliminating the low energy level factors, thus rendering the matrix hollow and thereafter decreasing the time required for calculation.

Radiative Heat Transfer in Multidimensional Emitting, Absorbing, and Anisotropic Scattering Media—Mathematical Formulation and Numerical Method

1989 ◽  
Vol 111 (1) ◽  
pp. 141-147 ◽  
Author(s):  
Zhiqiang Tan
Keyword(s):  
Heat Transfer ◽  
Integral Equations ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Numerical Technique ◽  
Mathematical Formulation ◽  
Internal Heat ◽  
Anisotropic Scattering ◽  
Scattering Media ◽  
Zonal Method

Thermal radiative transmission in multidimensional emitting, absorbing, and anisotropic scattering media is studied in this paper. In the first part, starting from basic formulae of radiative heat transfer, a set of integral equations for the problem is derived. Then the product-integration method is applied to discretize the integral equations. This method, while analogous to Hottel’s zonal method or Razzaque’s finite element method, requires evaluation of only three or two-dimensional integrals for three-dimensional systems. Finally the formulation and the numerical technique are applied to the problems of thermal radiation in emitting, absorbing, and linearly anisotropic scattering planar and square media with gray surfaces and with or without internal heat generations. Computed results are discussed and compared with available data.

Analytical Solution Under Two-Flux Approximation to Radiative Heat Transfer in Absorbing Emitting and Anisotropically Scattering Medium

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Xin-Lin Xia ◽  
Dong-Hui Li ◽  
Feng-Xian Sun
Keyword(s):  
Heat Transfer ◽  
High Temperature ◽  
Radiative Transfer ◽  
Analytical Solution ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Thermal Protection ◽  
Isotropic Scattering ◽  
Scattering Media ◽  
Flux Approximation

Radiative transfer in absorbing, emitting, and highly anisotropically scattering media is widely encountered in high temperature applications such as pulverized coal firing furnaces and high temperature thermal protection materials. Efficient and effective solution methods for the transfer process are very crucial, especially in thermal radiation related reverse problems and optimization designs. In this study, the analytical solution for radiative heat transfer in an absorbing, emitting, and anisotropically scattering slab between two parallel gray walls are derived under the two-flux approximation. Explicit expression for the radiative heat flux in a slab is obtained under two-flux approximation. The reliability and adaptability of an analytical solution is examined in case studies by comparing with the Monte Carlo results. Comparative studies indicate that the analytical solution can be used in radiative transfer calculation in an absorbing emitting and anisotropically scattering slab. It is much more applicable in a forward and isotropic scattering slab than in an absorbing one, especially in a forward scattering slab. Because of simplicity and high computing efficiency with the analytical solution, it may be useful in reverse radiative transfer problems, in optimization design, and in developing some numerical schemes on radiative heat transfer.

An Acceleration Technique for the Computation of Participating Radiative Heat Transfer

2009 ◽  
Author(s):  
Sanjay R. Mathur ◽  
Jayathi Y. Murthy
Keyword(s):  
Heat Transfer ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Radiation Heat Transfer ◽  
Solution Procedure ◽  
Discrete Ordinates ◽  
Average Intensity ◽  
Scattering Media ◽  
Acceleration Techniques

It is known that the finite volume and discrete ordinates methods for computing participating radiation are slow to converge when the optical thickness of the medium becomes large. This is a result of the sequential solution procedure usually employed to solve the directional intensities, which couples the ordinate directions and the energy equation loosely. Previously published acceleration techniques have sought to employ a governing equation for the angular-average of the radiation intensity to promote inter-directional coupling. These techniques have not always been successful, and even where successful, have been found to destroy the conservation properties of the radiative transfer equation. In this paper, we develop an algorithm called Multigrid Acceleration using Global Intensity Correction (MAGIC) which employs a multigrid solution of the average intensity and energy equations to significantly accelerate convergence, while ensuring that the conservative property of the radiative transfer equation is preserved. The method is shown to perform well for radiation heat transfer problems in absorbing, emitting and scattering media, both and without radiative equilibrium, and across a range of optical thicknesses.

Heat Transfer Enhancement in Separation Process of Ethanol from Ethanol Water Mixture by Using Surfactants

2020 ◽  
pp. 9-14 ◽  
Author(s):  
Acharya Anil Ramchandra ◽  
R. Kadam ◽  
A. T. Pise
Keyword(s):  
Heat Transfer ◽  
Ammonium Chloride ◽  
Sodium Dodecyl ◽  
Water Mixture ◽  
Transfer Enhancement ◽  
Surface Tension Reduction ◽  
Surface Active Agents ◽  
Surface Active ◽  
Time Required

Here the investigations are done while distillation of ethanol-water mixture for separating ethanol from fermentation process. Focus is to study reduction in time required and hence saving in energy for the distillation process of ethanol-water mixture under the influence of surface-active agents (Surfactants). This novelty is from observation of these surfactants to enhance heat transfer rate because of surface tension reduction in aqueous solutions. SDS (Sodium Dodecyl Sulphate), NH4Cl (Ammonium Chloride) and SLBS (Sodium lauryl benzene sulphonate) surfactants in different concentration are experimented. The concentration of these surfactant is varied from 1700 ppm to 2800 ppm. This range is decided by observing critical micelle concentration of used surfactants. Results showed that time is reduced and hence energy consumption is also reduced. Results shown by NH4Cl are found to be more useful as it is ecofriendly surfactant which is not affecting ethanol-water mixture. Use of ammonium chloride as surfactant in distillation is actually useful to reduce energy without hampering the quality of process is the novelty of this work.

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