A Conservative Formulation of the Discrete Transfer Method

1997 ◽  
Vol 119 (1) ◽  
pp. 118-128 ◽  
Author(s):  
P. J. Coelho ◽  
M. G. Carvalho
Keyword(s):  
Heat Transfer ◽  
Energy Conservation ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Three Dimensional ◽  
Isotropic Scattering ◽  
Two Dimensional ◽  
Scattering Media ◽  
Combustion Chambers ◽  
Transfer Method

The discrete transfer method, often employed to calculate radiative heat transfer in combustion chambers, is not conservative. The reason for this behavior is examined and a conservative formulation is proposed and evaluated. A simple treatment of isotropic scattering media is also presented. The original and the conservative formulation of the method are applied to two-dimensional and three-dimensional enclosures containing a participating medium. It is shown that the accuracy of the original and the conservative formulation is very similar, but the proposed formulation has the advantage of ensuring energy conservation.

Coupling a Discrete Transfer Method to a View Factors Technique for Radiative Heat Transfer Modeling in Industrial Furnaces

2005 ◽  
Author(s):  
Youssef Joumani ◽  
Guillaume Mougin ◽  
Fouad Ammouri ◽  
Marc Till
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Three Dimensional ◽  
Analytical Formula ◽  
Two Dimensions ◽  
Radiation Model ◽  
Participating Media ◽  
View Factors ◽  
Transfer Method

Air Liquide has been involved in the design of industrial furnaces (glass melting, reheating, aluminum, …) for several years. Thanks to that experience, known-how and expertise in modeling such applications have been developed. Dedicated simulation tools — 0D for global heat and mass balance, 1D for the prediction of longitudinal temperature profiles and 3D for detailed analysis — have been built. Each of them is very helpful when used relevantly and offers numerous opportunities at each step of the design of a furnace. In such kind of applications, the temperature levels are very high (up to 2500 K). As a consequence it is very crucial to simulate the radiative heat transfer as accurately as possible. This requires the use of a radiation model that can take into account complex geometries, non-isothermal media and various gas mixture compositions. Very often, three-dimensional simulations are necessary and reduction to smaller dimension problems is difficult or inadequate. The present paper introduces a new radiation model for computing two-dimensionally radiative heat transfer in an industrial furnace with a piecewise distributed load. To reduce the three-dimensional problem to two dimensions, the method consists in coupling the 2D radiation transport equation to a boundary condition based on view factors through an imaginary plane to homogenize the radiative behavior of the load surface. A solution procedure using the discrete transfer method associated to a weighted-sum-of-gray-gases database to deal with absorption and emission of a CO2-H2O mixture is proposed. Simulation results are finally compared to an analytical formula and then to a full-3D approach taking into account participating media, non-isothermal and gray walls. All tests show that this model can be used to simulate industrial configurations with a good accuracy.

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.

Solutions of Radiative Heat Transfer in Three-Dimensional Inhomogeneous, Scattering Media

2002 ◽  
Vol 124 (5) ◽  
pp. 985-988 ◽  
Author(s):  
L. M. Ruan ◽  
H. P. Tan
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Averaging Method ◽  
Three Dimensional ◽  
Unit Cube ◽  
Radiative Properties ◽  
Random Numbers ◽  
Scattering Media ◽  
Mc Simulation

In the present study, we use the Monte-Carlo (MC) method to simulate radiative heat transfer in three-dimensional inhomogeneous scattering unit cube with black or gray walls. The results show that the averaging method of non-uniform radiative properties in each medium element has influence on the results. One reasonable averaging method has been employed in our model. In mean while, several characters of exchange factor have been employed to estimate the performance of pseudo-random numbers generator and the numerical uncertainty of MC simulation.

Sign in / Sign up

Export Citation Format

Share Document