Discrete-Ordinates Solutions of the Radiative Transport Equation for Rectangular Enclosures

1984 ◽  
Vol 106 (4) ◽  
pp. 699-706 ◽  
Author(s):  
W. A. Fiveland
Keyword(s):  
Heat Transfer ◽  
Transfer Rate ◽  
Numerical Solutions ◽  
Surface Heat ◽  
Discrete Ordinates ◽  
Two Dimensional ◽  
Scattering Medium ◽  
Discrete Ordinates Method ◽  
Radiant Intensity ◽  
Radiative Transport Equation

The Sn discrete-ordinates method is used to find numerical solutions in a two-dimensional rectangular enclosure with a gray absorbing, emitting, and isotropically scattering medium. Results are obtained for the S2, S4, and S6 approximations that correspond to 4, 12, and 24 flux approximations, respectively, and are compared with exact solutions, numerical Hottel’s zone results, P3 differential approximations, and an approximation method developed by Modest. The S2 approximation solutions were found to be applicable only for several specific cases and are not recommended for general use. The S4 and S6 solutions compare favorably with other methods and can be used to predict radiant intensity and surface heat transfer rate for various surface and optical conditions.

Consideration of the Scattering Effects in the Glass As a Participating Medium Using the Discrete Ordinates Method

2001 ◽  
Author(s):  
S. Coutin Rodicio ◽  
B. Restrepo Torres
Keyword(s):  
Heat Flux ◽  
Radiative Heat ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Radiative Heat Exchange ◽  
Scattering Medium ◽  
Discrete Ordinates Method ◽  
Radiant Intensity ◽  
Scattering Coefficients ◽  
Scattering Effects

Abstract Three-dimensional radiative heat exchange in a commercial type of glass as a participating medium is predicted using the discrete ordinates method. The radiative transfer equation (RTE) is analyzed for an absorbing, re-emitting, and scattering medium enclosed by gray walls. The main objective of this work is to formulate the RTE in a three-dimensional enclosure represented by a rectangular glass furnace where scattering effects are considered in the prediction of the radiant intensity, temperature distribution, incident and emitted energy, and heat flux at the glass surface. A comparative study is performed for glass under scattering and non-scattering conditions. The influence of scattering effects in the radiant intensity will provide further understanding of their impact in the glass thermal behavior. Additionally, the results of a parametric study on the glass for different scattering coefficients, surface heat flux, wall emissivity, and the forward scattering are discussed. The S4 approximation of the discrete ordinates method is employed in this model.

Analysis of Radiative Heat Transfer in Complex Two-Dimensional Enclosures With Obstacles Using the Modified Discrete Ordinates Method

2001 ◽  
Vol 123 (5) ◽  
pp. 892-900 ◽  
Author(s):  
M. Sakami ◽  
A. El Kasmi ◽  
A. Charette
Keyword(s):  
Heat Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Discrete Ordinates ◽  
Solid Boundary ◽  
Two Dimensional ◽  
Discrete Ordinates Method ◽  
Radiative Intensity ◽  
The Media

In this work, an extension of a modified discrete ordinates method recently proposed by other researchers is presented. It is intended to counter the ray effect inherent in this method. The media analyzed are absorbing, emitting and isotropically or anisotropically scattering and the enclosure geometry is arbitrary. Cases with obstructions are emphasized. The radiative intensity is broken into two parts: the wall-related intensity and the medium-related intensity. The former is treated separately by rigorous integration over the entire solid boundary. A new differencing scheme based on quadrangular grids is also proposed and used for the treatment of the medium-related intensity. Results confirm that the proposed method is a good general remedy for anomalies caused by the ray effect due to the geometry.

scholarly journals Nanofluid Flow on a Shrinking Cylinder with Al2O3 Nanoparticles

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1612
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Friction Factor ◽  
Surface Heat Flux ◽  
Transfer Rate ◽  
Surface Heat ◽  
Al2o3 Nanoparticles ◽  
Nanofluid Flow ◽  
Curvature Parameter ◽  
Over Time

This study investigates the nanofluid flow towards a shrinking cylinder consisting of Al2O3 nanoparticles. Here, the flow is subjected to prescribed surface heat flux. The similarity variables are employed to gain the similarity equations. These equations are solved via the bvp4c solver. From the findings, a unique solution is found for the shrinking strength λ≥−1. Meanwhile, the dual solutions are observed when λc<λ<−1. Furthermore, the friction factor Rex1/2Cf and the heat transfer rate Rex−1/2Nux increase with the rise of Al2O3 nanoparticles φ and the curvature parameter γ. Quantitatively, the rates of heat transfer Rex−1/2Nux increase up to 3.87% when φ increases from 0 to 0.04, and 6.69% when γ increases from 0.05 to 0.2. Besides, the profiles of the temperature θ(η) and the velocity f’(η) on the first solution incline for larger γ, but their second solutions decline. Moreover, it is noticed that the streamlines are separated into two regions. Finally, it is found that the first solution is stable over time.

scholarly journals An Experimental Study on the Aerodynamics and the Heat Transfer of a Suction Side Film Cooled Large Scale Turbine Cascade

1999 ◽  
Author(s):  
Wolfgang Ganzert ◽  
Leonhard Fottner
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Film Cooling ◽  
Total Pressure ◽  
Large Scale ◽  
Suction Side ◽  
Surface Heat ◽  
Two Dimensional ◽  
Turbine Cascade ◽  
Surface Heat Transfer

As a part of a more complex research program systematic isothermal investigations on the aerodynamics and heat transfer of a large scale turbine cascade with suction side film cooling were carried out. The film cooling through a row of holes at forty percent chord length on the suction side was supplied by a large plenum chamber. Two injection geometries were hitherto tested and evaluated: cylindrical holes with thirty respectively fifty degrees axial inclination angle and no lateral inclination. Typical engine conditions for the Mach and Reynolds number as well as the inlet turbulence level were maintained. The aerodynamic studies are based on steady state pressure measurements. The static profile pressure distribution together with oil-and-dye flow visualisation gives information on the surface flow conditions and boundary layer development especially in the near hole region. The measured data also comprise local and integral total pressure loss coefficients obtained by pressure probe traversing at mid span downstream of the cascade. The heat transfer examination set-up is based on the steady state liquid crystal technique using a compound of a thermochromic sheet combined with an electrical surface heating layer attached on an adiabatic blade corpus. Two dimensional pseudo colour plots are used for the documentation of the local surface heat transfer coefficient distribution and hot spot estimation. Laterally averaged and statistically analysed data of the surface heat transfer is applied in overall heat transfer examinations. All this data is used for a joint aerodynamic flow and surface heat transfer optimisation of a blowing configuration in suction side film cooled turbine cascade. The most important conclusions can be summarised as follows: Aiming at an optimised design of cylindrical film cooling configurations the axial inclination of the holes should be kept low thus diminishing the suction peak value at the cooling position in the profile pressure distribution and decreasing the mainstream deceleration area upstream of the jets. This also leads to reduced total pressure losses. Through the high influence of the blowing on the aerodynamics the flow in the near hole mixing region is highly three-dimensional. This shows significant effects in the two-dimensional surface distribution and the laterally averaged heat transfer coefficient. Oil-and-dye pictures confirm the observations qualitatively.

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