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Configuration Factors for Diffuse Surfaces with Uniform Radiosity
Published in John R. Howell, M. Pinar Mengüç, Kyle Daun, Robert Siegel, Thermal Radiation Heat Transfer, 2020
John R. Howell, M. Pinar Mengüç, Kyle Daun, Robert Siegel
The discrete ordinates method, described in Chapter 13, was developed to determine radiative transfer in enclosures filled with a medium that absorbs, emits, and scatters radiation. The method involves following radiation along paths between surfaces of an enclosure with the radiative effects of the intervening medium included. By omitting the radiative interaction with the intervening medium, the discrete ordinates method can also be used to evaluate configuration factors, as considered in Sanchez and Smith (1992) and Byun and Smith (1997). The radiation exchange for a 3D rectangular box compared very well with those computed from the known formulas for exchange between rectangles. In addition, the effect of an obstruction in the view between the enclosure surfaces in the form of a rectangular solid was introduced and investigated.
Radiation Transport Simulation
Published in Harry E. Martz, Clint M. Logan, Daniel J. Schneberk, Peter J. Shull, X-Ray Imaging, 2016
Harry E. Martz, Clint M. Logan, Daniel J. Schneberk, Peter J. Shull
The discrete ordinates method is a deterministic method of solving radiation transport problems. It is a point-to-point solution and, in its basic form, accommodates neither time nor energy as a variable. This method lacks versatility in accommodating complex shapes and material variations. It is not useful for computing radiographs. But, it is the method of choice for so-called deep-penetration problems. This occurs in the design of shielding, where attenuation in the shield is often required to be 106 or more. In these problems, time dependence is not of interest. Energy dependence is easily incorporated by performing several calculations at different energies and then integrating them to simulate the source spectrum.
Nonlinear Diffusion
Published in M. Necati Özişik, Helcio R.B. Orlande, Marcelo José Colaço, Renato Machado Cotta, Finite Difference Methods in Heat Transfer, 2017
M. Necati Özişik, Helcio R.B. Orlande, Marcelo José Colaço, Renato Machado Cotta
Different techniques can be found in the literature for the numerical solution of the equation of radiative transfer, such as, for example, the discrete ordinates method (Chandrasekhar 1960; Özişik 1973; Barichello and Siewert 1999, 2002; Siegel and Howell 2002; Barichello 2011; Modest 2013) and the finite volume method (Raithby and Chui 1990; Chui and Raithby 1993; Raithby 1999; Kim and Huh 2000). In this section, the finite volume method is applied to the physical problem examined by Wellele et al. (2006), related to the heat transfer processes taking place in the application of the flash method at high temperatures (André and Degiovanni 1995).
Numerical investigation of combined effects of radiation and convection heat transfer from tube banks placed in a participating medium
Published in Numerical Heat Transfer, Part A: Applications, 2023
Combined convection and radiation heat transfer from tube-banks in transparent [56–61] or participating media [62–68] also has a substantial place for engineering applications. Mirhosseini et al. [57] studied the flow over a single rotating cylinder subjected to natural and forced convection as well as surface radiation. They additionally examined the heat transfer characteristics in the case of the cylinder and absorber on top of it. Similarly, Kang et al. [59] utilized billets at high temperatures for the waste heat recovery process. In the research where a participating medium constituted by flue gases because of the combustion of propane was studied, Kaminski et al. [62] investigated flow over a single cylinder for = 500 of a non-gray and non-scattering medium. They utilized approximation for the related study. Similarly, Pachpute et al. [65] numerically investigated unsteady laminar and turbulent flow over a single cylinder placed in a participating medium. They utilized discrete ordinates method (DOM) to solve the radiative transfer equation. Mazgar et al. [68] examined the non-gray gas flow through a partially heated pipe in the case of natural convection. They concluded that lateral heating of the pipe was more energy efficient than heating from the top of the pipe.
A Maximum Entropy-Inspired Interpolative Closure for the Prediction of Radiative Heat Transfer in Laminar Co-Flow Diffusion Flames
Published in Combustion Science and Technology, 2022
J. A. R. Sarr, C. P. T. Groth, J. C. T. Hu
The discrete ordinates method (Fiveland 1984) is used to transform the equation of radiative transfer into a set of PDEs with only spatial and temporal dependence. This angular discretization technique makes use of the assumption that the radiation is transported only along a finite set of discrete directions, instead of the effectively infinite number of directions allowed in Eq. (8) by a continuous representation of the solid angle. In other words, the solid angle is divided into a finite number, , of discrete directions (or ordinates) , . In this way, the RTE is transformed into a system of coupled equations given by
Combined Effect of Mixed Convection and Surface Radiation Heat Transfer for Thermally Developing Flow in Vertical Channels
Published in Heat Transfer Engineering, 2018
Rajamohan Ganesan, Ramesh Narayanaswamy, Kumar Perumal
Wei and Hung [5] performed numerical simulations to investigate the effects of radiation on mixed convection for a gray fluid in a vertical duct. The radiative equation was solved by the discrete ordinates method. The results showed that radiation significantly reduces the buoyancy effects and affects the total Nusselt number. Ramesh and Venkateshan [6] conducted experiments on natural convection heat transfer in an enclosure. This study included differentially heated walls with uniform heat flux. The experimental study was carried out using a differential interferometer. The experiments achieved adiabatic conditions for bottom and top walls of the enclosure and the results were correlated for convective Nusselt number for a wide range of various parameters to understand the effect of the interaction of wall surface on natural convection. Their experimental analysis provided valid information for future research, particularly for those using experimental and numerical methods in analyzing problems.