Nonorthogonal Finite-Volume Solutions of Radiative Heat Transfer in a Three-Dimensional Enclosure

Baek, Seung Wook; Kim, Man Young; Kim, Jeong Soo

doi:10.1080/10407799808915066

Cited by 68 publications

(29 citation statements)

References 17 publications

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“…(4). In this work, the finite volume method (FVM) for radiation suggested by Chui and Raithby, 8) and developed by Chai et al 9) and Baek et al 10) is adopted to discretize the RTE. More detailed information on the FVM can be easily found in the literature.…”

Section: Solution Methodsmentioning

confidence: 99%

Prediction of Furnace Heat Transfer and Its Influence on the Steel Slab Heating and Skid Mark Formation in a Reheating Furnace

et al. 2008

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In this work, a mathematical heat transfer model of a walking-beam type reheating furnace has been developed. The model can predict the heat flux distribution within the furnace and the temperature distribution in the slab throughout the reheating furnace process by considering the heat exchange between the slab and its surroundings in the furnace, including the radiant heat transfer among the slabs, the skids, the hot gases and the furnace wall as well as the gas convection heat transfer in the furnace. The furnace filled with hot combustion gases such as H 2 O, CO 2 , O 2 , and N 2 is modeled as radiating medium with spatially varying temperature. After the predictions of the present model were compared with the data from an in situ measurement in the furnace, the effect of the skids on the slab heating, the heat transfer characteristics and temperature behavior of the slab were investigated by changing such parameters as residence time and emissivities of the slab and the furnace wall.KEY WORDS: reheating furnace; steel slab heating; radiative heat flux; convective heat flux; skid mark formation; finite volume method. 1325© 2008 ISIJ considering the quasi-steady two dimensional heat transfer transverse to the marching direction of the slab in the reheating furnace. Recently, Kim 5) developed a heat transfer model to predict the transient heating of the slab in a directfired walking-beam type reheating furnace by considering thermal radiation. This model is simple and accurate but requires less computational time than the first approach.In the work, a mathematical heat transfer model is suggested in order to predict the heat flux impinging on the slab surface and thereby temperature distribution inside the slab, which can be categorized as the second approach. In other words, firstly, the total heat flux including radiative and convective heat flux is calculated in the furnace gas field by using the experimental data related to the temperature and concentration distributions of the furnace gas as well as the temperature distribution of the furnace wall, and then the heat conduction analysis of the slab is performed by applying the total heat flux as the boundary condition of the transient heat conduction equation. Therefore, the model can predict the thermal behavior of the slab throughout the furnace.The furnace in this paper is modeled as radiating medium with spatially varying temperature and is filled with hot combustion gases that consist of H 2 O, CO 2 , O 2 , and N 2 , and have highly spectral radiative characteristics. Accordingly, the weighted sum of gray gas model (WSGGM) 6) is used to consider the nongray behavior of the combustion gases. In the following sections, after describing the methodology adopted here for the prediction of furnace processes within the reheating furnace, the effects of such parameters as the furnace charging speed (or residence time) and emissivities of the slab and furnace wall on the heat transfer characteristics and thermal behavior of the slab are investigated. Finally, ...

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Section: Solution Methodsmentioning

confidence: 99%

Prediction of Furnace Heat Transfer and Its Influence on the Steel Slab Heating and Skid Mark Formation in a Reheating Furnace

et al. 2008

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“…As mentioned, to simulate the thermal radiation exchange under non-grey gas conditions the conservative variant of the discrete ordinates (DO) radiation model, called the finite-volume (FV) scheme and implemented in the FLUENT software package, is used [12][13][14]. The DO-FV method can be considered as a higher-order flux method and spans the entire range of optical thicknesses unlike the six-flux methods that are sufficiently accurate for optically thick media [15].…”

Section: Radiationmentioning

confidence: 99%

Evaluation of high-emissivity coatings in steam cracking furnaces using a non-grey gas radiation model

Stefanidis

Geem

Heynderickx

et al. 2008

Chemical Engineering Journal

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The efficiency of the application of high-emissivity coatings on the furnace walls in steam cracking technology can only be evaluated on the basis of a description of radiative heat transfer distinguishing between the frequency bands. To this end, a non-grey gas radiation model based on the exponential wide band model (EWBM) has been developed and applied in the context of three-dimensional CFD simulations of an industrial naphtha cracking furnace with side-wall radiation burners. Applying a high-emissivity coating on the furnace wall decreases the net outgoing radiation from the furnace wall in the absorption bands and increases the net outgoing radiation from the furnace wall in the clear windows. Since radiation that is emitted by the furnace wall and travels through the flue gas in the clear windows can reach the reactor tubes without partially being absorbed by the flue gas, contrary to radiation that is emitted by the furnace wall and travels through the flue gas in the absorption bands, the thermal efficiency of the furnace increases. It was found that application of a high-emissivity coating on the furnace walls improves the thermal efficiency of the furnace (∼1%), the naphtha conversion (∼1%) and the ethylene yield (∼0.5%). These differences are small but, considering the industrial importance and scale of the steam cracking process, significant.

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“…Davis (1984) recommends the use of the Integration Method, for interfaces between adjacent regions. Most of the recent applications of the CVF are in computational fluid dynamics (Vijayan & Kallinderis, 1994;Versteeg & Malalasekera, 1995;Moder, Chai, Parthasarathy, Lee & Patankar, 1996;Cordero, De Biase & Pennati, 1997;Baek, Kim & Kim, 1998;Noh & Song, 1998;Shahcheragui & Dwyer, 1998;Thynell, 1998;Chan & Anastasiou, 1999;Munz, Schneider, Sonnendrucker, Stein, Voss & Westermann, 1999;Sohankar, Norberg & Davison, 1999;Su, Tang & Fu, 1999).…”

Section: Introductionmentioning

confidence: 99%

Comparison of finite difference and control volume methods for solving differential equations

Botte

Ritter

White

2000

Computers & Chemical Engineering

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Nonorthogonal Finite-Volume Solutions of Radiative Heat Transfer in a Three-Dimensional Enclosure

Cited by 68 publications

References 17 publications

Prediction of Furnace Heat Transfer and Its Influence on the Steel Slab Heating and Skid Mark Formation in a Reheating Furnace

Prediction of Furnace Heat Transfer and Its Influence on the Steel Slab Heating and Skid Mark Formation in a Reheating Furnace

Evaluation of high-emissivity coatings in steam cracking furnaces using a non-grey gas radiation model

Comparison of finite difference and control volume methods for solving differential equations

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