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Research Papers

The Radiative Boundary Design of a Hexagonal Furnace Filled With Gray and Nongray Participating Gases

[+] Author and Article Information
B. Moghadassian

Engineering Department,
Khatam Al-Anbia University of Technology,
Behbahan, Iran
e-mail: b.moghadassian@ut.ac.ir

F. Kowsary

Mechanical Engineering Department,
College of Engineering,
University of Tehran,
Tehran, Iran
e-mail: fkowsari@ut.ac.ir

M. Mosavati

Department of Mechanical Engineering,
Science and Research Branch,
Islamic Azad University,
Tehran, Iran
e-mail: maziar_mosavati@yahoo.com

1Corresponding author.

Manuscript received March 7, 2012; final manuscript received December 29, 2012; published online June 24, 2013. Assoc. Editor: Chenn Zhou.

J. Thermal Sci. Eng. Appl 5(3), 031005 (Jun 24, 2013) (11 pages) Paper No: TSEA-12-1039; doi: 10.1115/1.4023598 History: Received March 07, 2012; Revised December 29, 2012

The inverse radiative boundary design problem in a hexagonal furnace is numerically investigated. The aim of this study is to find the strength of heaters in a two-dimensional (2D) enclosure to produce the desired temperature and heat flux distribution on the design surface. Conjugate gradients method is chosen to perform the iterative search procedure for obtaining the optimal solution. The medium is considered participating and both gray and nongray cases are studied. FTn finite volume method (FVM) with nonorthogonal grid is employed to solve the radiative transfer equation in the furnace. In nongray cases, the medium is filled with combustive gas products. To predict nongray behavior properly, the SLW model is used. In problems with gray medium, the effects of wall emissivity, absorption coefficient, and scattering albedo are studied. For nongray problems, the effects of gas concentration and temperature of single species and gas mixtures are analyzed. In all cases, heater power can be estimated precisely and as the results show, estimated heat flux on the design surface is very close to the desired value. For this reason, the maximum root mean square error is less than 1.6%.

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Figures

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Fig. 1

(a) The physical domain and (b) the computational domain with 20 × 20 nonorthogonal grid

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Fig. 2

(a) The angular discretization for popular FVM, (b) the angular discretization for FT6 FVM, and (c) an arbitrary control volume with its representative node and surface normal vectors

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Fig. 3

The configuration of a general thermal boundary design problem

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Fig. 4

The solution algorithm

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Fig. 5

The verification check for FT6 FVM with nonorthogonal grid (a) the geometry and grid and (b) the heat flux on the line of y = 0 and z = 0.5 m

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Fig. 6

The verification check for SLW FT6 FVM (a) the geometry, (b) heat flux on the left wall (x = 0) for anisothermal and inhomogeneous H2O, and (c) radiative source term of the midsection (y = 0.5) for anisothermal and inhomogeneous CO2

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Fig. 7

The results for gray cases. The effect of (a) β, (b) εr, (c) εh, (d) ω with radiative equilibrium condition, and (e) ω with uniform temperature condition.

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Fig. 13

The calculated heat flux in different inverse iteration for qd0 = 9 kW/m2

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Fig. 12

The effect of nonuniform desired heat flux in the furnace of mixture of CO2 and H2O on (a) heater temperature and (b) heater power

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Fig. 11

The effect of H2O volume fraction on the heater temperature

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Fig. 10

The convergence history of the inverse cycle

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Fig. 9

The effect of CO2 temperature field on the (a) heater temperature and (b) heater power

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Fig. 8

The temperature field of Eq. (26) for T0 = 600 K

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