Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31103
Transient Combined Conduction and Radiation in a Two-Dimensional Participating Cylinder in Presence of Heat Generation

Authors: Raoudha Chaabane, Faouzi Askri, Sassi Ben Nasrallah


Simultaneous transient conduction and radiation heat transfer with heat generation is investigated. Analysis is carried out for both steady and unsteady situations. two-dimensional gray cylindrical enclosure with an absorbing, emitting, and isotropically scattering medium is considered. Enclosure boundaries are assumed at specified temperatures. The heat generation rate is considered uniform and constant throughout the medium. The lattice Boltzmann method (LBM) was used to solve the energy equation of a transient conduction-radiation heat transfer problem. The control volume finite element method (CVFEM) was used to compute the radiative information. To study the compatibility of the LBM for the energy equation and the CVFEM for the radiative transfer equation, transient conduction and radiation heat transfer problems in 2-D cylindrical geometries were considered. In order to establish the suitability of the LBM, the energy equation of the present problem was also solved using the the finite difference method (FDM) of the computational fluid dynamics. The CVFEM used in the radiative heat transfer was employed to compute the radiative information required for the solution of the energy equation using the LBM or the FDM (of the CFD). To study the compatibility and suitability of the LBM for the solution of energy equation and the CVFEM for the radiative information, results were analyzed for the effects of various parameters such as the boundary emissivity. The results of the LBMCVFEM combination were found to be in excellent agreement with the FDM-CVFEM combination. The number of iterations and the steady state temperature in both of the combinations were found comparable. Results are found for situations with and without heat generation. Heat generation is found to have significant bearing on temperature distribution.

Keywords: heat generation, cylindrical coordinates; RTE;transient; coupled conduction radiation; heat transfer; CVFEM; LBM

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1882


[1] S. Succi, The Lattice Boltzmann Method for Fluid Dynamics and Beyond, Oxford University Press, (2001).
[2] R. Benzi, S. Succi, M. Vergassola, The lattice Boltzmann equation: theory and applications Authors, Phys. Rep. 222 (1992) 145-197.
[3] F.J. Higuera, S. Succi, R. Benzi, Lattice gas dynamics with enhanced collisions, Europhys. Lett. 9 (1989) 345-349.
[4] X. Shan, Simulation of Rayleigh-Benard convection using a lattice Boltzmann method, Phys. Rev. E 55 (1977) 2780-2788.
[5] F.J. Higuera, J. Jiménez, Boltzmann approach to lattice gas simulations, Europhys. Lett. 9 (1989) 663-668.
[6] F. Massaioli, R. Benzi, S. Succi, Exponential tails in two-dimensional Rayleigh-Bénard convection, Europhys. Lett. 21 (1993) 305-310.
[7] S. Chen, G.D. Doolen, Lattice Boltzamann method for fluid flows, Ann. Rev. Fluid Mech. 30 (1998) 329-364.
[8] X. He, S. Chen, G.D. Doolen, A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys. 146 (1998) 282-300.
[9] D.A. Wolf-Gladrow, Lattice-Gas Cellular Automata and Lattice Boltzmann Models: An Introduction, Springer-Verlag, Berlin- Heidelberg, (2000).
[10] R.R. Nourgaliev, T.N. Dinh, T.G. Theofanous, D. Joseph, The lattice Boltzmann equation method: theoretical interpretation, numerics and implications, Int. J. Multiphase Flow 29 (2003) 117-169.
[11] Menguc- MP, Viskanta R. Radiative transfer in axisymmetric finite cylindrical enclosures. J Heat Transfer 1986;108:271-6.
[12] Yin Z, Jaluria Y. Zonal method to model radiative transport in an optical fiber drawing furnace. J Heat Transfer 1997;119:597-603.
[13] Kaminski DA. Radiative transfer from a gray, absorbing emitting, isothermal medium in a conical enclosure. J Sol Energy Eng 1989;111:324-9.
[14] Fernandes R, Francis J. Combined conductive and radiative heat transfer in an absorbing, emitting and scattering cylindrical medium. J Heat Transfer 1982;104:594-601.
[15] Nunes EM, Modi V, Naraghi MHN. Radiative transfer in arbitrarilyshaped axisymmetric enclosures with anisotropic scattering media. Int J Heat Mass Transfer 2000;43:3275-85.
[16] Sutton WH, Chen XL. A general integration method for radiative transfer in 3D non-homogeneous cylindrical media with anisotropic scattering. JQSRT 2004;84:65-103.
[17] Chen XL, Sutton WH. Radiative transfer in finite cylindrical media using transformed integral equations. JQSRT 2003;77:233-71.
[18] Cui X, Li BQ. Discontinuous finite element solution of 2D radiative transfer with and without axisymmetry. JQSRT 2005;96:383-407.
[19] Ruan LM, Xie M, Qi H, An W, Tan HP. Development of a finite element model for coupled radiative and conductive heat transfer in participating media. JQSRT 2006;102:190-202.
[20] Carlson BG, Lathrop KD. Transport theoryÔÇöthe method of discreteordinates. In: Computing methods in reactor physics. New York: Gordon and Breach; 1968.
[21] Fiveland WA. A discrete ordinates method for predicting radiative heat transfer in axisymmetric enclosure. ASME 1982;82-HT-20.
[22] Jamaluddin AS, Smith PJ. Predicting radiative transfer in axisymmetric cylindrical enclosures using the discrete ordinates method. Combust Sci Technol 1988;62:173-86.
[23] Li HY, Ozisik MN, Tsai JR. Two-dimensional radiation in a cylinder with spatially varying albedo. AIAA J Thermophys Heat Transfer 1991;6:180-2.
[24] Jamaluddin AS, Smith PJ. Discrete-ordinates solution of radiative transfer equation in nonaxisymmetric cylindrical enclosures. J Thermophys Heat Transfer 1992;6:242-5.
[25] Beak SW, Kim TY, Lee JS. Transient cooling of a finite cylindrical medium in the rarefied cold environment. Int J Heat Mass Transfer 1993;36:3949-56.
[26] Baek SW, Kim MY. Modification of the discrete ordinates method in an axisymmetric cylindrical geometry. Numer Heat Transfer (B) 1997;31:313-26.
[27] Baek SW, Kim MY. Analysis of radiative heating of a rocket plume base with the finite volume method. Int J Heat Mass Transfer 1997;40:1501-8.
[28] Rousse D, Baliga R. Formulation of a control volume finite element method for radiative transfer in participating media. In: Proceedings of the seventh international conference on numerical methods thermal problems, Stanford, 1991. p. 95-786.
[29] Ben Salah M, Askri F, Rousse D, Ben Nasrallah S. Control volume finite element method for radiation. JQSRT 2005;92:9-30.ARTICLE IN PRESS
[30] Grissa H, Askri F, Ben Salah M, Ben Nasrallah S. Three-dimensional radiative transfer modeling using the control volume finite element method. JQSRT 2007;105:388-404.
[31] Ben Salah M, Askri F, Ben Nasrallah S. Unstructured control volume finite element method for radiative heat transfer in a complex 2Dgeometry. Numer Heat Transfer (B) 2005;48:1-21.
[32] Asllanaj F, Feldhemi V, Lybaert P. Solution of radiative heat transfer in 2-D geometries by a modified finite volume method based on a cell vertex scheme using unstructured triangular meshes. In: Proceedings of the Eurotherm 78 on computational thermal radiation in participating media, 2006.
[33] H. Grissa, F. Askri, M. Ben Salah, S. Ben Nasrallah, Journal of Quantitative Spectroscopy &Radiative Transfer 109 (2008) 494-513, Nonaxisymmetric radiative transfer in inhomogeneous cylindrical media with anisotropic scattering
[34] Rousse D. Numerical predictions of two-dimensional conduction, convection, and radiation heat transfer. I. Formulation. Int J Thermal Sci 2000;39:315-31.
[35] Rousse D. Numerical predictions of two-dimensional conduction, convection, and radiation heat transfer. II. Validation. Int J Thermal Sci 2000;39:332-53.
[36] Ben Salah M, Askri F, Jemni A, Ben Nasrallah S. Numerical analyses of radiative heat transfer in any arbitrarily-shaped axisymmetric enclosures. JQSRT 2006;97:395-414.
[37] J.C. Chai, H.S. Lee, S.V. Patankar. Finite volume method for radiation heat transfer. J Thermophys Heat Transfer (1994) 8(3).
[38] K.-H. Wu, C.-Y. Wu, transient two-dimensional radiative and conductive heat transfer in an axisymmetric medium, heat and mass transfer 33 (1998) 327-331. springer-Verlag 1998.
[39] R. Chaabane, F. Askri, S.B. Nasrallah, A new hybrid algorithm for solving transient combined conduction radiation heat transfer problems, Journal of thermal science.
[40] Raoudha CHAABANE, Faouzi ASKRI, Sassi Ben NASRALLAH, «Analysis of two-dimensional transient conduction-radiation problems in an anisotropically scattering participating enclosure using the lattice Boltzmann method and the control volume finite element method», Journal of Computer Physics Communications.
[41] Raoudha CHAABANE, Faouzi ASKRI, Sassi Ben NASRALLAH, «Parametric study of simultaneous transient conduction and radiation in a two-dimensional participating medium», Communications in Nonlinear Science and Numerical Simulation (2011).
[42] Raoudha CHAABANE, Faouzi ASKRI, Sassi Ben NASRALLAH, «Application of the lattice Boltzmann method to transient conduction and radiation heat transfer in cylindrical media», J. Quantitative Spectroscopy Radiative Transfer.