Transient Combined Conduction and Radiation in a Two-Dimensional Participating Cylinder in Presence of Heat Generation
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.
[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.
[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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:51117", author = "Raoudha Chaabane and Faouzi Askri and Sassi Ben Nasrallah", title = "Transient Combined Conduction and Radiation in a Two-Dimensional Participating Cylinder in Presence of Heat Generation", abstract = "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", volume = "5", number = "7", pages = "1211-6", }
