Solving Transient Conduction and Radiation Using Finite Volume Method
Radiative heat transfer in participating medium was
carried out using the finite volume method. The radiative transfer
equations are formulated for absorbing and anisotropically scattering
and emitting medium. The solution strategy is discussed and the
conditions for computational stability are conferred. The equations
have been solved for transient radiative medium and transient
radiation incorporated with transient conduction. Results have been
obtained for irradiation and corresponding heat fluxes for both the
cases. The solutions can be used to conclude incident energy and
surface heat flux. Transient solutions were obtained for a slab of heat
conducting in slab and by thermal radiation. The effect of heat
conduction during the transient phase is to partially equalize the
internal temperature distribution. The solution procedure provides
accurate temperature distributions in these regions. A finite volume
procedure with variable space and time increments is used to solve
the transient radiation equation. The medium in the enclosure
absorbs, emits, and anisotropically scatters radiative energy. The
incident radiations and the radiative heat fluxes are presented in
graphical forms. The phase function anisotropy plays a significant
role in the radiation heat transfer when the boundary condition is
non-symmetric.
[1] G. O. Young, “Synthetic structure of industrial plastics (Book style with
paper title and editor),” in Plastics, 2nd ed. vol. 3, J. Peters, Ed. New
York: McGraw-Hill, 1964, pp. 15–64.
[2] M. N. Borjini ,C. Mbow ,M. Daguenet ,” Numerical analysis of
combined radiation and unsteady natural convection within a horizontal
annular space,” Int J Numer Methods Heat Fluid Flow,vol.9,pp.742-
764, 1999.
[3] C. Y. Han ,S. W. Baek ,” The effects of radiation on natural convection
in a rectangular enclosure divided by two partitions,” Numer Heat
Transfer, vol.37,pp.249–270,2000.
[4] G. D. Raithby , E. H. Chui,” A finite-volume method for predicting a
radiant heat transfer in enclosures with participating media,” J Heat
Transfer , vol.112, pp. 415–23,1990.
[5] J. C. Chai , S. V. Patankar ,” Finite volume method for radiation heat
transfer ,” Adv Numer Heat Transfer ,vol.2, pp.110–35,2000.
[6] W. A. Fiveland ,” Discrete-ordinates solution of the radiative transport
equation for rectangular enclosures,” J Heat Transfer, vol.106,pp.:699–
706, 1984.
[7] W. A. Fiveland ,” Discrete ordinate methods for radiative heat transfer
in isotropically and anisotropically scattering media,” J Heat Transfer,
vol.12,pp.109-809,1987.
[8] W. A. Fiveland ,” Three-dimensional radiative heat-transfer solutions by
the discrete-ordinates method,” J Thermophys Heat Transfer,
vol.2,pp.309-316, 1988.
[9] J. S. Truelove ,” Three-dimensional radiation in absorbing–emitting–
scattering media using the discrete-ordinates approximation,” JQSRT,
vol.39,pp.27-31,1988.
[10] D. Balsara ,”Fast and accurate discrete ordinates methods for
multidimensional radiative transfer,” JQSRT,vol-7,pp.669-671, 2001.
[11] M.F. Modest ,” Radiative heat transfer,”. 2nd ed. New York: Academic
Press; 2003.
[12] L.H. Liu ,L.M. Ruan,H.P. Tan ,” On the discrete ordinates method for
radiative heat transfer in anisotropically scattering media,” Int J Heat
Mass Transfer, vol.45,pp.3259-3262, 2002.
[13] R. Koch,W. Krebs, Wittig S, Viskanta R,” Discrete ordinate quadrature
schemes for multidimensional radiative transfer,” JQSRT ,
vol.53,pp.353-372,1995.
[14] C.P. Thurgood , A. Pollard ,H. A. Becker,” The TN quadrature set for
the discrete ordinates method,” J Heat Transfer, vol-117,pp.1068-1070,
1995.
[15] B. W. Li, Q. Yao,X. Y. Cuo, K. F. Cen ,” A new discrete ordinates
quadrature scheme for three-dimensional radiative heat transfer,” J Heat
Transfer, vol-120,pp.514-518, 1998.
[16] R. Koch,R. Becker,” Evaluation of quadrature schemes for the discrete
ordinates method,” JQSRT , vol-84,pp.423-435,2004.
[17] H.S. Li, G. Flamant ,J.D. Lu ,” A new discrete ordinate algorithm for
computing radiative transfer in one-dimensional atmospheres,” JQSRT,
vol.83, pp.407–421, 2004.
[18] M.A. Ramankutty, A. L. Crosbie ,” Modified discrete ordinates solution
of radiative transfer in two-dimensional radiative rectangular
enclosures,” JQSRT, vol.57,pp.107-114, 1997.
[19] P. S. Cumber,”Improvements to the discrete transfer method of
calculating radiative heat transfer,” Int. J Heat Mass Transfer, vol.8 ,
pp.2251-2258, 1995.
[20] S. H. Kim, K. Y. Huh,” A new angular discretization scheme of the
finite volume method for 3D radiative heat transfer in absorbing,
emitting and anisotropically scattering media,” Int. J Heat Mass
Transfer , vol-43, pp.1233-1242, 2000.
[21] J. C. Chai ,” One-dimensional transient radiation heat transfer modeling
using a finite-volume method,” Numer. Heat Transf., vol-44, pp.187-
208, 2003.
[22] J. C. Chai, H. S. Lee , S. V. Patankar,” Finite volume method for
radiation heat transfer,” J. Thermophys. Heat Transf., vol-3, pp.419-425,
1994.
[1] G. O. Young, “Synthetic structure of industrial plastics (Book style with
paper title and editor),” in Plastics, 2nd ed. vol. 3, J. Peters, Ed. New
York: McGraw-Hill, 1964, pp. 15–64.
[2] M. N. Borjini ,C. Mbow ,M. Daguenet ,” Numerical analysis of
combined radiation and unsteady natural convection within a horizontal
annular space,” Int J Numer Methods Heat Fluid Flow,vol.9,pp.742-
764, 1999.
[3] C. Y. Han ,S. W. Baek ,” The effects of radiation on natural convection
in a rectangular enclosure divided by two partitions,” Numer Heat
Transfer, vol.37,pp.249–270,2000.
[4] G. D. Raithby , E. H. Chui,” A finite-volume method for predicting a
radiant heat transfer in enclosures with participating media,” J Heat
Transfer , vol.112, pp. 415–23,1990.
[5] J. C. Chai , S. V. Patankar ,” Finite volume method for radiation heat
transfer ,” Adv Numer Heat Transfer ,vol.2, pp.110–35,2000.
[6] W. A. Fiveland ,” Discrete-ordinates solution of the radiative transport
equation for rectangular enclosures,” J Heat Transfer, vol.106,pp.:699–
706, 1984.
[7] W. A. Fiveland ,” Discrete ordinate methods for radiative heat transfer
in isotropically and anisotropically scattering media,” J Heat Transfer,
vol.12,pp.109-809,1987.
[8] W. A. Fiveland ,” Three-dimensional radiative heat-transfer solutions by
the discrete-ordinates method,” J Thermophys Heat Transfer,
vol.2,pp.309-316, 1988.
[9] J. S. Truelove ,” Three-dimensional radiation in absorbing–emitting–
scattering media using the discrete-ordinates approximation,” JQSRT,
vol.39,pp.27-31,1988.
[10] D. Balsara ,”Fast and accurate discrete ordinates methods for
multidimensional radiative transfer,” JQSRT,vol-7,pp.669-671, 2001.
[11] M.F. Modest ,” Radiative heat transfer,”. 2nd ed. New York: Academic
Press; 2003.
[12] L.H. Liu ,L.M. Ruan,H.P. Tan ,” On the discrete ordinates method for
radiative heat transfer in anisotropically scattering media,” Int J Heat
Mass Transfer, vol.45,pp.3259-3262, 2002.
[13] R. Koch,W. Krebs, Wittig S, Viskanta R,” Discrete ordinate quadrature
schemes for multidimensional radiative transfer,” JQSRT ,
vol.53,pp.353-372,1995.
[14] C.P. Thurgood , A. Pollard ,H. A. Becker,” The TN quadrature set for
the discrete ordinates method,” J Heat Transfer, vol-117,pp.1068-1070,
1995.
[15] B. W. Li, Q. Yao,X. Y. Cuo, K. F. Cen ,” A new discrete ordinates
quadrature scheme for three-dimensional radiative heat transfer,” J Heat
Transfer, vol-120,pp.514-518, 1998.
[16] R. Koch,R. Becker,” Evaluation of quadrature schemes for the discrete
ordinates method,” JQSRT , vol-84,pp.423-435,2004.
[17] H.S. Li, G. Flamant ,J.D. Lu ,” A new discrete ordinate algorithm for
computing radiative transfer in one-dimensional atmospheres,” JQSRT,
vol.83, pp.407–421, 2004.
[18] M.A. Ramankutty, A. L. Crosbie ,” Modified discrete ordinates solution
of radiative transfer in two-dimensional radiative rectangular
enclosures,” JQSRT, vol.57,pp.107-114, 1997.
[19] P. S. Cumber,”Improvements to the discrete transfer method of
calculating radiative heat transfer,” Int. J Heat Mass Transfer, vol.8 ,
pp.2251-2258, 1995.
[20] S. H. Kim, K. Y. Huh,” A new angular discretization scheme of the
finite volume method for 3D radiative heat transfer in absorbing,
emitting and anisotropically scattering media,” Int. J Heat Mass
Transfer , vol-43, pp.1233-1242, 2000.
[21] J. C. Chai ,” One-dimensional transient radiation heat transfer modeling
using a finite-volume method,” Numer. Heat Transf., vol-44, pp.187-
208, 2003.
[22] J. C. Chai, H. S. Lee , S. V. Patankar,” Finite volume method for
radiation heat transfer,” J. Thermophys. Heat Transf., vol-3, pp.419-425,
1994.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:71086", author = "Ashok K. Satapathy and Prerana Nashine", title = "Solving Transient Conduction and Radiation Using Finite Volume Method", abstract = "Radiative heat transfer in participating medium was
carried out using the finite volume method. The radiative transfer
equations are formulated for absorbing and anisotropically scattering
and emitting medium. The solution strategy is discussed and the
conditions for computational stability are conferred. The equations
have been solved for transient radiative medium and transient
radiation incorporated with transient conduction. Results have been
obtained for irradiation and corresponding heat fluxes for both the
cases. The solutions can be used to conclude incident energy and
surface heat flux. Transient solutions were obtained for a slab of heat
conducting in slab and by thermal radiation. The effect of heat
conduction during the transient phase is to partially equalize the
internal temperature distribution. The solution procedure provides
accurate temperature distributions in these regions. A finite volume
procedure with variable space and time increments is used to solve
the transient radiation equation. The medium in the enclosure
absorbs, emits, and anisotropically scatters radiative energy. The
incident radiations and the radiative heat fluxes are presented in
graphical forms. The phase function anisotropy plays a significant
role in the radiation heat transfer when the boundary condition is
non-symmetric.
", keywords = "Participating media, finite volume method, radiation coupled with conduction, heat transfer.", volume = "8", number = "3", pages = "645-5", }
