Abstract
One of the major difficulties in the numerical solution of multi-mode heat transfer problems in radiatively participating media involves grid compatibility between conductive and radiative computational domains. Since the grid density of the conductive modes must often be much greater than that of the radiative grid, a two-grid approach is often employed, requiring some degree of interpolation between grids. Implementation of the boundary element method, as opposed to finite-difference or finite-element schemes, overcomes the incompatibility problem. An exchange factor method is used to provide the radiation flux vector in the energy equation, and the boundary element formulation for the energy equation in the presence of radiation involves both a surface and a domain integral. However, in the iterative solution of the problem, the domain integral is computed using the radiative grid break-up. Details of the formulation are presented. A benchmark problem is used to validate the approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Siegel, R., and Howell, H.R., Thermal Radiation Heat Transfer, 2nd Edition, Hemisphere Publishing, New York, 1981.
Ratzel, A.C., and Howell, J.R., Two-Dimensional Energy Transfer in Radiatively articipating Media with Conduction by the P-N Approximation, Vol. 2, pp. 535–540, Proceedings of the Seventh International Heat Transfer Conference, 1982.
Larsen, M.E., The Exchange Factor Method: An Alternative Zonal Formulation for Analysis of Radiating Enclosures Containing Participating Media, Ph.D. Dissertation, University of Texas at Austin, 1983.
Razzaque, M.M., Howell, J.R., and Klein, D.E., Coupled Radiative and Conductive Heat Transfer in a Two-Dimensional Rectangular Enclosure with Gray Participating Media Using Finite Elements, ASME Journal of Heat Transfer, Vol. 106, pp. 613–619, 1984.
Yuen, W.W., and Takara, E.E., Analysis of Combined Conductive-Radiative Heat Transfer in a Two-Dimensional Rectangular Enclosure with a Gray Medium, ASME Journal of Heat Transfer, Vol. 110, pp. 468–474, 1988.
Saltiel, C, and Naraghi, M.H.N., Combined-Mode Heat Transfer in Radiatively Participating Media Using the Discrete Exchange Factor Method with Finite Elements, Heat Transfer 1990, (Ed. Hestroni, G.), Vol. 6, pp. 391–396, Hemisphere, New York, 1990.
Naraghi, M.H.N., and Saltiel, C, Combined-Mode Heat Transfer in Radiatively Participating Media: Computational Considerations, Radiation Heat Transfer: Fundamentals and Applications, (Ed. Smith, T.F., Modest, M.F., Smith, A.M., and Thynell, S.T.), ASME Publication HTD-VOL. 137, p. 133–140, 1990.
Baek, S.W., and Kim, T.Y., The Conductive and Radiative Heat Transfer in Rectangular Enclosure Using the Discrete Ordinates Method, Heat Transfer 1990, (Ed. Hestroni, G.), Vol. 6, pp. 433–438, Hemisphere, New York, 1990.
Fernandes, R., and Francis, J., Combined Conductive and Radiative Heat Transfer in an Absorbing, Emitting, and Scattering Cylindrical Media, ASME Journal of Heat Transfer, Vol. 104, pp. 594–601, 1982.
Saltiel, C, and Naragi, M.H.N., Analysis of Radiative Heat Transfer in Participating Media Using Arbitrary Nodal Distribution, Numerical Heat Transfer-PartB, Fundamentals, Vol. 17, pp. 227–243, 1990.
Brebbia, C.A., Telles, J.C.F., and Wrobel, L.C. Boundary Element Techniques, Springer-Verlag, New York, 1984.
Brebbia, C.A. and Walker, S. Boundary Element Techniques in Engineering, Newnes-Butterworth, Boston, 1980.
Bialecki, R.B. and Nowak, A.J. Boundary value Problems in Heat Conduction With Nonlinear Material And Nonlinear Boundary Conditions, Applied Mathematical Modelling, Vol 5, pp.417–421, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Computational Mechanics Publications
About this chapter
Cite this chapter
Kassab, A.J., Saltiel, C.J. (1991). Boundary Element Solution of Combined-Mode Heat Transfer in Radiatively Participating Media. In: Brebbia, C.A., Gipson, G.S. (eds) Boundary Elements XIII. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3696-9_26
Download citation
DOI: https://doi.org/10.1007/978-94-011-3696-9_26
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-85166-696-6
Online ISBN: 978-94-011-3696-9
eBook Packages: Springer Book Archive