Chebyshev collocation spectral domain decomposition method for coupled conductive and radiative heat transfer in a 3D L-shaped enclosure

References

• T. Xie, Y. L. He, and Z. J. Hu, Theoretical Study on Thermal Conductivities of Silica Aerogel Composite Insulating Material, Int. J. Heat Mass Transfer, vol. 58, no. 1–2, pp. 540–552, 1979.
   Web of Science ®Google Scholar
• A. Milandri, F. Asllanaj, G. Jeandel, and J. R. Roche, Heat Transfer by Radiation and Conduction in Fibrous Media without Axial Symmetry, J. Quant. Spectrosc. Radiat. Transfer, vol. 74, no. 5, pp. 585–603, 2002.
   Web of Science ®Google Scholar
• P. Sadooghi, Transient Combined Radiative and Conductive Heat Transfer in Plastics, J. Vinyl Addit. Tech., vol. 11, no. 1, pp. 28–37, 2005.
   Web of Science ®Google Scholar
• G. Miliauskas, Regularities of Unsteady Radiative-Conductive Heat Transfer in Evaporating Semitransparent Liquid Droplets, Int. J. Heat Mass Transfer, vol. 44, no. 4, pp. 785–798, 2001.
   Web of Science ®Google Scholar
• J. R. Howell, The Monte Carlo Method in Radiative Heat Transfer, ASME J. Heat Transfer, vol. 120, no. 3, pp. 547–560, 1998.
   Web of Science ®Google Scholar
• J. C. Henson and W. M. G. Malalasekera, Comparison of the Discrete Transfer and Monte Carlo Methods for Radiative Heat Transfer in 3D Nonhomogenous Scattering Media, Numer. Heat Transfer Part A, vol. 32, no. 1, pp. 19–36, 1997.
   Web of Science ®Google Scholar
• J. J. Noble, The Zone Method: Explicit Matrix Relations for Total Exchange Areas, Int. J. Heat Mass Transfer, vol. 18, pp. 261–269, 1975.
   Web of Science ®Google Scholar
• W. A. Fiveland, Discrete Ordinates Solutions of Transport Equation for Rectangular Enclosures, ASME J. Heat Transfer, vol. 106, pp. 699–706, 1984.
   Web of Science ®Google Scholar
• T. Y. Kim and S. W. Baek, Analysis of Combined Conductive and Radiative Heat Transfer in a Two-Dimensional Rectangular Enclosure Using the Discrete Ordinates Method, Int. J. Heat Mass Transfer, vol. 34, no. 9, pp. 2265–2273, 1991.
   Web of Science ®Google Scholar
• M. M. Razzaque, J. R. Howell, and D. E. Klein, Coupled Radiative and Conductive Heat Transfer in a Two-Dimensional Rectangular Enclosure with Gray Participating Media Using Finite Elements, ASME J. Heat Transfer, vol. 106, no. 3, pp. 613–619, 1984.
   Web of Science ®Google Scholar
• L. M. Ruan, M. Xie, H. Qi, W. An, and H. P. Tan, Development of a Finite Element Model for Coupled Radiative and Conductive Heat Transfer in Participating media, J. Quant. Spectrosc. Radiat. Transfer, vol. 102, no. 2, pp. 190–202, 2006.
   Web of Science ®Google Scholar
• J. C. Chai, G. Parthasarathy, H. S. Lee, and S. V. Patankar, Finite Volume Radiative Heat Transfer Procedure for Irregular Geometries, J. Thermophys. Heat Transfer, vol. 9, no. 3, pp. 410–415, 1995.
   Web of Science ®Google Scholar
• M. N. Borjini, H. Farhat, and M. Sassi, Analysis of Radiative Heat Transfer in a Partitioned Idealized Furnace, Numer. Heat Transfer Part A, vol. 44, no. 2, pp. 199–218, 2003.
   Web of Science ®Google Scholar
• G. Kamel, B. M. Naceur, M. Rachid, and S. Rachid, Formulation and Testing of the FTn Finite Volume Method for Radiative in 3-D Complex Inhomogeneous Participating Media, J. Quant. Spectrosc. Radiat. Transfer, vol. 98, no. 3, pp. 425–445, 2006.
   Web of Science ®Google Scholar
• M. Gazdallah, V. Feldheim, K. Claramunt, and C. Hirsch, Finite Volume Method for Radiative Heat Transfer in an Unstructured Flow Solver for Emitting, Absorbing and Scattering Media, J. Phys. Conf. Ser., vol. 369, no. 1, pp. 12020–12029, 2012.
   Google Scholar
• J. M. Zhao and L. H. Liu, Least-Squares Spectral Element Method for Radiative Heat Transfer in Semitransparent Media, Numer. Heat Transfer Part B, vol. 50, no. 5, pp. 473–489, 2006.
   Web of Science ®Google Scholar
• J. M. Zhao and L. H. Liu, Solution of Radiative Heat Transfer in Graded Index Media by Least Square Spectral Element Method, Int. J. Heat Mass Transfer, vol. 50, no. 13–14, pp. 2634–2642, 2007.
   Web of Science ®Google Scholar
• W. M. Malalasekera and F. C. Lockwood, Computer Simulation of the King's Cross Fire: Effect of Radiative Heat Transfer on Fire Spread, Proc. Inst. Mech. Eng., vol. 205, pp. 201–208, 1991.
   PubMed Web of Science ®Google Scholar
• M. Sakami, A. Charette, and V. L. Le Dez, Application of the Discrete Ordinates Methods to Combined Conductive, and Radiative Heat Transfer in a Two-Dimensional Complex Geometry, J. Quant. Spectrosc. Radiat. Transfer, vol. 56, no. 4, 517–533, 1996.
   Web of Science ®Google Scholar
• P. F. Hsu, and Z. Q. Tan, Radiative, and Combined-mode Heat Transfer within L-shaped Nonhomogeneous, and Nongray Participating Media, Numer. Heat Transfer Part A, vol. 31, no. 8, pp.819–835, 1997.
   Web of Science ®Google Scholar
• J. Y. Tan, L. H. Liu, and B. X. Li, Least-squares Collocation Meshless Approach for Coupled Radiative and Conductive Heat Transfer, Numer. Heat Transfer Part B, vol. 49, no. 2, pp. 179–195, 2006.
   Web of Science ®Google Scholar
• K. Lari and S. A. Gandjalikhan Nassab, Analysis of Combined Radiative and Conductive Heat Transfer in Three-dimensional Complex Geometries Using Blocked-off Method, Iran. J. Sci Technol. Trans. Mech. Eng., vol. 35, pp. 107–119, 2011.
   Web of Science ®Google Scholar
• K. Lari and S. A. Gandjalikhan Nassab, Modeling of the Conjugate Radiation and Conduction Problem in a 3-D Complex Multi-burner Furnace, Thermal Sci., vol. 16, no. 4, pp. 1187–1200, 2012.
   Web of Science ®Google Scholar
• Y. Zhang, Y. Ma, H. L. Yi, and H. P. Tan, Natural Element Method for Solving Radiative Transfer with or without Conduction in Three-Dimensional Complex Geometries, J. Quant. Spectrosc. Radiat. Transfer, vol. 129, pp. 118–130, 2013.
   Web of Science ®Google Scholar
• W. An, T. Zhu, and N. P. Gao, Accelerative Iteration for Coupled Conductive-radiative Heat Transfer Computation in Semitransparent Media, Int. J. Heat Mass Transfer, vol. 82, pp. 503–509, 2015.
   Web of Science ®Google Scholar
• R. Peyret, Spectral Method for Incompressible Viscous Flow, Springer Verlag, New York, 2002.
   Google Scholar
• T. C. Chawla and S. H. Chan, Solution of Radiation-conduction Problems with Collocation Method Using B-splines as Approximating Functions, Int. J. Heat Transfer, vol. 22, no. 12, pp. 1657–1667, 1979.
   Web of Science ®Google Scholar
• D. C. Kuo, J. C. Morales, and K. S. Ball, Combined Natural Convection, and Volumetric Radiation in a Horizontal Annulus: Spectral, and Finite Volume Predictions, ASME J. Heat Transfer, vol. 121, no. 3, pp. 610–615, 1999.
   Web of Science ®Google Scholar
• X. H. Luo, B. W. Li, J. K. Zhang, and Z. M. Hu, Simulation of Thermal Radiation Effects on MHD Free Convection in a Square Cavity Using Chebyshev Collocation Spectral Method, Numer. Heat Transfer Part A, vol. 66, no. 7, pp. 792–815, 2014.
   Web of Science ®Google Scholar
• O. Turk and M. Tezer-Sezgin, Chebyshev Spectral Collocation Method for Unsteady MHD Flow and Heat Transfer of a Dusty Fluid between Parallel Plates, Numer. Heat Transfer Part A, vol. 64, no. 7, pp. 597–610, 2013.
   Web of Science ®Google Scholar
• J. V. P. De Oliveira, A. V. Cardona, M. T. Vilhena, and R. C. Barros, A Semi-analytical Numerical Method for Time-dependent Radiative Transfer Problems in Slab Geometry with Coherent Isotropic Scattering, J. Quant. Spectrosc. Radiat. Transfer, vol. 73, no. 1, pp. 55–62, 2002.
   Web of Science ®Google Scholar
• B. W. Li, Y. S. Sun, and Y. Yu, Iterative and Direct Chebyshev Collocation Spectral Methods for One-dimensional Radiative Heat Transfer, Int. J. Mass Heat Transfer, vol. 51, pp. 5887–5894, 2008.
   Web of Science ®Google Scholar
• B. W. Li, S. Tian, Y. S. Sun, and Z. M. Hu, Schur-decomposition for 3D Matrix Equations and Its Application in Solving Radiative Discrete Ordinates Equations Discretized by Chebyshev Collocation Spectral Method, J. Comput. Phys., vol. 229, no. 4, pp. 1198–1212, 2010.
   Web of Science ®Google Scholar
• Y. S. Sun, J. Ma, and B. W. Li, Chebyshev Collocation Spectral Method for Three-dimensional Transient Coupled Radiative-conductive Heat Transfer, ASME J. Heat Transfer, vol. 134, no. 9, pp. 092701, 2012.
   Google Scholar
• Y. S. Sun, J. Ma, B. W. Li, and Z. X. Guo, Prediction of Nonlinear Heat Transfer in Convective-radiative Fin with Temperature-dependent Properties by the Collocation Spectral Method, Numer. Heat Transfer Part B, vol. 69, no. 1, pp. 68–83, 2016.
   Web of Science ®Google Scholar
• G. J. Li, J. Ma, and B. W. Li, Collocation Spectral Method for the Transient Conduction-radiation Heat Transfer with Variable Thermal Conductivity in Two-dimensional Rectangular Enclosure, ASME J. Heat Transfer, vol. 137, no. 3, pp. 032701, 2015.
   Google Scholar
• N. Li, B. Meng, X. Feng, and D. Gui, The Spectral Collocation Method for the Stochastic Allen-Cahn Equation via Generalized Polynomial Chaos, Numer. Heat Transfer Part B, vol. 68, no. 1, pp. 11–29, 2015.
   Web of Science ®Google Scholar
• Y. S. Sun and B. W. Li, Prediction of Radiative Heat Transfer in 2D Irregular Geometries Using the Collocation Spectral Method Based on Body-fitted Coordinates, J. Quant. Spectrosc. Radiat. Transfer, vol. 113, no. 17, pp. 2205–2212, 2012.
   Web of Science ®Google Scholar
• S. S. Chen and B. W. Li, Application of Collocation Spectral Domain Decomposition Method to Solve Radiative Heat Transfer in 2D partitioned Domains, J. Quant. Spectrosc. Radiat. Transfer, vol. 149, pp. 275–284, 2014.
   Web of Science ®Google Scholar
• Z. Wang, Z. Huang, W. Zhang, and G. Xi, A Multidomain Chebyshev Pseudo-spectral Method for Fluid Flow and Heat Transfer from Square Cylinders, Numer. Heat Transfer Part B, vol. 68, no. 3, pp. 224–238, 2015.
   Web of Science ®Google Scholar
• W. M. Malalasekera and E. H. James, Radiative Heat Transfer Calculations in Three-dimensional Complex Geometries, ASME J. Heat Transfer, vol. 118, no. 1, pp. 225–228, 1996.
   Web of Science ®Google Scholar
• P. Mahanta, and S. C. Mishra, Collapsed Dimension Method Applied to Radiative Transfer Problems in Complex Enclosure with Participating Medium, Numer. Heat Transfer Part B, vol. 42, no. 4, pp. 367–388, 2002.
   Web of Science ®Google Scholar
• C. A. Wang, H. Sadat, V. Ledez, and D. Lemonnier, Meshless Method for Solving Radiative Transfer Problems in Complex Two-dimensional and Three-dimensional Geometries, Int. J. Thermal Sci., vol. 49, no. 12, pp. 2282–2288, 2010.
   Web of Science ®Google Scholar
• B. W. Li, Q. Yao, X. Y. Cao, and K. F. Cen, A New Discrete Ordinates Quadrature Scheme for Three-dimensional Radiative Heat Transfer, ASME J. Heat Transfer, vol. 120, no. 2, pp. 514–518, 1998.
   Web of Science ®Google Scholar
• H. L. Chen, Y. H. Su, and B. D. Shizgal, A Direct Spectral Collocation Poisson Solver in Polar and Cylindrical Coordinates, J. Comput. Phys., vol. 160, no. 2, pp. 453–469, 2000.
   Web of Science ®Google Scholar