The collocation spectral method (CSM) is further developed to solve the transient conduction–radiation heat transfer in a two-dimensional (2D) rectangular enclosure with variable thermal conductivity. The energy equation and the radiative transfer equation (RTE) are all discretized by Chebyshev–Gauss–Lobatto collocation points in space after the discrete ordinates method (DOM) discretization of RTE in angular domain. The treatment of variable thermal conductivity is executed using the array multiplication. The present method can deal with different boundary conditions with high accuracy, the Dirichlet one and mixed one, for example. Based on our new method, the effects of several parameters on heat transfer processes are analyzed.
Issue Section:
Radiative Heat Transfer
References
1.
Wu
, C. Y.
, and Ou
, N. R.
, 1994
, “Transient Two-Dimensional Radiative and Conductive Heat Transfer in a Scattering Medium
,” Int. J. Heat Mass Transfer
, 37
(7
), pp. 2675
–2686
.10.1016/0017-9310(94)90384-02.
Talukdar
, P.
, and Mishra
, S. C.
, 2002
, “Analysis of Conduction–Radiation Problem in Absorbing, Emitting and Anisotropically Scattering Media Using the Collapsed Dimension Method
,” Int. J. Heat Mass Transfer
, 45
(10
), pp. 2159
–2168
.10.1016/S0017-9310(01)00305-23.
Mishra
, S. C.
, and Lankadasu
, A.
, 2005
, “Transient Conduction–Radiation Heat Transfer in Participating Media Using the Lattice Boltzmann Method and the Discrete Transfer Method
,” Numer. Heat Transfer, Part A
, 47
(9
), pp. 935
–954
.10.1080/104077805909219354.
Mishra
, S. C.
, Lankadasu
, A.
, and Beronov
, K. N.
, 2005
, “Application of the Lattice Boltzmann Method for Solving the Energy Equation of a 2-D Transient Conduction–Radiation Problem
,” Int. J. Heat Mass Transfer
, 48
(17
), pp. 3648
–3659
.10.1016/j.ijheatmasstransfer.2004.10.0415.
Mishra
, S. C.
, and Roy
, H. K.
, 2007
, “Solving Transient Conduction and Radiation Heat Transfer Problems Using the Lattice Boltzmann Method and the Finite Volume Method
,” J. Comput. Phys.
, 223
(1
), pp. 89
–107
.10.1016/j.jcp.2006.08.0216.
Mondal
, B.
, and Mishra
, S. C.
, 2007
, “Application of the Lattice Boltzmann Method and the Discrete Ordinates Method for Solving Transient Conduction and Radiation Heat Transfer Problems
,” Numer. Heat Transfer, Part A
, 52
(8
), pp. 757
–775
.10.1080/104077807013476637.
Mondal
, B.
, and Mishra
, S. C.
, 2008
, “Lattice Boltzmann Method Applied to the Solution of the Energy Equations of the Transient Conduction and Radiation Problems on Non-Uniform Lattices
,” Int. J. Heat Mass Transfer
, 51
(1–2
), pp. 68
–82
.10.1016/j.ijheatmasstransfer.2007.04.0308.
Das
, R.
, Mishra
, S. C.
, Ajith
, M.
, and Uppaluri
, R.
, 2008
, “An Inverse Analysis of a Transient 2-D Conduction-Radiation Problem Using the Lattice Boltzmann Method and the Finite Volume Method Coupled With the Genetic Algorithm
,” J. Quant. Spectrosc. Radiat. Transfer
, 109
(11
), pp. 2060
–2077
.10.1016/j.jqsrt.2008.01.0119.
Yi
, H. L.
, Zhang
, H. C.
, and Tan
, H. P.
, 2009
, “Transient Radiation and Conduction Heat Transfer Inside a Plane-Parallel Participating Gray Medium With Boundaries Having Different Reflecting Characteristics
,” J. Quant. Spectrosc. Radiat. Transfer
, 110
(18
), pp. 1978
–1992
.10.1016/j.jqsrt.2009.06.00310.
Chaabane
, R.
, Askri
, F.
, and Nasrallah
, S. B.
, 2011
, “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
,” Comput. Phys. Commun.
, 182
(7
), pp. 1402
–1413
.10.1016/j.cpc.2011.03.00611.
Li
, B. W.
, Sun
, Y. S.
, and Zhang
, D. W.
, 2009
, “Chebyshev Collocation Spectral Methods for Coupled Radiation and Conduction in a Concentric Spherical Participating Medium
,” ASME J. Heat Transfer
, 131
(6
), p. 062701
.10.1115/1.309061712.
Sun
, Y. S.
, and Li
, B. W.
, 2010
, “Chebyshev Collocation Spectral Approach for Combined Radiation and Conduction Heat Transfer in One-Dimensional Semitransparent Medium With Graded Index
,” Int. J. Heat Mass Transfer
, 53
(7–8
), pp. 1491
–1497
.10.1016/j.ijheatmasstransfer.2009.11.04713.
Sun
, Y. S.
, and Li
, B. W.
, 2010
, “Spectral Collocation Method for Transient Conduction–Radiation Heat Transfer
,” J. Thermophys. Heat Transfer
, 24
(4
), pp. 823
–832
.10.2514/1.4340014.
Sun
, Y. S.
, and Li
, B. W.
, 2010
, “Spectral Collocation Method for Transient Combined Radiation and Conduction in an Anisotropic Scattering Slab With Graded Index
,” ASME J. Heat Transfer
, 132
(5
), p. 052701
. 10.1115/1.400044415.
Sun
, Y. S.
, Ma
, J.
, and Li
, B. W.
, 2012
, “Chebyshev Collocation Spectral Method for Three-Dimensional Transient Coupled Radiative–Conductive Heat Transfer
,” ASME J. Heat Transfer
, 134
(9
), p. 092701
.10.1115/1.400659616.
Chu
, H. S.
, and Tseng
, C. J.
, 1992
, “Conduction–Radiation Interaction in Absorbing, Emitting, and Scattering Media With Variable Thermal Conductivity
,” J. Thermophys. Heat Transfer
, 6
(3
), pp. 537
–540
.10.2514/3.39317.
Krishnaprakas
, C. K.
, 1998
, “Combined Conduction and Radiation Heat Transfer in a Cylindrical Medium
,” J. Thermophys. Heat Transfer
, 12
(4
), pp. 605
–608
.10.2514/2.638518.
Talukdar
, P.
, and Mishra
, S. C.
, 2002
, “Transient Conduction and Radiation Heat Transfer With Variable Thermal Conductivity
,” Numer. Heat Transfer, Part A
, 41
(8
), pp. 851
–867
.10.1080/1040778029005938719.
Mishra
, S. C.
, Talukdar
, P.
, Trimis
, D.
, and Durst
, F.
, 2005
, “Two-Dimensional Transient Conduction and Radiation Heat Transfer With Temperature Dependent Thermal Conductivity
,” Int. Commun. Heat Mass Transfer
, 32
(3–4
), pp. 305
–314
.10.1016/j.icheatmasstransfer.2004.05.01520.
Gupta
, N.
, Gorthi
, R. C.
, and Mishra
, S. C.
, 2006
, “Lattice Boltzmann Method Applied to Variable Thermal Conductivity Conduction and Radiation Problems
,” J. Thermophys. Heat Transfer
, 20
(4
), pp. 895
–902
.10.2514/1.2055721.
Mishra
, S. C.
, Krishna
, N. A.
, Gupta
, N.
, and Chaitanya
, G. R.
, 2008
, “Combined Conduction and Radiation Heat Transfer With Variable Thermal Conductivity and Variable Refractive Index
,” Int. J. Heat Mass Transfer
, 51
(1–2
), pp. 83
–90
.10.1016/j.ijheatmasstransfer.2007.04.01822.
Das
, R.
, Mishra
, S. C.
, and Uppaluri
, R.
, 2009
, “Retrieval of Thermal Properties in a Transient Conduction–Radiation Problem With Variable Thermal Conductivity
,” Int. J. Heat Mass Transfer
, 52
(11–12
), pp. 2749
–2758
.10.1016/j.ijheatmasstransfer.2008.12.00923.
Li
, B. W.
, Yao
, Q.
, Cao
, X. Y.
, and Cen
, K. F.
, 1998
, “A New Discrete Ordinates Quadrature Scheme for Three-Dimensional Radiative Heat Transfer
,” ASME J. Heat Transfer
, 120
(2
), pp. 514
–518
.10.1115/1.282427924.
Li
, B. W.
, Tian
, S.
, Sun
, Y. S.
, and Hu
, Z. M.
, 2010
, “Schur-Decomposition for 3D Matrix Equations and Its Application in Solving Radiative Discrete Ordinates Equations Discretized by Chebyshev Collocation Spectral Method
,” J. Comput. Phys.
, 229
(4
), pp. 1198
–1212
.10.1016/j.jcp.2009.10.02525.
Mishra
, S. C.
, Talukdar
, P.
, Trimis
, D.
, and Durst.
, F.
, 2003
, “Computational Efficiency Improvements of the Radiative Transfer Problems With or Without Conduction—A Comparison of the Collapsed Dimension Method and the Discrete Transfer Method
,” Int. J. Heat Mass Transfer
, 46
(16
), pp. 3083
–3095
.10.1016/S0017-9310(03)00075-926.
Mahapatraa
, S. K.
, Dandapata
, B. K.
, and Sarkar
, A.
, 2006
, “Analysis of Combined Conduction and Radiation Heat Transfer in Presence of Participating Medium by the Development of Hybrid Method
,” J. Quant. Spectrosc. Radiat. Transfer
, 102
(2
), pp. 277
–292
.10.1016/j.jqsrt.2006.02.015Copyright © 2015 by ASME
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