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.

References

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)90384-0
2.
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)00305-2
3.
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
.10.1080/10407780590921935
4.
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.2004.10.041
5.
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.2006.08.021
6.
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
.10.1080/10407780701347663
7.
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.2007.04.030
8.
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.2008.01.011
9.
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.2009.06.003
10.
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.2011.03.006
11.
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
.10.1115/1.3090617
12.
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.2009.11.047
13.
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
.10.2514/1.43400
14.
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
. 10.1115/1.4000444
15.
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
.10.1115/1.4006596
16.
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
.10.2514/3.393
17.
Krishnaprakas
,
C. K.
,
1998
, “
Combined Conduction and Radiation Heat Transfer in a Cylindrical Medium
,”
J. Thermophys. Heat Transfer
,
12
(
4
), pp.
605
608
.10.2514/2.6385
18.
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
.10.1080/10407780290059387
19.
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.2004.05.015
20.
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
.10.2514/1.20557
21.
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.2007.04.018
22.
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.2008.12.009
23.
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
.10.1115/1.2824279
24.
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.2009.10.025
25.
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)00075-9
26.
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.2006.02.015
You do not currently have access to this content.