This paper deals with the analysis of the effects of combined dual-phase-lag (DPL) heat conduction and radiation in a concentric spherical enclosure with diffuse-gray surfaces. The enclosed medium is optically participating, i.e., it is radiatively absorbing, emitting, and scattering. Lattice Boltzmann method (LBM) is used to solve the energy equation, and finite volume method (FVM) is used to compute the radiative information. To establish the accuracy of this approach, the combined energy equation is also solved with the finite difference method. Radial temperature profiles and energy contributions by conduction and radiation at various instances and prior to steady-state are elaborated for different kind of thermal perturbations Influence of numerous conductive and radiative parameters over the heat transport process have been investigated in detail. It is observed that higher contribution of radiation to the heat transport process can destroy the thermal wave in the medium completely. Sample results for pure non-Fourier heat conduction, pure radiation, and steady-state response of combined Fourier conduction and radiation in spherical geometry are compared with the results available in literature. In all the cases, comparison shows good agreement with the reported results.

References

References
1.
Petrov
,
V. A.
,
1997
, “
Combined Radiation and Conduction Heat Transfer in High Temperature Fiber Thermal Insulation
,”
Int. J. Heat Mass Transfer
,
40
(
9
), pp.
2241
2247
.
2.
Spinnler
,
M.
,
Winter
,
E. R. F.
, and
Viskanat
,
R.
,
2004
, “
Studies on High-Temperature Multilayer Thermal Insulations
,”
Int. J. Heat Mass Transfer
,
47
(
6–7
), pp.
1305
1312
.
3.
Lapka
,
P.
, and
Furmanski
,
P.
,
2012
, “
Fixed Cartesian Grid Based Numerical Model for Solidification Process of Semi-Transparent Materials I: Modelling and Verification
,”
Int. J. Heat Mass Transfer
,
55
(
19–20
), pp.
4941
4952
.
4.
Yi
,
H. L.
,
Wang
,
C. H.
,
Tan
,
H. P.
, and
Zhou
,
Y.
,
2012
, “
Radiative Heat Transfer in Semitransparent Solidifying Slab Considering Space–Time Dependent Refractive Index
,”
Int. J. Heat Mass Transfer
,
55
(
5–6
), pp.
1724
1731
.
5.
Sghaier
,
T.
,
Cherif
,
B.
, and
Sifaoui
,
M. S.
,
2002
, “
Theoretical Study of Combined Radiative Conductive and Convective Heat Transfer in Semi-Transparent Porous Medium in a Spherical Enclosure
,”
J. Quant. Spectrosc. Radiat. Transfer
,
75
(
3
), pp.
257
271
.
6.
Keshtkar
,
M. M.
, and
Nassab
,
S. A. G.
,
2009
, “
Theoretical Analysis of Porous Radiant Burners Under 2-D Radiation Field Using Discrete Ordinates Method
,”
J. Quant. Spectrosc. Radiat. Transfer
,
110
(
17
), pp.
1894
1907
.
7.
Lee
,
S.
, and
Cunnington
,
G. R.
,
2000
, “
Conduction and Radiation Heat Transfer in High-Porosity Fiber Thermal Insulation
,”
J. Thermophys. Heat Transfer
,
14
(
2
), pp.
121
136
.
8.
Jaunich
,
M.
,
Raje
,
S.
,
Kim
,
K.
,
Mitra
,
K.
, and
Guo
,
Z.
,
2008
, “
Bio-Heat Transfer Analysis During Short Pulse Laser Irradiation of Tissues
,”
Int. J. Heat Mass Transfer
,
51
(
23–24
), pp.
5511
5521
.
9.
Sakurai
,
A.
,
Maruyama
,
S.
, and
Matsubara
,
K.
,
2010
, “
The Radiation Element Method Coupled With the Bioheat Transfer Equation Applied to the Analysis of the Photothermal Effect of Tissues
,”
Numer. Heat Transfer, Part A
,
58
(
8
), pp.
625
640
.
10.
Baek
,
S. W.
,
Park
,
J. H.
, and
Kang
,
S. J.
,
2001
, “
Transient Cooling of a Two-Phase Medium of Spherical Shape When Exposed to the Rarefied Cold Environment
,”
Int. J. Heat Mass Transfer
,
44
(
12
), pp.
2345
2356
.
11.
Kim
,
M. Y.
,
Baek
,
S. W.
, and
Lee
,
Y. C.
,
2008
, “
Prediction of Radiative Heat Transfer Between Two Concentric Spherical Enclosures With the Finite Volume Method
,”
Int. J. Heat Mass Transfer
,
51
(
19–20
), pp.
4820
4828
.
12.
Baumeister
,
K. J.
, and
Hamill
,
T. D.
,
1969
, “
Hyperbolic Heat-Conduction Equation-a Solution for the Semi-Infinite Body Problem
,”
ASME J. Heat Transfer
,
91
(
4
), pp.
543
548
.
13.
Kaminski
,
W.
,
1990
, “
Hyperbolic Heat Conduction Equation for Materials With a Nonhomogeneous Inner Structure
,”
ASME J. Heat Transfer
,
112
(
3
), pp.
555
560
.
14.
Mitra
,
K.
,
Kumar
,
S.
,
Vedavarz
,
A.
, and
Moallemi
,
M. K.
,
1995
, “
Experimental Evidence of Hyperbolic Heat Conduction in Processed Meat
,”
ASME J. Heat Transfer
,
117
(
3
), pp.
568
573
.
15.
Frankel
,
J. J.
,
Vick
,
B.
, and
Ozisik
,
M. N.
,
1987
, “
General Formulation and Analysis of Hyperbolic Heat Conduction in Composite Media
,”
Int. J. Heat Mass Transfer
,
30
(
7
), pp.
1293
1305
.
16.
Cattaneo
,
C.
,
1958
, “
A Form of Heat Conduction Equation Which Eliminates the Paradox of Instantaneous Propagation
,”
Compte Rendus
,
247
, pp.
431
433
.
17.
Vernotee
,
P.
,
1958
, “
Les Paradoxes De La Theorie Continue De Equationdel La Chaleur
,”
Compte R.
,
246
, pp.
3154
3155
.
18.
Ozisik
,
M. N.
, and
Tzou
,
D. Y.
,
1994
, “
On the Wave Theory in Heat Conduction
,”
ASME J. Heat Transfer
,
116
(
3
), pp.
526
535
.
19.
Tzou
,
D. Y.
,
1995
, “
A Unified Field Approach for Heat Conduction From Macro to Micro Scales
,”
ASME J. Heat Transfer
,
117
(
1
), pp.
8
14
.
20.
Tzou
,
D. Y.
,
1995
, “
Experimental Support for the Lagging Behaviour in Heat Propagation
,”
J. Thermophys. Heat Transfer
,
9
(
4
), pp.
686
693
.
21.
Jiang
,
F.
,
2002
, “
Non-Fourier Heat Conduction Phenomena in Porous Material Heated by Microsecond Laser Pulse
,”
Microscale Thermophys. Eng.
,
6
(
4
), pp.
331
346
.
22.
Zhou
,
J.
, and
Zhang
,
Y.
,
2009
, “
An Axisymmetric Dual-Phase-Lag Bioheat Model for Laser Heating of Living Tissues
,”
Int. J. Therm. Sci.
,
48
(
8
), pp.
1477
1485
.
23.
Xu
,
F.
,
Seffen
,
K. A.
, and
Lu
,
T. J.
,
2008
, “
Non-Fourier Analysis of Skin Biothermomechanics
,”
Int. J. Heat Mass Transfer
,
51
(
9–10
), pp.
2237
2259
.
24.
Narasimhan
,
A.
, and
Sadashivam
,
S.
,
2013
, “
Non-Fourier Bio Heat Transfer Modelling of Thermal Damage During Retinal Laser Irradiation
,”
Int. J. Heat Mass Transfer
,
60
, pp.
591
597
.
25.
Chen
,
T.
,
2007
, “
Numerical Solution of Hyperbolic Heat Conduction in Thin Surface Layers
,”
Int. J. Heat Mass Transfer
,
50
(
21–22
), pp.
4424
4429
.
26.
Lee
,
H. L.
,
Chen
,
W. L.
,
Chang
,
W. J.
,
Wei
,
E. J.
, and
Yang
,
Y. C.
,
2013
, “
Analysis of Dual-Phase-Lag Heat Conduction in Short-Pulse Laser Heating of Metals With a Hybrid Method
,”
Appl. Therm. Eng.
,
52
(
2
), pp.
275
283
.
27.
Jia
,
T.
,
Lan
,
H.
, and
Gang
,
L.
,
2006
, “
Numerical Simulation of the Non-Fourier Heat Conduction in a Solid-State Laser Medium
,”
Chin. Phys. Lett.
,
23
, p.
2487
28.
Al. Nimr
,
M. A.
, and
Khadrawi
,
A. F.
,
2004
, “
Thermal Behavior of a Stagnant Gas Confined in a Horizontal Microchannel as Described by the Dual-Phase-Lag Heat Conduction Model
,”
Int. J. Thermophys.
,
25
(
6
), pp.
1953
1960
.
29.
Vadasz
,
P.
,
2005
, “
Absence of Oscillations and Resonance in Porous Media Dual-Phase-Lagging Fourier Heat Conduction
,”
ASME J. Heat Transfer
,
127
(
3
), pp.
307
314
.
30.
Glass
,
D. E.
,
Özisik
,
M. N.
, and
McRae
,
D. S.
,
1987
, “
Hyperbolic Heat Conduction With Radiation in an Absorbing and Emitting Medium
,”
Numer. Heat Transfer
,
12
(
3
), pp.
321
333
.
31.
Liu
,
L. H.
, and
Tan
,
H. P.
,
2001
, “
Non-Fourier Effects on Transient Coupled Radiative–Conductive Heat Transfer in One-Dimensional Semitransparent Medium Subjected to a Periodic Irradiation
,”
J. Quant. Spectrosc. Radiant. Transfer
,
71
(
1
), pp.
11
24
.
32.
Chu
,
H.
,
Lin
,
S.
, and
Lin
,
C.
,
2002
, “
Non-Fourier Heat Conduction With Radiation in an Absorbing, Emitting, and Isotropically Scattering Medium
,”
J. Quant. Spectrosc. Radiant. Transfer
,
73
(
6
), pp.
571
582
.
33.
Liu
,
L. H.
,
Tan
,
H. P.
, and
Tong
,
T. W.
,
2001
, “
Non-Fourier Effects on Transient Temperature Response in Semi-Transparent Medium Caused by Laser Pulse
,”
Int. J. Heat Mass Transfer
,
44
(
17
), pp.
3335
3344
.
34.
Mishra
,
S. C.
,
Mondal
,
B.
, and
Kumar
,
T. V. P.
,
2008
, “
Lattice Boltzmann Method Applied to the Solution of Energy Equation of a Radiation and Non-Fourier Heat Conduction Problem
,”
Numer. Heat Transfer, Part A
,
54
(
8
), pp.
798
818
.
35.
Dai
,
W.
,
Shen
,
L.
,
Nassar
,
R.
, and
Zhu
,
T.
,
2004
, “
A Stable and Convergent Three-Level Finite Difference Scheme for Solving a Dual-Phase-Lagging Heat Transport Equation in Spherical Coordinates
,”
Int. J. Heat Mass Transfer
,
47
(
8–9
), pp.
1817
1825
.
36.
Ho
,
J. R.
,
Kuo
,
C. P.
, and
Jiaung
,
W. S.
,
2003
, “
Study of Heat Transfer in Multilayered Structure Within the Framework of Dual-Phase-Lag Heat Conduction Model Using Lattice Boltzmann Method
,”
Int. J. Heat Mass Transfer
,
46
(
1
), pp.
55
69
.
37.
Mcdonough
,
J. M.
,
Kunadian
,
I.
,
Kumar
,
R. R.
, and
Yang
,
T.
,
2006
, “
An Alternative Discretization and Solution Procedure for the Dual Phase-Lag Equation
,”
J. Comput. Phys.
,
219
(
1
), pp.
163
171
.
38.
Liu
,
K. C.
, and
Cheng
,
P.
,
2006
, “
Numerical Analysis of Dual-Phase-Lag Heat Conduction in Layered Films
,”
Numer. Heat Transfer, Part A
,
49
(
6
), pp.
589
606
.
39.
Mohamad
,
A. A.
,
2011
,
Lattice Boltzmann Method: Fundamental and Engineering Applications With Computer Codes
,
Springer-Verlag
,
London
.
40.
Chen
,
T. M.
, and
Chen
,
C. C.
,
2010
, “
Numerical Solution for the Hyperbolic Heat Conduction Problems in the Radial–Spherical Coordinate System Using a Hybrid Green's Function Method
,”
Int. J. Therm. Sci.
,
49
(
7
), pp.
1193
1196
.
41.
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
.
42.
Dlala
,
A.
,
Sghaier
,
T.
, and
Seddiki
,
E.
,
2007
, “
Numerical Solution of Radiative and Conductive Heat Transfer in Concentric Spherical and Cylindrical Media
,”
J. Quant. Spectrosc. Radiat. Transfer
,
107
(
3
), pp.
443
457
.
43.
Bertman
,
B.
, and
Sandiford
,
D. J.
,
1970
, “
Second Sound in Solid Helium
,”
Sci. Am.
,
222
(
5
), pp.
92
101
.
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