Lattice Boltzmann method (LBM) is performed to study numerically combined natural convection and surface radiation inside an inclined two-dimensional open square cavity. The cavity is heated by a constant temperature at the wall facing the opening. The walls normal to the heated surface are assumed to be adiabatic, diffuse, gray, and opaque while the open boundary is assumed to be black at ambient temperature. A Bathnagar, Gross and Krook (BGK) collision model with double distribution function (D2Q9-D2Q4) is adopted. Effects of surface radiation, inclination angle, and Rayleigh number on the heat transfer are analyzed and discussed. Results are presented in terms of isotherms, streamlines, and Nusselt number. It was found that the presence of surface radiation enhances the heat transfer. The convective Nusselt number decreases with increasing surface emissivity as well as with Rayleigh number, while the total Nusselt number increases with increasing surface emissivity and Rayleigh number. The inclination angle has also a significant effect on flow and heat transfer inside the cavity. However, the magnitude of total heat transfer decreases considerably when open cavity is tilted downward.

References

References
1.
Balaji
,
C.
, and
Venkateshan
,
S. P.
,
1994
, “
Interaction of Radiation With Free Convection in an Open Cavity
,”
Int. J. Heat Fluid Flow
,
15
(
4
), pp.
317
324
.
2.
Wang
,
Z.
,
Yang
,
M.
,
Li
,
L.
, and
Zhang
,
Y.
,
2011
, “
Combined Heat Transfer by Natural Convection-Conduction and Surface Radiation in an Open Cavity Under Constant Heat Flux Heating
,”
Numer. Heat Transfer, Part A
,
60
(
4
), pp.
289
304
.
3.
Vahl Davis
,
G. D.
,
1983
, “
Natural Convection of Air in Square Cavity, a Bench Mark Numerical Solution
,”
Int. J. Numer. Method Fluid
,
3
(
3
), pp.
249
264
.
4.
Cianfrini
,
C.
,
Corcione
,
M.
, and
Dell'Omo
,
P. P.
,
2005
, “
Natural Convection in Tilted Square Cavities With Differentially Heated Opposite Walls
,”
Int. J. Therm. Sci.
,
44
(
5
), pp.
441
451
.
5.
Martyushev
,
S. G.
, and
Sheremet
,
M. A.
,
2014
, “
Conjugate Natural Convection Combined With Surface Thermal Radiation in an Air Filled Cavity With Internal Heat Source
,”
Int. J. Therm. Sci.
,
76
, pp.
51
67
.
6.
Bahlaoui
,
A.
,
Raji
,
A.
,
Hasnaoui
,
M.
,
Ouardi
,
C.
,
Naïmi
,
M.
, and
Makayssi
,
T.
,
2011
, “
Height Partition Effect on Combined Mixed Convection and Surface Radiation in a Vented Rectangular Cavity
,”
J. Appl. Fluid Mech.
,
4
(
1
), pp.
89
96
.http://jafmonline.net/JournalArchive/download?file_ID=15275&issue_ID=203
7.
Yang
,
H. Q.
,
Yang
,
K. T.
, and
Lloyd
,
J. R.
,
1987
, “
Laminar Natural-Convection Flow Transitions in Tilted Three-Dimensional Longitudinal Rectangular Enclosures
,”
Int. J. Heat Mass Transfer
,
30
(
8
), pp.
1637
1644
.
8.
Altaç
,
Z.
, and
Kurtul
,
O.
,
2007
, “
Natural Convection in Tilted Rectangular Enclosures With a Vertically Situated Hot Plate Inside
,”
Appl. Therm. Eng.
,
27
(
11–12
), pp.
1832
1840
.
9.
Bouali
,
H.
,
Mezrhab
,
A.
,
Amaoui
,
H.
, and
Bouzidi
,
M.
,
2006
, “
Radiation-Natural Convection Heat Transfer in an Inclined Rectangular Enclosure
,”
Int. J. Therm. Sci.
,
45
(
6
), pp.
553
566
.
10.
Vivek
,
V.
,
Sharma
,
A. K.
, and
Balaji
,
C.
,
2012
, “
Interaction Effects Between Laminar Natural Convection and Surface Radiation in Tilted Square and Shallow Enclosures
,”
Int. J. Therm. Sci.
,
60
, pp.
70
84
.
11.
Lin
,
C. X.
, and
Xin
,
M. D.
,
1992
, “
Turbulent Mixed Convection-Radiation Interactions in a Cavity
,”
J. Therm. Sci.
,
1
(
3
), pp.
189
195
.
12.
Polat
,
O.
, and
Bilgen
,
E.
,
2002
, “
Laminar Natural Convection in Inclined Open Shallow Cavities
,”
Int. J. Therm. Sci.
,
41
(
4
), pp.
360
368
.
13.
Bilgen
,
E.
, and
Oztop
,
H.
,
2005
, “
Natural Convection Heat Transfer in Partially Open Inclined Square Cavities
,”
Int. J. Heat Mass Transfer
,
48
(
8
), pp.
1470
1479
.
14.
Singh
,
D. K.
, and
Singh
,
S. N.
,
2016
, “
Combined Free Convection and Surface Radiation in Tilted Open Cavity
,”
Int. J. Therm. Sci.
,
107
, pp.
111
120
.
15.
Frisch
,
U.
,
Hasslacher
,
B.
, and
Pomeau
,
Y.
,
1986
, “
Lattice Gas Automata for the Navier-Stokes Equation
,”
Phys. Rev. Lett.
,
56
(
14
), pp.
1505
1508
.
16.
McNamara
,
G. R.
, and
Zanetti
,
G.
,
1988
, “
Use of the Soltzmann Equation to Simulate Lattice-Gas Automata
,”
Phys. Rev. Lett.
,
61
(
20
), pp.
2332
2335
.
17.
Higuera
,
F. J.
,
Succi
,
S.
, and
Benzi
,
R.
,
1989
, “
Lattice Gas Dynamics With Enhanced Collisions
,”
Europhys. Lett.
,
9
(
4
), pp.
345
349
.
18.
Qian
,
Y. H.
,
D'Humieres
,
D.
, and
Lallemand
,
P.
,
1992
, “
Lattice BGK Models for Navier-Stokes Equation
,”
Europhys. Lett.
,
17
(
6
), pp.
479
484
.
19.
Succi
,
S.
,
2001
,
The Lattice Boltzmann Equation for Fluid Dynamics and Beyond
,
Calrendon Press
,
Oxford
, UK.
20.
Chen
,
S.
, and
Doolen
,
G. D.
,
1998
, “
Lattice Boltzmann Method for Fluid Flows
,”
Annu. Rev. Fluid Mech.
,
30
(
1
), pp.
329
364
.
21.
Bhatnagar
,
P. L.
,
Gross
,
E. P.
, and
Krook
,
M.
,
1954
, “
A Model for Collision Processes in Gases—I: Small Amplitude Processes in Charged and Neutral One-Component Systems
,”
Phys. Rev.
,
94
(
3
), pp.
511
525
.
22.
Hasan
,
M. F.
,
Himika, T. A.
, and
Molla, M.
,
2016
, “
Lattice Boltzmann Simulation of Airflow and Heat Transfer in a Model Ward of a Hospital
,”
ASME J. Therm. Sci. Eng. Appl.
,
9
(
1
), p. 011011.
23.
Alexander
,
F. J.
,
Chen
,
S.
, and
Sterling
,
J. D.
,
1993
, “
Lattice Boltzmann Thermohydrodynamics
,”
Phys. Rev. E
,
47
(
4
), p. R2249.
24.
Chen
,
Y.
,
Ohashi
,
H.
, and
Akiyama
,
M.
,
1994
, “
Thermal Lattice Bhatnagar-Gross-Krook Model Without Nonlinear Deviation in Macrodynamic Equations
,”
Phys. Rev. E
,
50
(
4
), pp.
2776
2783
.
25.
Pavlo
,
P.
,
Vahala
,
G.
, and
Vahala
,
L.
,
1998
, “
Higher Order Isotropic Velocity Grids in Lattice Methods
,”
Phys. Rev. Lett.
,
80
(
18
), pp.
3960
3963
.
26.
Filippova
,
O.
, and
Hanel
,
D.
,
2000
, “
A Novel Lattice BGK Approach for Low Mach Number Combustion
,”
J. Comput. Phys.
,
158
(2), pp.
139
160
.
27.
Lallemand
,
P.
, and
Luo
,
L. S.
,
2003
, “
Hybrid Finite-Difference Thermal Lattice Boltzmann Equation
,”
Int. J. Mod. Phys. B
,
17
(
01n02
), pp.
41
47
.
28.
Eggels
,
J. G. M.
, and
Somers
,
J. A.
,
1995
, “
Numerical Simulation of Free Convective Flow Using the Lattice-Boltzmann Scheme
,”
Int. J. Heat Fluid Flow
,
16
(
5
), pp.
357
364
.
29.
Shan
,
X.
,
1997
, “
Simulation of Rayleigh-Bénard Convection Using a Lattice Boltzmann Method
,”
Phys. Rev. E
,
55
(
3
), pp.
2780
2788
.
30.
He
,
X.
,
Chen
,
S.
, and
Doolen
,
G. D.
,
1998
, “
A Novel Thermal Model for the Lattice Boltzmann Method in Incompressible Limit
,”
J. Comput. Phys.
,
146
(
1
), pp.
282
300
.
31.
Rahmati
,
A. R.
, and
Najjarnezami
,
A.
,
2016
, “
A Double Multi-Relaxation-Time Lattice Boltzmann Method for Simulation of Magneto Hydrodynamics Natural Convection of Nanofluid in a Square Cavity
,”
J. Appl. Fluid Mech.
,
9
(
3
), pp.
1201
1214
.
32.
Gorban
,
A. N.
, and
Karlin
,
I. V.
,
1992
, “
Structure and Approximation of the Chapman-Enskog Expansion for Linearized Grad Equations
,”
Trans. Theory Stat. Phys.
,
21
(1–2), pp. 101–117.
33.
Gallivan
,
M. A.
,
Noble
,
D. R.
,
Georgeadis
,
J. G.
, and
Buckius
,
R. O.
,
1997
, “
An Evaluation of the Bounce-Back Boundary Condition for Lattice Boltzmann Simulation
,”
Int. J. Numer. Methods Fluids
,
25
(
3
), pp.
249
263
.
34.
Chen
,
S.
,
Martinez
,
D.
, and
Mei
,
R.
,
1996
, “
On Boundary Conditions in Lattice Boltzmann Methods
,”
Phys. Fluids
,
8
(
9
), pp.
2527
2536
.
35.
Mohamad
,
A. A.
,
2011
,
Lattice Boltzmann Method, Fundamentals and Engineering Applications With Computer Codes
,
Springer
,
London
.
36.
Siegel
,
R.
, and
Howell
,
J. R.
,
1992
,
Thermal Radiation Heat Transfer
,
3rd ed.
, Hemispheres Publishing, New York.
37.
Modest
,
M. F.
,
2003
,
Radiative Heat Transfer
,
2nd ed.
,
Elsevier
,
Amsterdam, The Netherlands
.
38.
Howell
,
J. R.
,
1982
,
A Catalog of Radiation Configuration Factors
,
McGraw-Hill
,
New York
.
39.
Wang
,
H.
,
Xin
,
S.
, and
Le Quéré
,
P.
,
2006
, “
Étude Numérique Du Couplage De La Convection Naturelle Avec Le Rayonnement De Surfaces En Cavité Carrée Remplie D'air
,”
C. R. Méc.
,
334
(
1
), pp.
48
57
.
41.
Martyushev
,
S. G.
, and
Sheremet
,
M. A.
,
2015
, “
Numerical Analysis of 3D Regimes of Natural Convection and Surface Radiation in a Differentially Heated Enclosure
,”
J. Eng. Thermophys.
,
24
(
1
), pp.
22
32
.
42.
Vanka
,
S. P.
,
1986
, “
Block-Implicit Multigrid Solution of Navier-Stokes Equations in Primitive Variables
,”
J. Comput. Phys.
,
65
(
1
), pp.
138
158
.
43.
Schreiber
,
R.
, and
Keller
,
H. B.
,
1983
, “
Driven Cavity Flows by Efficient Numerical Techniques
,”
J. Comput. Phys.
,
49
(
2
), pp.
310
333
.
44.
Ghia
,
U.
,
Ghia
,
K. N.
, and
Shin
,
C. T.
,
1982
, “
High-Re Solutions for Incompressible Flow Using the Navier-Stokes Equations and a Multigrid Method
,”
J. Comput. Phys.
,
48
(
3
), pp.
387
411
.
45.
Hou
,
S.
,
Zou
,
Q.
,
Chen
,
S.
, and
Doolen
,
G.
,
1995
, “
Simulation of Cavity Flow by Lattice Boltzmann Method
,”
J. Comput. Phys.
,
118
(
2
), pp.
329
347
.
46.
Hinojosa
,
J. F.
,
Alvarez
,
G.
, and
Estrada
,
C. A.
,
2006
, “
Three-Dimensional Numerical Simulation of the Natural Convection in an Open Tilted Cubic Cavity
,”
Rev. Mex. Fis.
,
52
(
2
), pp.
111
119
.https://rmf.smf.mx/pdf/rmf/52/2/52_2_111.pdf
47.
Prakash
,
M.
,
2013
, “
Numerical Study on Natural Convection Heat Loss From Open Cubical Cavities
,”
J. Eng.
,
2013
, p. 320647.
48.
Hinojosa
,
J. F.
,
Estrada
,
C. A.
,
Cabanillas
,
R. E.
, and
Alvarez
,
G.
,
2005
, “
Numerical Study of Transient and Steady-State Natural Convection and Surface Thermal Radiation in a Horizontal Square Open Cavity
,”
Numer. Heat Transfer
,
48
(
2
), pp.
179
196
.
You do not currently have access to this content.