## Abstract

The use of approximate boundary conditions at the opening of the cavities leads to restriction of the computational domain and, hence, the reduction in computational effort. However, the accuracy of the restricted domain approach (RDA) had been evaluated only for the natural convection inside open cavities and that too only for one aspect ratio (AR). The validity of the approach had not been evaluated for inclined, as well as, shallow cavities. This study focuses on the analysis of the accuracy of RDA against extended domain approach (EDA) in open cavities of different ARs, at different inclinations and different Rayleigh numbers (Ra). The results show that the difference between the approaches is only significant in very shallow cavities (AR is defined as the height of the hot wall divided by the depth of the cavity) at low Ra. For Ra higher than $106$ and an AR greater than 0.2, the maximum difference between the two approaches is around 5% and hence RDA can be recommended in these ranges, resulting in increased computational efficiency without significant loss in the accuracy. Moreover, the maximum difference in the results for the two methods is for intermediate inclinations. Even there, an increase in the difference is more pronounced at lower Ra. Furthermore, distribution of the exit velocity and temperature at the opening as well as the distribution of the Nusselt number at the hot wall is compared for RDA and EDA to explain the behavior of error at different ARs and inclinations.

## References

1.
Clausing
,
A. M.
,
1983
, “
Convective Losses From Cavity Solar Receivers—Comparisons Between Analytical Predictions and Experimental Results
,”
ASME J. Sol. Energy Eng.
,
105
(
1
), pp.
29
33
.10.1115/1.3266342
2.
Quere
,
P. L.
,
Humphrey
,
J. A. C.
, and
Sherman
,
F. S.
,
1981
, “
Numerical Calculation of Thermally Driven Two-Dimensional Unsteady Laminar Flow in Cavities of Rectangular Cross Section
,”
Numer. Heat Transfer, Part A
,
4
(
3
), pp.
249
283
.10.1080/01495728108961792
3.
Penot
,
F.
,
1982
, “
Numerical Calculation of Two-Dimensional Natural Convection in Isothermal Open Cavities
,”
Numer. Heat Transfer, Part A
,
5
(
4
), pp.
421
437
.10.1080/10407788208913457
4.
Skok
,
H.
,
,
S.
, and
Schoenhals
,
R. J.
,
1991
, “
Natural Convection in a Side-Facing Open Cavity
,”
Int. J. Heat Fluid Flow
,
12
(
1
), pp.
36
45
.10.1016/0142-727X(91)90006-H
5.
Chan
,
Y. L.
, and
Tien
,
C. L.
,
1985
, “
A Numerical Study of Two-Dimensional Natural Convection in Square Open Cavities
,”
Numer. Heat Transfer
,
8
(
1
), pp.
65
80
.10.1080/01495728508961842
6.
Chan
,
Y. L.
, and
Tien
,
C. L.
,
1985
, “
A Numerical Study of Two-Dimensional Laminar Natural Convection in Shallow Open Cavities
,”
Int. J. Heat Mass Transfer
,
28
(
3
), pp.
603
612
.10.1016/0017-9310(85)90182-6
7.
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
.10.1016/0142-727X(94)90017-5
8.
Singh
,
S. N.
, and
Venkateshan
,
S. P.
,
2004
, “
Numerical Study of Natural Convection With Surface Radiation in Side-Vented Open Cavities
,”
Int. J. Therm. Sci.
,
43
(
9
), pp.
865
876
.10.1016/j.ijthermalsci.2004.01.002
9.
Singh
,
D. K.
, and
Singh
,
S. N.
,
2016
, “
Combined Free Convection and Surface Radiation in a Tilted Open Cavity
,”
Int. J. Therm. Sci.
,
107
, pp.
111
120
.10.1016/j.ijthermalsci.2016.04.001
10.
Prakash
,
M.
,
Kedare
,
S. B.
, and
Nayak
,
J. K.
,
2012
, “
Numerical Study of Natural Convection Loss From Open Cavities
,”
Int. J. Therm. Sci.
,
51
, pp.
23
30
.10.1016/j.ijthermalsci.2011.08.012
11.
Prakash
,
M.
,
2013
, “
Numerical Studies on Natural Convection Heat Losses From Open Cubical Cavities
,”
J. Eng.
,
2013
, pp.
1
33
.10.1155/2013/320647
12.
Hinojosa
,
J. F.
,
Cabanillas
,
R. E.
,
Alvarez
,
G.
, and
,
C. E.
,
2005
, “
Nusselt Number for the Natural Convection and Surface Thermal Radiation in a Square Tilted Open Cavity
,”
Int. Commun. Heat Mass Transfer
,
32
(
9
), pp.
1184
1192
.10.1016/j.icheatmasstransfer.2005.05.007
13.
Hinojosa
,
J. F.
,
,
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, Part A
,
48
(
2
), pp.
179
196
.10.1080/10407780590948936
14.
Octavio
,
J.
,
Hinojosa
,
J. F.
,
Perfecto
,
J.
, and
Pérez
,
M.
,
2011
, “
Numerical Study of Natural Convection in an Open Cavity Considering Temperature-Dependent Fluid Properties
,”
Int. J. Therm. Sci.
,
50
(
11
), pp.
2184
2197
.10.1016/j.ijthermalsci.2011.05.017
15.
Polat
,
O.
, and
Bilgen
,
E.
,
2002
, “
Laminar Natural Convection in Inclined Open Shallow Cavities
,”
Int. J. Therm. Sci.
,
41
(
4
), pp.
360
368
.10.1016/S1290-0729(02)01326-1
16.
Polat
,
O.
, and
Bilgen
,
E.
,
2003
, “
Conjugate Heat Transfer in Inclined Open Shallow Cavities
,”
Int. J. Heat Mass Transfer
,
46
(
9
), pp.
1563
1573
.10.1016/S0017-9310(02)00427-1
17.
Polat
,
O.
, and
Bilgen
,
E.
,
2005
, “
Natural Convection and Conduction Heat Transfer in Open Shallow Cavities With Bounding Walls
,”
Heat Mass Transfer
,
41
(
10
), pp.
931
939
.10.1007/s00231-004-0597-2
18.
Mezrhab
,
A.
,
Amraqui
,
S.
, and
Abid
,
C.
,
2010
, “
Modeling of Combined Surface Radiation and Natural Convection in a Vented «T» Form Cavity
,”
Int. J. Heat Fluid Flow
,
31
(
1
), pp.
83
92
.10.1016/j.ijheatfluidflow.2009.10.004
19.
Amraqui
,
S.
,
Mezrhab
,
A.
, and
Abid
,
C.
,
2011
, “
Computation of Coupled Surface Radiation and Natural Convection in an Inclined «T» Form Cavity
,”
Energy Conserv. Manage.
,
52
(
2
), pp.
1166
1174
.10.1016/j.enconman.2010.09.011
20.
Singh
,
O.
,
Singh
,
S.
, and
Kedare
,
S. B.
,
2016
, “
Effect of Thermal Radiation on Accuracy of Restricted Domain Approach in a Square Open Cavity
,”
ASME
Paper No. IMECE2016-66380.10.1115/IMECE2016-66380.
21.
Vierendeels
,
J.
,
Merci
,
B.
, and
Dick
,
E.
,
2003
, “
Benchmark Solutions for the Natural Convective Heat Transfer Problem in a Square Cavity With Large Horizontal Temperature Differences
,”
Int. J. Numer. Methods Heat Fluid Flow
,
13
(
8
), pp.
1057
1078
.10.1108/09615530310501957