Natural convection in triangular enclosures is an important problem. It displays well the generic attributes of this class of convection, with its dependence on enclosure geometry, orientation and thermal boundary conditions. It is particularly rich in its variety of flow regimes and thermal fields as well as having significant practical application. In this paper, a comprehensive view of the research area is sought by critically examining the experimental and numerical approaches adopted in studies of this problem in the literature. Different thermal boundary conditions for the evolution of the flow regimes and thermal fields are considered. Effects of changes in pitch angle and the Rayleigh number on the flow and thermal fields are examined in detail. Although most of the past studies are in the laminar regime, the review extends up to the recent studies of the low turbulent regime. Finally, areas of further research are highlighted.
References
1.
Bejan
, A.
, 2004, Convection Heat Transfer
, 3rd ed., Wiley
, New York
.2.
Del Campo
, E. M.
, Sen
, M.
, and Ramos
, E.
, 1988, “Analysis of Laminar Natural Convection in Triangular Enclosure
,” Numer. Heat Transfer
, 13
, pp. 353
–372
.3.
Hasani
, S. M. F.
and Chung
, B. T. F.
, 1997, “Laminar Natural Convection in a Triangular Enclosure
,” Proc. ASME Ocean Engineering Division
, D. T.
Valentine
, and C. C.
Jahnke
, eds., pp. 107
–116
.4.
Probert
, S. D.
and Thirst
, T. J.
, 1977, “Thermal Insulation Provided by Triangular Sectioned Attic Spaces
,” Appl. Energy
, 3
(1
), pp. 41
–50
.5.
Thirst
, T. J.
and Probert
, S. D.
, 1978, “Heat Transfer Versus Pitch Angle for Nonventilated Triangular-Sectioned, Apex-Upward Air-Filled Spaces
,” ASTM Spec. Tech. Publ.
660
, pp. 203
–210
.6.
Flack
, R. D.
, 1980, “The Experimental Measurement of Natural Convection Heat Transfer in Triangular Enclosures Heated or Cooled From Below
,” J. Heat Transfer
, 102
, pp. 770
–772
.7.
Bejan
, A.
and Poulikakos
, D.
, 1982, “Natural Convection in an Attic-Shaped Filled With Porous Material
,” J. Heat Transfer
, 104
, pp. 241
–247
.8.
Poulikakos
, D.
and Bejan
, A.
, 1983, “Natural Convection Experiments in a Triangular Space
,” J. Heat Transfer
, 105
, pp. 652
–655
.9.
Poulikakos
, D.
and Bejan
, A.
, 1983, “Numerical Study of Transient High Rayleigh Number Convection in an Attic-Shaped Porous Layer
,” J. Heat Transfer
, 105
, pp. 476
–484
.10.
Poulikakos
, D.
and Bejan
, A.
, 1983, “The Fluid Dynamics of an Attic Space
,” J. Fluid Mech.
131
, pp. 251
–269
.11.
Holtzman
, G. A.
, Hill
, R. W.
, and Ball
, K.S.
, 2000, “Laminar Natural Convection in Isosceles Triangular Enclosures Heated From Below and Symmetrically Cooled From Above
,” J. Heat Transfer
, 122
(3
), pp. 485
–491
.12.
Flack
, R. D.
and Witt
, C. L.
, 1979, “Laser Velocimeter Measurements in Natural Convection Flows in Triangular Enclosures
,” Proc. 3rd Int. Workshop on Laser Velocimetry (LV–III)
, pp. 445
–454
.13.
Flack
, R. D.
and Witt
, C. L.
, 1979, “Velocity Measurements in Two Natural Convection Air Flows Using a Laser Velocimeter
,” J. Heat Transfer
, 101
, pp. 256
–260
.14.
Flack
, R. D.
, Konopnicki
, T. T.
, and Rooke
, J. H.
, 1979, “The Measurement of Natural Convection Heat Transfer in Triangular Enclosures
,” J. Heat Transfer
, 101
, pp. 648
–654
.15.
Flack
, R. D.
, Brun
, K.
, and Schnipke
, R. J.
, 1995, “Measurement and Prediction of Natural Convection Velocities in Triangular Enclosures
,” Int. J. Heat Fluid Flow
, 16
, pp. 106
–113
.16.
Coleman
, T. A.
, 1980, “Heat Transfer by Steady Laminar Free Convection in Triangular Enclosures
,” Ph.D thesis, University of Lagos, Nigeria.17.
Akinsete
, V. A.
and Coleman
, T. A.
, 1982, “Heat Transfer by Steady Laminar Free Convection in Triangular Enclosures
,” Int. J. Heat Mass Transfer
, 25
(7
), pp. 991
–998
.18.
Akinsete
, V. A.
and Coleman
, T. A.
, 1979, “Heat Transfer by Steady Laminar Free Convection Within Triangular Enclosures
,” Numerical Methods in Thermal Problems
, Pineridge Press, Ltd.
, Swansea, Wales
, pp. 259
–268
.19.
Akinsete
, V. A.
and Coleman
, T. A
, 1979, “Heat Transfer by Steady Laminar Free Convection in Triangular Enclosures
,” Proc. Int. Congress Brasileiro De Engenharia Mecanica
, Brazil
.20.
Kihm
, K. D.
, Kim
, J. H.
, and Fletcher
, L.S.
, 1991, “Effects of Partial Openings on Natural Convection Heat Transfer in Triangular Enclosures
,” Heat Transfer in Enclosures
, ASME
New York
, ASME-HTD-177, pp. 51
–56
.21.
Blom
, P.
, 2001, “Venting of Attics and Pitched, Insulated Roofs
,” J. Thermal Envelope & Building Science
, 25
, pp. 32
–50
.22.
Gershuni
, G. Z.
, Zhukhovitskiy
, E. M.
, and Shvartzblat
, D. L.
, 1974, “Overcritical Convective Motions in Asymmetric Region
,” Hydrodynamics
, 7
, pp. 89
–95
.23.
Ghassemi
, M.
and Roux
, J. A.
, 1989, “Numerical Investigation of Natural Convection Within a Triangular Shaped Enclosure
,” Heat Transfer in Convective Flows
, R. K.
Shah
, ed., ASME
, New York
, pp. 169
–175
.24.
Salmun
, H.
, 1995, “Convection Patterns in a Triangular Domain
,” Int. J. Heat Mass Transfer
, 38
(2
), pp. 351
–362
.25.
Salmun
, H.
, 1995, “The Stability of a Single-Cell Steady-State Solution in a Triangular Enclosure
,” Int. J. Heat Mass Transfer
, 38
(2
), pp. 363
–369
.26.
Hasani
, S. M. F.
and Chung
, B. T.F.
, 1998, “Combined Natural Convection and Radiation in a Triangular Enclosure
,” Proc. 7th AIAA/ASME Joint ThermoPhysics & Heat Transfer Conference
, Vol. 357
(1
), pp. 63
–72
.27.
Hasani
, S. M. F.
and Chung
, B. T. F.
, 1997, “Laminar Natural Convection in a Triangular Enclosure
,” Proc. ASME Ocean Engineering Division
, D. T.
Valentine
and C. C.
Jahnke
, eds., ASME
, New York
, pp. 107
–116
.28.
Lam
, S. W.
, Gani
, R.
, and Symons
, J. G.
, 1989, “Experimental and Numerical Studies of Natural Convection in Trapezoidal Cavities
,” J. Heat Transfer
, 111
, pp. 372
–377
.29.
Gaskell
, P. H.
, Thompson
, H. M.
, and Savage
, M. D.
, 1999, “A Finite Element Analysis of Steady Viscous Flow in Triangular Cavities
,” Proc. Inst. Mech. Engrs. Part C: J. Mechanical Engineering Science
, 213
(3
), pp. 263
–276
.30.
Lei
, C.
and Patterson
, J. C.
, 2002, “Unsteady Natural Convection in a Triangular Enclosure Induced by the Absorption of Radiation
,” J. Fluid Mech.
460
, pp. 181
–209
.31.
Volker
, S.
, Burton
, T.
, and Vanka
, S. P.
, 1996, “Finite-Volume Multigrid Calculation of Natural Convection Flows on Unstructured Grids
,” Numer. Heat Transfer, Part B
, 30
(1
), pp. 1
–22
.32.
Tynjälä
, T.
, Hajiloo
, A.
, Polashenski
, W.
, Jr., and Zamankhan
, P.
, 2002, “Magnetodissipation in Ferrofluids
,” J. Magn. Magn. Mater.
252
, pp. 123
–125
.33.
Ridouane
, E. H.
and Campo
, A.
, 2006, “Time-Depending Pitchfork Bifurcation in the Thermal Convection Flow Confined to an Isosceles Triangular Cavity Heated From Below
,” Proc. 9th AIAA/ASME Joint Thermophysics Heat Transfer Conference
, California
.34.
Ridouane
, E. H.
and Campo
, A.
, 2007, “Effects of Attaching Baffles Onto the Inclined Walls of Attic Frames for Purposes of Energy Conservation
,” Heat Transfer Eng.
28
(2
), pp. 103
–111
.35.
Sahar
, G.
, Islam
, T.
, Saha
, S.
, and Islam
, Q.
, 2007, “Natural Convection in a Tilted Isosceles Triangular Enclosure With Discrete Bottom Heating
,” Thammasat Int. J. Sci. Tech.
, 12
(4
), pp. 24
–35
.36.
Omri
, A.
, Najjari
, M.
, and Nasrallah
, S. B.
, 2007, “Numerical Analysis of Natural Buoyancy-Induced Regimes in Isosceles Triangular Cavities
,” Numer. Heat Transfer, Part A
, 52
(7
), pp. 661
–678
.37.
Kent
, E. F.
, 2009, “Numerical Analysis of Laminar Natural Convection in Isosceles Triangular Enclosures
,” Proc. Inst. Mech. Eng.
223
(5
), pp. 1157
–1169
.38.
Roy
, S.
, Basak
, T.
, Thirumalesha
, C.
, and Krishna
, C. M.
, 2008, “Finite Element Simulation on Natural Convection Flow in a Triangular Enclosure due to Uniform and Nonuniform Bottom Heating
,” J. Heat Transfer
, 130
, 032501
.39.
Varol
, Y.
, Koca
, A.
, and Oztop
, H. F.
, 2006, “Natural Convection in a Triangle Enclosure With Flush Mounted Heater on the Wall
,” Int. Commun. Heat Mass Transfer
33
(8
), pp. 951
–958
.40.
Oztop
, H. F.
, Varol
, Y.
, and Koca
, A.
, 2007, “Laminar Natural Convection Heat Transfer in a Shed Roof With or Without Eave for Summer Season
,” Appl. Therm. Eng.
27
(13
), pp. 2252
–2265
.41.
Varol
, Y.
, Oztop
, H. F.
, and Yilmaz
, T.
, 2007, “Natural Convection in Triangular Enclosures With Protruding Isothermal Heater
,” Int. J. Heat Mass Trans.
50
, pp. 2451
–2462
.42.
Koca
, A.
, Oztop
, H. F.
, and Varol
, Y.
, 2008, “Numerical Analysis of Natural Convection in Shed Roofs With Eave of Buildings for Cold Climates
,” Computers and Mathematics with Applications
, 56
, pp. 3165
–3174
.43.
Basak
, T.
, Roy
, S.
, Babu
, S. K.
, and Pop
, I.
, 2008, “Finite Element Simulations of Natural Convection Flow in an Isosceles Triangular Enclosure Filled With a Porous Medium: Effects of Various Thermal Boundary Conditions
,” Int. J. Heat Mass Trans.
51
, pp. 2733
–2741
.44.
Basak
, T.
, Roy
, S.
, and Babu
, S. K.
, 2008, “Natural Convection and Flow Simulation in Differentially Heated Isosceles Triangular Enclosures Filled With Porous Medium
,” Chem.Eng. Sci.
63
, pp. 3328
–3340
.45.
Basak
, T.
, Roy
, S.
, Ramakrishna
, D.
, and Pop
, I.
, 2010, “Visualization of Heat Transport During Natural Convection Within Porous Triangular Cavities via Heatline Approach
,” Numer. Heat Transfer, Part A
, 57
(6
), pp. 431
–452
.46.
Basak
, T.
, Roy
, S.
, and Thirumalesha
, C.
, 2008, “Finite Element Simulations of Natural Convection in a Right-Angled Triangular Enclosure Filled With a Porous Medium: Effects of Various Thermal Boundary Conditions
,” J. Porous Media
, 11
(2
), pp. 159
–178
.47.
Varol
, Y.
, Oztop
, H. F.
, and Pop
I.
, 2009, “Entropy Generation due to Natural Convection in Non–Uniformly Heated Porous Isosceles Triangular Enclosures at Different Positions
,” International J. Heat Mass Trans.
52
, pp. 1193
–1205
.48.
Oztop
, H. F.
, Varol
, Y.
, and Pop
I.
, 2009, “Investigation of Natural Convection in Triangular Enclosure Filled With Porous Media Saturated With Water Near 4°C
,” Energy Convers. Manage.
50
, pp. 1473
–1480
.49.
Asan
, H.
and Namli
, L.
, 2000, “Laminar Natural Convection in a Pitched Roof of Triangular Cross-Section: Summer Day Boundary Conditions
,” J. Energy & Buildings
, 33
, pp. 69
–73
.50.
Talabi
, S. O.
and Nwabuko
, U
, 2001, “Heat Transfer by Steady Laminar Free Convection in Triangular Enclosures - A Second Look
,” J. Engineering Research
, 8
(1/2
), pp. 67
–86
.51.
Karyakin
, Y. E.
, Martynenko
, O. G.
, Sokovishin
, Y. A.
, and Ustok
, K. Z.
, 1985, “Numerical Simulation of Unsteady-State Natural Convection in Triangular Enclosures
,” Heat Transfer–Sov. Res.
17
(3
), pp. 1
–33
.52.
Karyakin
, Y. E.
and Sokovishin
, Y. A.
, 1985, “Unsteady Natural Convection in a Triangular Enclosure
,” Fluid Dyn;.
20
, pp. 811
–815
.53.
Karyakin
, Y. E.
and Sokovishin
, Y. A.
, 1985, “Unsteady-State Natural Convection in a Triangular Enclosure With Isothermal Walls
,” Izv. AN SSSR, Ser. Fiz. Energ. Nauk
, 4
, pp. 104
–110
.54.
Karyakin
, Y. E.
and Sokovishin
, Y. A.
, 1985, “Unsteady-State Natural Convection in an Enclosure of Triangular Cross-Section
,” Izv. AN SSSR, Mekh. Zhidk, Gaza
, 5
, pp. 169
–173
.55.
Karyakin
, Y. E.
, Sokovishin
, Y. A.
, and Martynenko
, O. G.
, 1988, “Transient Natural Convection in Triangular Enclosures
,” Int. J. Heat Mass Trans.
31
(9
), pp. 1759
–1766
.56.
Ridouane
, E. H.
, Campo
, A.
, and McGarry
, M.
, 2005, “Numerical Computation of Buoyant Airflows Confined to Attic Spaces Under Opposing Hot and Cold Wall Conditions
,” Int. J. Therm. Sci.
44
, pp. 944
–952
.57.
Basak
, T.
, Roy
, S.
, and Thirumalesha
, C.
, 2007, “Finite Element Analysis of Steady Natural Convection in Triangular Enclosure: Effects of Various Thermal Boundary Conditions
,” Chem. Eng. Sci.
62
(9
), pp. 2623
–2640
.58.
Basak
, T.
, Roy
, S.
, Babu
, S. K.
, and Balakrishnan
, A. R.
, 2008, “Finite Element Analysis of Natural Convection Flow in a Isosceles Triangular Enclosure due to Uniform and Non-Uniform Heating at the Side Walls
,” Int. J. Heat Mass Trans.
51
, pp. 4496
–4505
.59.
Kimura
, S.
and Bejan
, A.
, 1983, “The Heatline Visualization of Convective Heat Transfer
,” J. Heat Transfer
, 105
(4
), pp. 916
–919
.60.
Costa
, V. A. F.
, 2006, “Bejan’s Heatlines and Masslines for Convection Visualization and Analysis
,” Appl. Mech. Rev.
59
, pp. 126
–145
.61.
Basak
, T.
, Aravind
, G.
, and Roy
, S.
, 2009, “Visualization of Heat Flow due to Natural Convection Within Triangular Cavities Using Bejan’s Heatline Concept
,” Int. J. Heat Mass Trans.
52
, pp. 2824
–2833
.62.
Kaluri
, R. S.
, Anandalakshmi
, R.
, and Basak
, T.
, 2010, “Bejan’s Heatline Analysis of Natural Convection in Right-Angled Triangular Enclosures: Effects of Aspect-Ratio and Thermal Boundary Conditions
,” Int. J. Therm. Sci.
49
, pp. 1576
–1592
.63.
Basak
, T.
, Aravind
, G.
, Roy
, S.
, and Balakrishnan
, A. R.
, 2010, “Heatline Analysis of Heat Recovery and Thermal Transport in Materials Confined Within Triangular Cavities
,” Int. J. Heat Mass Trans.
53
, pp. 3615
–3628
.64.
Basak
, T.
, Roy
, S. D.
, Ramakrishna
, D.
and Pop
, I.
, 2010, “Visualization of Heat Transport due to Natural Convection for Hot Materials Confined Within Two Entrapped Porous Triangular Cavities via Heatline Concept
,” Int. J. Heat Mass Trans.
53
, pp. 2100
–2112
.65.
Basak
, T.
, Roy
, S.
, and Aravind
, G.
, 2009, “Analysis of Heat Recovery and Thermal Transport Within Entrapped Fluid Based on Heatline Approach
,” Chem. Eng. Sci.
64
, pp. 1673
–1686
.66.
Basak
, T.
, Roy
, S. D.
, Ramakrishna
, D.
, and Pandey
, B. D.
, 2010, “Analysis of Heat Recovery and Heat Transfer Within Entrapped Porous Triangular Cavities via Heatline Approach
,” Int. J. Heat Mass Trans.
53
, pp. 3655
–3669
.67.
Collatz
, L.
, 1966, Numerical Treatment of Differential Equations
, Springer
, Berlin
.68.
Haese
, P. M.
and Teubner
, M. D.
, 2002, “Heat Exchange in an Attic Space
,” Int. J. Heat Mass Trans.
45
, pp. 4925
–4936
.69.
Ridouane
, E. H.
, Campo
, A.
, and Hasnaoui
, M.
, 2006, “Turbulent Natural Convection in an Air-Filled Isosceles Triangular Enclosure
,” Int. J. Heat Fluid Flow
, 27
, pp. 476
–489
.70.
Kamiyo
, O. M.
, Collins
, M. W.
, and Karayiannis
, T. G.
, 2005, “Numerical Investigation of Turbulent Natural Convection Within a Triangular-shaped Cavity in a Tropical Environment
,” Proc. 4th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
, Meyer
, J. G.
, ed., Cairo
, Egypt
.71.
Kamiyo
, O. M.
, Collins
, M. W.
, and Karayiannis
, T. G.
, 2005, “Low Turbulence Natural Convection in Square and Triangular Enclosures
,” Proc. 9th UK National Heat Transfer Conference
, B. A.
Launder
, ed., University of Manchester, Manchester
, UK
, pp. 1
–10
.72.
Talabi
, S. O.
, Olunloyo
, V. O. S.
, Kamiyo
, O. M.
, Collins
, M. W.
, and Karayiannis
, T. G.
, 2006, “Flow Field and Reynolds Stress Distribution in Low Turbulence Natural Convection in a Triangular Cavity
,” Proc. Fifth International Symposium on Turbulence, Heat and Mass Transfer
, Hanjalic
, K.
, Nagano
, Y.
, and Jakirlic
, S.
, eds., Dubrovnik
, Croatia
, pp. 511
–514
.73.
Kamiyo
, O. M.
, Olunloyo
, V. O. S.
, Talabi
, S. O.
, and Collins
, M. W.
, 2009, “Natural Convection Within Triangular Enclosures: Applications in Building Attics
,” Proc. 4th University of Lagos Research Conference
, Ogunlesi
, M. M.
, ed., pp. 25
–34
.74.
Ghassemi
, M.
, Keshavarz
, A.
, and Fathabadi
, J.
, 2003, “Numerical Investigation of Turbulent Natural Convection in a Triangular Shaped Enclosure
,” Proc. 6th ASME-JSME Thermal Engineering Joint Conference
, pp. 1
–7
.75.
Ghassemi
, M.
, Fathabadi
, M.
, and Shadaram
, A.
, 2008, “Numerical Analysis of Turbulent Natural Convection Heat Transfer Inside a Triangular-Shaped Enclosure Utilizing Computational Fluid Dynamic Code
,” International Journal of Numerical Methods Heat & Fluid Flow
, 18
(1
), pp. 14
–23
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