Volume 44 Issue 1
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Feng XU, Huimin CUI. Natural convection in a differentially heated cavity[J]. Advances in Mechanics, 2014, 44(1): 201403. doi: 10.6052/1000-0992-14-003
Citation: Feng XU, Huimin CUI. Natural convection in a differentially heated cavity[J]. Advances in Mechanics, 2014, 44(1): 201403. doi: 10.6052/1000-0992-14-003

Natural convection in a differentially heated cavity

doi: 10.6052/1000-0992-14-003
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  • Corresponding author: Feng XU
  • Received Date: 2014-01-06
  • Publish Date: 2014-11-30
  • The study of natural convection in a differentially heated cavity is of practical significance in nature and industry. It is of scientific value to review the studies of natural convection flows, their flow properties, dynamical mechanisms, dimensional controlling parameter dependencies and heat transfer driven by the horizontal temperature gradient in the cavity. As shown by previous studies, the development of natural convection suddenly enforced by the horizontal temperature gradient between the sidewalls of the cavity includes an initial stage, a transitional stage and a steady or a quasi-steady stage. The transient flows in the different stages are determined by the Rayleigh number, the Prandtl number and the aspect ratio. The flow in the steady or quasi-steady stage could be a steady laminar, a periodic or a turbulent flow. In addition, the studies of instability and turbulence of natural convection in the cavity are reviewed, and the prospects for the study of natural convection in the cavity are presented.

     

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  • [1]
    代民果, 高智. 2006. 同位网格摄动有限体积格式求解浮力驱动方腔流. 力学学报, 38: 733-740 (Dai MG, Gao Z. 2006. Solving 2-D buoyancy-driven cavity flow on collocated meshes by perturbational finitevolume scheme. Acta Mechanica Sinica, 38: 733-740 )
    [2]
    董韶峰, 李荫堂, 刘艳华. 2003. 涡量{ 流函数方法模拟不同高宽比和角度的腔内自然对流. 低温与特气, 21: 16-18 (Dong S F, Li Y T, Liu Y H. 2003. Simulation of the natural convection in a closedcavity with vortex-stream function method. Low Temperature and Specialty Gases,21: 16-18 )
    [3]
    鞠向阳, 伍小平, 何世平. 1996. 用胶囊式液晶粒子同时测量流场的温度和速度. 力学学报, 28: 503-506(Ju X Y, Wu X P, He S P. 1996. Simultaneous fluid velocity and temperature measurements by usingencapsulated liquid crystal particles. Acta Mechanica Sinica, 28: 503-506 )
    [4]
    李光正, 李贵, 张宁. 2002. 封闭腔内自然对流数值方法研究. 华中科技大学学报, 19: 20-22. (Li G Z,Li G, Zhang N. 2002. Study of the numerical method for solving the natural convection in an enclosure.Journal of HUST. (Urban Science Edition), 19: 20-22)
    [5]
    李光正, 马洪林. 2004. 封闭腔内高瑞利数层流自然对流数值模拟. 华中科技大学学报, 21: 14-17 (LiG Z, Ma H L. 2004. Numerical simulation for the laminar natural convection of high Rayleigh numbers in an enclosure. Journal of HUST, (Urban Science Edition) 21: 14-17 )
    [6]
    李世武, 熊莉芳. 2007. 封闭方腔自然对流换热的研究. 工业加热, 36: 10-13 (Li S W, Xiong L F. 2007.Study of natural convection in closed a square cavity. Industrial Heating, 36: 10-13 )
    [7]
    刘滔, 林文贤, 高文峰等. 2008. 低普朗特数数流体自然对流边界层流动的直接数值模拟. 力学与实践, 30: 28-33 (Liu T, Lin W X, Gao W F et al. 2008. Direct numerical simulation of natural convectionboundary-layer flow of low Prandtl number fluid. Mechanics and Engineering, 30: 28-33 )
    [8]
    马丽娟, 徐丰, 胡非等. 2006. 侧加热腔体内重力波演化过程的数值模拟. 力学与实践, 28: 19-23 (MaL J, Xu F, Hu F et al. 2006. Numerical simulation of the formation and development of internal gravitywave in a differentially heated cavity. Mechanics and Engineering, 28: 19-23 )
    [9]
    秦国良, 徐忠. 2001. 谱元方法求解正方形封闭空腔内的自然对流换热. 计算物理, 18: 119-124 (QinG L, Xu Z. 2001. Computation of natural convection in two-dimensional cavity using spectral elementmethod. Chinese Journal of Computational Physics, 18: 119-124 )
    [10]
    童长青, 何雅玲, 王勇, 刘迎文. 2007. 封闭方腔自然对流的格子{Boltzmann 方法动态模拟. 西安交通大学学报, 41: 33-36 (Tong C Q, He Y L, Wang Y, Liu Y W. 2007. Simulation of transient naturalconvection in square cavity with incompressible thermal lattice-Boltzmann method. Journal of Xi'anJiaotong University, 41: 33-36 )
    [11]
    王小华, 朱文芳. 2010. 长方腔自然对流第一次分岔突变现象的数值分析. 力学学报, 42: 389-399 (WangX H, Zhu W F. 2010.Numerical research on the sudden change characteristic of the first bifurcation fornatural convection of air enclosure in 2D rectangular cavity. Acta Mechanica Sinica, 42: 389-399)
    [12]
    王烨. 2011. 封闭腔湍流自然对流修正k-! 模型及其应用. [博士论文]. 兰州:兰州交通大学. (Wang Y.2011. Revised turbulent model and its application for turbulent natural convection in enclosures. [PhDThesis].Lanzhou: LanZhou JiaoTong University )
    [13]
    王晋军, 夏克青. 1999. Rayleigh-Bénard 湍流对流实验研究进展. 力学进展, 29: 557-566 (Wang J, XiaK. 1999. Advances in experimental investigation of Rayleigh-Bénard turbulent. Advances in Mechanics,29: 557-566 )
    [14]
    赵秉文, 邢荣鹏, 张世将, 等. 2008. 矩形方腔湍流自然对流数值模拟研究. 浙江理工大学学报, 25:458-460 (Zhao B W, Xing R P, Zhang S J, et al. 2008. The numerical simulation study of turbulencenatural convection in rectangular cavity. Journal of Zhejiang Sci-Tech University, 25: 458-460)
    [15]
    周全, 夏克青. 2012. Rayleigh-Bénard 湍流热对流研究的进展、现状及展望. 力学进展, 42: 231-251(Zhou Q, Xia K Q. 2012. Advances and outlook in turbulent Rayleigh-Bénard convection. Advances inMechanics, 42: 231-251)
    [16]
    Anderson R Bejan A. 1981. Heat transfer through single and double vertical walls in natural convection:Theory and experiment. Int. J. Heat Mass Transfer, 24: 1611-1620.
    [17]
    Armfield S W, Janssen R J A. 1996. A direct boundary-layer stability analysis of steady-state cavityconvection flow. Int. J. Heat Fluid Flow, 17: 539-546.
    [18]
    Armfield S W, Patterson J C. 1991. Direct simulation of wave interactions in unsteady natural convectionin a cavity. Int. J. Heat Mass Transfer, 34: 929-940.
    [19]
    Armfield S W, Patterson J C. 1992. Wave properties of natural convection boundary layers. J. Fluid Mech.,239: 195-212.
    [20]
    Armfield S W, Patterson J C. 2000. Start-up flow on a vertical semi-infinite heated plate. In: Proceedingsof the 7th Australasian Heat and Mass Transfer, Townsville, 7: 37-43.
    [21]
    Armfield S W, Patterson J C, Lin W X. 2007. Scaling investigation of the natural convection boundarylayer on an evenly heated plate. Int. J. Heat Mass Transfer, 50: 1592-1602.
    [22]
    Antohe B V, Lage J L. 1996. Experimental investigation on pulsation horizontal heating of an enclosurefilled with water. ASME J. Heat Transfer, 118: 889-896.
    [23]
    Bachelor G K. 1954. Heat transfer by free convection across a closed cavity between vertical boundaries atdifferent temperatures. Quart. Appl. Math., 12: 209-233.
    [24]
    Bertolotti F P, Herbert T, Spalart P R. 1992. Linear and nonlinear stability of the Blasius boundary layer.J. Fluid Mech., 242: 441-474.
    [25]
    Bednarz T, Fornalik E, Ozoe H, Szmyd J S, Patterson J C, Lei C. 2008. Influence of a horizontal magneticfield on the natural convection of paramagnetic fluid in a cube heated and cooled from two vertical sidewalls. Int. J. Therm. Sci., 47: 669-679.
    [26]
    Bednarz T, Lei C, Patterson J C, Ozoe H. 2009. Suppressing RayleighBénard convection in a cube using astrong magnetic field Experimental heat transfer rate measurements and flow visualization. Int. Comm.Heat Mass Transfer, 36: 97-102.
    [27]
    Bednarz T, Xu F, Lei C, Patterson J C. 2009. Visualization techniques for estimating thermal boundarylayers of natural convection flows. In: 7th World Conference on Experimental Heat Transfer, FluidMechanics and Thermodynamics, Krakow, Poland.
    [28]
    Bodenschatz E, Pesch W, Ahlers G. 2000. Recent developments in Rayleigh-Bénard convection. Annu. Rev.Fluid Mech., 32: 709-778.
    [29]
    Brassington G B, Patterson J C, Lee M. 2002. A new algorithm for analysing shadowgraph images. J. FlowVisual. Image Process, 9: 25-51.
    [30]
    Brooker A M H, Patterson J C, Armfield S W. 1997. Non-parallel linear stability analysis of the verticalboundary layer in a differentially heated cavity. J. Fluid Mech., 352: 265-281.
    [31]
    Brooker A M H, Patterson J C, Graham T, Schöpf W. 2000. Convective instability in a time-dependentbuoyancy driven boundary layer. Int. J. Heat Mass Transfer, 43: 297-310.
    [32]
    Brown S N, Riley N. 1973. Flow past a suddenly heated vertical plate. J. Fluid Mech., 59: 225-237.
    [33]
    Carrière P, Monkewitz P A. 1999. Convective versus absolute instability in mixed Rayleigh-Bénard-Poiseuilleconvection. J. Fluid Mech., 384: 243-262.
    [34]
    Catton I. 1978. Natural convection in enclosures. In: Proceedings of the 6th International Heat TransferConference, Toronto, 6: 13-30.
    [35]
    Cheesewright R, King K J, Ziai S. 1986. Experimental data for the validation of computer code for the pre-diction of two-dimensional buoyancy cavity flows. In: ASME Winter Annual Meeting, HTD-60, Anaheim,75-81.
    [36]
    Chen Q. 1996. Prediction of room air motion by Reynolds-Stress models. Building Environ., 31: 233-244.Chenoweth D R, Paolucci S. 1986. Natural convection in an enclosed vertical air layer with large horizontaltemperature differences. J. Fluid Mech. 169: 173-210.
    [37]
    Choi S K, Kim E K, Kim S O. 2004. Computation of turbulent natural convection in a rectangular cavitywith the k-ε-v2-f model. Numer. Heat Transfer, Part B, 45: 159-179.
    [38]
    Choi S K, Kim S O. 2012. Turbulence modeling of natural convection in enclosures: A review. J. Mech.Sci. Tech., 26: 283-297.
    [39]
    Cormack D E, Leal L G, Imberger J. 1974. Natural convection in a shallow cavity with differentially heatedend walls, Part 1, Asymptotic theory. J. Fluid Mech., 65: 209-229.
    [40]
    Cormack D E, Leal L G, Seinfeld J H. 1974. Natural convection in a shallow cavity with differentially heatedend walls, Part 2, Numerical solutions. J. Fluid Mech., 65: 231-246.
    [41]
    Daniels P G, Patterson J C. 1997. On the long-wave instability of natural-convection boundary layers. J.Fluid Mech., 335: 57-73.
    [42]
    Daniels P G, Patterson J C. 2001. On the short-wave instability of natural convection boundary layers.Proc. Roy. Soc. Lond. A, 457: 519-538.
    [43]
    Davey A. 1973. A simple numerical method for solving Orr-Sommerfield problems. Q. J. Mech. Appl.Maths., 26: 401-411.
    [44]
    De Vahl Davis G. 1983. Natural convection of air in a square cavity: A bench mark numerical solution. Int.J. Numer. Meth. Fluids, 3: 249-264.
    [45]
    De Vahl Davis G, Jones. 1983. Natural convection in a square cavity: A comparison exercise. Int. J.Numer. Meth. Fluids, 3: 227-248.
    [46]
    Dixit H N, Babu V. 2006. Simulation of high Rayleigh number natural convection in a square cavity usingthe lattice Boltzmann method. Int. J. Heat Mass Transfer, 49: 727-739.
    [47]
    Dol H S, Hanjali K. 2001. Computational study of turbulent natural convection in a side-heated near-cubicenclosure at a high-Rayleigh number. Int. J. Heat Mass Transfer, 44: 2323-2344.
    [48]
    Dol H S, Hanjali K, Kenjereš S. 1997. A comparative assessment of the second-moment differential andalgebraic models in turbulent natural convection. Int. J. Heat Fluid Flow, 18: 4-14.
    [49]
    Drazin P G. 2001. Introduction to Hydrodynamic Stability. Cambridge University Press, Cambridge, 45-61.Dring R, Gebhart B. 1968. A theoretical investigation of disturbance amplification in external laminarnatural convection. J. Fluid Mech., 34: 551.
    [50]
    Eckert E R G, Carlson W O. 1961. Natural convection in an air layer enclosed between two vertical platesat different temperatures. Int. J. Heat Mass Transfer, 2: 106-120.
    [51]
    Eckert E R G, Hartnett J P, Irvine T F. 1960. Flow-visualization studies of transition to turbulence infree-convection flow. ASME Paper, 60: 250.
    [52]
    Elder J W. 1965a.Laminar free convection in a vertical slot. J. Fluid Mech., 23: 77-98.
    [53]
    Elder J W. 1965b.Turbulent free convection in a vertical slot. J. Fluid Mech., 23: 99-111.
    [54]
    Fasel H, Konzelmann U. 1990. Nonparallel stability of a flat-plate boundary-layer using the complete Navier-Stokes equations. J. Fluid Mech., 221: 311-347.
    [55]
    Fu W S, Shieh W J. 1992. A study of thermal convection in an enclosure induced simultaneously by gravityand vibration. Int. J. Heat Mass Transfer, 35:1695-1710.
    [56]
    Fu W S, Shieh W J. 1993. Transient thermal convection in an enclosure induced simultaneously by gravityand vibration. Int. J. Heat Mass Transfer, 36: 437-452.
    [57]
    Gadoin E, Le Quere P, Daube O. 2001. A general methodology for investigating flow instabilities in complexgeometries: application to natural convection in enclosures. Int. J. Numer. Meth. Fluids, 37: 175-208.
    [58]
    Gebhart B.1969. Natural convection flow, instability and transition. J. Heat Transfer, 91: 293-309.
    [59]
    Gebhart B. 1973. Instability, transition & turbulence in buoyancy-induced flows. Annu. Rev. Fluid Mech.,5: 213-246.
    [60]
    Gebhart B. 1988. Transient response and disturbance growth in vertical buoyancy-driven flows. J. HeatTransfer, 110: 1166-1174.
    [61]
    Gebhart B, Mahajan R L. 1975. Characteristic disturbance frequency in vertical natural convection flow.Int. J. Heat Mass Transfer, 18: 1143-1148.
    [62]
    Gebhart B, Mahajan R L. 1982. Instability and transition in buoyancy induced flows. Adv. Appl. Mech.,22: 231-315.
    [63]
    Gill A E. 1966. The boundary-layer regime for convection in a rectangular cavity. J. Fluid Mech., 26:515-536.
    [64]
    Gill A E, Davey A. 1969. Instabilities of buoyancy-driven system. J. Fluid Mech., 35: 775-798.
    [65]
    Goldstein R J, Briggs D G. 1964. Transient free convection about vertical plates and cylinders. J. HeatTransfer, 86: 490-500.
    [66]
    Gresho P M, Lee R L, Chan S T. Sani RL. 1980. Solution of the time-dependent incompressible Navier-Stokes and Boussinesq equations using the Galerkin finite element method. In: Approximation Methodsfor Navier-Stokes problems. Lecture Notes in Mathematics, Springer, 771: 203-222.
    [67]
    Hanjali? K, Kenjereš S, Durst F. 1996. Natural convection in partitioned two-dimensional enclosures athigher Rayleigh numbers. Int. J. Heat Mass Transfer, 39: 1407-1427.
    [68]
    Hanjali? K, Vasic S. 1993. Some further exploration of turbulence models for buoyancy driven flows. Tur-bulent Shear Flows (Edited by Durst et al.), Springer, Berlin, 8: 319- 341.
    [69]
    Henkes R A W M. 1990. Natural-Convection Boundary Layers. [PhD thesis], Delft University of Technology,Delft, The Netherlans.
    [70]
    Henkes R A W M, Hoogendoorn C J. 1993. Scaling of the laminar natural-convection flow in a heated squarecavity. Int. J. Heat Mass Transfer, 36: 2913-2925.
    [71]
    Henkes R A W M, Hoogendoorn C J. 1995. Comparison exercise for computations of turbulent naturalconvection in enclosures. Numer. Heat Transfer, Part B, 28: 59-78.
    [72]
    Herbert T. 1997. Parabolized stability equations. Annu. Rev. Fluid Mech., 29: 245-283.
    [73]
    Hieber C A, Gebhart B. 1971. Stability of vertical natural convection boundary layers: Some numericalsolutions. J. Fluid Mech., 48: 625-646.
    [74]
    Holtzman G A, Hill R W, Ball K S, 2000. Laminar natural convection in isosceles triangular enclosuresheated from below and symmetrically cooled from above. J. Heat Transfer, 122: 485-491.
    [75]
    Hyun J M. 1994. Unsteady buoyant convection in an enclosure. Adv. Heat Transfer, 24: 277-320.
    [76]
    Hughes G O, Gri±ths R W. 2008. Horizontal convection. Annu. Rev. Fluid Mech., 40: 185-209.
    [77]
    Illingworth C R. 1950. Unsteady laminar flow of gas near an infinite flat plate. Proc. Camb. Phil. Soc.,46: 603-611.
    [78]
    Imberger J. 1974. Natural convection in a shallow cavity with differentially heated end walls, Part 3,Experimental results. J. Fluid Mech., 65: 247-260.
    [79]
    Inagaki T, Komori K. 1995. Heat transfer and fluid flow of natural convection along a vertical flat plate inthe transition region: experimental analysis of the wall temperature field. Int. J. Heat Mass Transfer,38: 3485-3495.
    [80]
    Ivey G N. 1984. Experiment on transient natural convection in a cavity. J. Fluid Mech. 144: 389-401.Iwatsu R, Hyun J M, Kuwahara K. 1992. Convection in a differentially heated square cavity with atorsionally-oscillating lid. Int. J. Heat Mass Transfer, 35: 1069-1076.
    [81]
    Jaluria Y, Gebhart B. 1973. An experimental study of nonlinear disturbance behavior in natural convection.J. Fluid Mech., 61: 337-365.
    [82]
    Jaluria Y, Gebhart B. 1974. On transition mechanisms in vertical natural convection flow. J. Fluid Mech.,66: 309-337.
    [83]
    Janssen R J A. 1994. Instabilities in natural-convection flows in cavities. [PhD thesis], The Netherlandthe:Delft University of Technology.
    [84]
    Janssen R J A, Armfield S. 1996. Stability properties of the vertical boundary layers in differentially heatedcavities. Int. J. Heat and Fluid Flow, 17: 547-556.
    [85]
    Janssen R J A, Henkes R A W M. 1995. Influence of Prandtl number on instability mechanisms andtransition in a differentially heated square cavity. J. Fluid Mech., 290: 319-344.
    [86]
    Joshi Y, Gebhart B. 1987. Transition of transient vertical natural convection flows in water. J. Fluid Mech.,179: 407-438.
    [87]
    Kim S K, Kim S Y, Choi Y D. 2002. Resonance of natural convection in a side heated enclosure with amechanically oscillating bottom wall. Int. J. Heat Mass Transfer, 45: 3155-3162.
    [88]
    Kim S K, Kim S Y, Choi Y D. 2005. Amplification of boundary layer instability by hot wall thermaloscillation in a side heated cavity. Phys. Fluids, 17: 014103.
    [89]
    Knowles C P, Gebhart B. 1968. The stability of the natural convection boundary layer. J. Fluid Mech., 34:657-686.
    [90]
    Kwak H S, Hyun J M. 1996. Natural convection in an enclosure having a vertical sidewall with time-varyingtemperature. J. Fluid Mech., 329: 65-88.
    [91]
    Kwak H S, Kuwahara K, Hyun J M. 1998. Resonant enhancement of natural convection heat transfer in asquare enclosure. Int. J. Heat Mass Transfer, 41: 2837-2846.
    [92]
    Lage J L, Bejan A. 1993. The resonance of natural convection in an enclosure heated periodically from theside. Int. J. Heat Mass Transfer, 36: 2027-2038.
    [93]
    Le Quéré P. 1990. Transition to unsteady natural convection in a tall water-filled cavity. Phys. Fluids, 2:503-515.
    [94]
    Le Quéré P, Alziary de Roquefort T. 1985. Computation of natural convection in two dimensional cavitieswith Chebyshev polynomials. J. Comput. Phys., 57: 210-228.
    [95]
    Le Quéré P, Behnia M. 1998. From onset of unsteadiness to chaos in a differentially heated square cavity.J. Fluid Mech., 359: 81-107.
    [96]
    Lei C, Patterson J C. 2002. Natural convection in a reservoir sidearm subject to solar radiation: Experimentalobservations. Exp. Fluids, 32: 590-599.
    [97]
    Lei C, Patterson J C. 2003. A direct stability analysis of a radiation-induced natural convection boundarylayer in a shallow wedge. J. Fluid Mech., 480: 161-184.
    [98]
    Lohse D, Xia K Q. 2010. Small-Scale properties of turbulent Rayleigh-Bénard convection. Annu. Rev.Fluid Mech., 42: 335-364.
    [99]
    Lin W, Armfield S W, Patterson J C. 2007. Cooling of a Pr < 1 fluid in a rectangular container. J. FluidMech., 574: 85-108.
    [100]
    Mahajan R L, Gebhart B. 1978. Leading edge effects in transient natural convection flow adjacent to avertical surface. J. Heat Transfer, 100: 731-733.
    [101]
    Mergui S, Penot F. 1996. Natural convection in a differentially heated square cavity: Experimental investi-gation at Ra = 1:69×109. Int. J. Heat Mass Transfer, 39: 563-574.
    [102]
    Merzkirch W. 1974, Flow Visualization, Academic Press, New York.
    [103]
    Nicolas X, Mojtabi A, Platten J K. 1997. Two-dimensional numerical analysis of the Poiseuille-Bénard flowin a rectangular channel heated from below. Phys. Fluids, 9: 337-348.
    [104]
    Nicolas X. 2012. Bibliographic review on the Poiseuille-Rayleigh-Bénard flows: the mixed convection flowsin horizontal rectangular ducts heated from below. Int. J. Therm. Sci., 41: 961-1016.
    [105]
    Nishimura T, Shiraishi M, Nagasawa F, Kawamura Y. 1988. Natural convection heat transfer in enclosureswith multiple vertical partitions. Int. J. Heat Mass Transfer, 31: 1679-1686.
    [106]
    Niu J, Zhu Z. 2004. Numerical evaluation of weakly turbulent flow patterns of natural convection in a squareenclosure with differentially heated side walls. Numer. Heat Transfer A, 45: 551-568.
    [107]
    Olshanskii M A. 2012. A fluid solver based on vorticity-helical density equations with application to anatural convection in a cubic cavity. Int. J. Numer. Meth. Fluids, 69: 983-994.
    [108]
    Ostrach S. 1964. Laminar flows with body forces. In Theory of Laminar Flows. Princeton University Press,Princeton.
    [109]
    Ostrach S. 1988. Natural Convection in Enclosures. J. Heat Transfer, 110: 1175-1190.
    [110]
    Paolucci S. 1990. Direct numerical simulation of two-dimensional turbulent natural convection in an enclosedcavity. J. Fluid Mech., 215: 229-262.
    [111]
    Paolucci S, Chenoweth D R. 1989. Transition to chaos in a differentially heated vertical cavity. J. FluidMech., 201: 379-410.
    [112]
    Partankar S V. 1980. Numerical Heat Transfer and Fluid Flow, Hemisphere, New.York
    [113]
    Patterson J C. 1984. On the existence of an oscillatory approach to steady natural convection in cavities.J. heat Transfer, 106: 104-108.
    [114]
    Patterson J C, Armfield S W. 1990. Transient features of natural convection in a cavity. J. Fluid Mech.,219: 469-497.
    [115]
    Patterson J C, Graham T, Schopf W, Armfield S W. 2002. Boundary layer development on a semi-infinitesuddenly heated vertical plate. J. Fluid Mech., 453: 39-55.
    [116]
    Patterson J C, Imberger J. 1980.Unsteady natural convection in a rectangular cavity. J. Fluid Mech., 100:65-86.
    [117]
    Peng S H, Davidson L. 1998. Comparasion of sub grid-scale models in LES for turbulent convection flowwith heat transfer. Turbulent Heat Transfer, 2: 524-535.
    [118]
    Peng S H, Davidson L. 1999. Computation of turbulent buoyant flows in enclosures with low-Reynolds-number k-! models. Int. J. Heat Fluid Flow, 20: 172-184.
    [119]
    Peng S H, Davidson L. 2001. Large eddy simulation for turbulent buoyant flow in a confined cavity. Int. J.Heat Fluid Flow, 22: 323-331.
    [120]
    Penot F, Ndame A, Le Quere P. 1990. Investigation of the route to turbulence in a differentially heatedcavity. In Proceedings of the 9th International Heat Transfer Conference, 2: 417-422.
    [121]
    Prandtl L. 1952. Essentials of Fluid Dynamics. Blackie, London
    [122]
    Plapp J E. 1957. The analytic study of the laminar boundary layer stability in free convection. J. Aeron.Sci., 24: 318-319.
    [123]
    Ravi M R R, Henkes R A W M, Hoogendoorn C J. 1994. On the high-Rayleigh-number structure of steadylaminar natural-convection flow in a square enclosure. J. Fluid Mech., 262: 325-351.
    [124]
    Rhee H S, Koseff J R, Street R L. 1984. Flow visualization of a recirculating flow by rheoscopic liquid andliquid crystal techniques. Exp. Fluids, 2: 57-64.
    [125]
    Schetz J A, Eichorn R. 1962. Unsteady natural convection in the vicinity of a doubly infinite vertical plate.J. Heat Transfer, 84: 334-338.
    [126]
    Schladow S G. 1990. Oscillatory motion in a side-heated cavity. J. Fluid Mech., 213: 589-610.
    [127]
    Schladow S G, Patterson J C, Street R L. 1989. Transient flow in a side heated cavity at high-Rayleighnumber: a numerical study. J. Fluid Mech., 200: 121-148.
    [128]
    Schöpf W, Patterson J C. 1995. Natural convection in a side-heated cavity: visualization of the initial flowfeatures. J. Fluid Mech., 295: 279-357.
    [129]
    Schöpf W, Patterson J C. 1996. Visualization of natural convection in a side-heated cavity: transition tothe final steady state. Int. J. Heat Mass Transfer, 39: 3497-3509.
    [130]
    Schöpf W, Patterson J C, Brooker A M H. 1996. Evaluation of the shadowgraph method for the convectiveflow in a side-heated cavity. Exp. Fluids, 21: 331-340.
    [131]
    Schöpf W, Stiller O. 1997. Three-dimensional patterns in a transient, stratified intrusion flow. Phys. Rev.Lett., 79: 4373-4376.
    [132]
    Settles G S. 2001. Schlieren and Shadowgraph Techniques. Springer-verlag, New York.Severin J, Herwig H. 2001. Higher order stability effects in a natural convection boundary layer over avertical heated wall. Heat Mass Transfer, 38: 97-110.
    [133]
    Shapiro A, Fedorovich E. 2004. Unsteady convectively driven flow along a vertical plate immersed in a stablestratified fluid. J. Fluid Mech., 498: 333-352.
    [134]
    Shapiro A, Fedorovich E. 2006. Natural convection in a stably stratified fluid along vertical plates andcylinders with temporally periodic surface temperature variations. J. Fluid Mech., 546: 295-311.
    [135]
    Siegel R. 1958. Transient free convection from a vertical flat plate. J. Heat Transfer, 80: 347-360.
    [136]
    Staehle B, Hahne E. 1982. Overshooting and damped oscillations of transient natural convection flows incavities. In: Proceedings of the 7th Internaltional Heat Transfer Conference, Munich, 2: 287-292.
    [137]
    Stiller O, Schöpf W. 1997. Thermal instability of flows with a horizontal temperature gradient. Phys. Rev.Lett., 79: 1674-1677.
    [138]
    Stiller O, Schöpf W, Patterson J C, Shultz A. 1998. Effect of spatial and temporal variations of the boundarytemperature on the thermal stability of horizontal flows. Phys. Rev. E, 57: 5578-5584.
    [139]
    Szewczyk A A. 1962. Stability and transition of the free-convection layer along a vertical flat plate. Int. J.Heat Mass Transfer, 5: 903-914.
    [140]
    Tao J, Le Quere P, Xin S. 2004a. Absolute and convective instabilities of natural convection flow in boundary-layer regime. Phys. Rev. E, 70: 066311.
    [141]
    Tao J, Le Quere P, Xin S. 2004b. Spatio-temporal instability of the natural convection boundary layer inthermally stratified medium. J. Fluid Mech., 518: 363-379.
    [142]
    Tian Y S, Karayiannis T G. 2000a. Low turbulence natural convection in an air filled cavity. Part I: thethermal and fluid flow fields. Int. J. Heat Mass Transfer, 43: 849-866.
    [143]
    Tian Y S, Karayiannis T G. 2000b. Low turbulence natural convection in an air filled cavity. Part II: theturbulence quantities. Int. J. Heat Mass Transfer, 43: 867-884.
    [144]
    Turan O, Poole R J. Chakraborty N. 2012. Influences of boundary conditions on laminar natural convectionin rectangular enclosures with differentially heated side wall. Int. J. Heat Fluid Flow, 33: 131-146.
    [145]
    Turan O, Sachdeva A, Poole R J, Chakraborty N. 2013. Aspect ratio and boundary conditions effects onlaminar natural convection of power-law fluids in a rectangular enclosure with differentially heated sidewalls. Int. J. Heat Mass Transfer, 60: 722-738.
    [146]
    Williamson N, Armfield S W Kirkpatrick M P. 2012 Transition to oscillatory flow in a differentially heatedcavity with a conducting partition J. Fluid Mech., 693: 93-114.
    [147]
    Wright N T, Gebhart B. 1994. The entrainment flow adjacent to an isothermal vertical surface. Int. J.Heat Mass Transfer, 37: 213-231.
    [148]
    Xu F. 2006. Natural convection in a suddenly differentially heated cavity with or without a finned sidewall.[Ph.D. Thesis], Australia: James Cook University.
    [149]
    Xu F. 2014. Convective instability of the vertical thermal boundary layer in a differentially heated cavity.Int. Comm. Heat Mass Transfer, 52: 8-14.
    [150]
    Xu F, Patterson J C, Lei C. 2004. Oscillations of the horizontal intrusion in a side-heated cavity. In:Proceedings of the 15th Australian fluid mechanics conference, Sydney, Australia, 779-782
    [151]
    Xu F, Patterson J C, Lei C. 2005. Shadowgraph observations of the transition of the thermal boundarylayer in a side-heated cavity. Exp. Fluids, 38: 770-779
    [152]
    Xu F, Patterson J C, Lei C. 2006. Experimental observations of the thermal flow around a square obstructionon a vertical wall in a side-heated cavity. Exp. Fluids, 40: 363-371.
    [153]
    Xu F, Patterson J C, Lei C. 2008a. An experimental study of the unsteady thermal flow around a thin finon a sidewall of a differentially heated cavity. Int. J. Heat Fluid Flow, 29: 1139-1153.
    [154]
    Xu F, Patterson J C, Lei C. 2008b. On the double-layer structure of the thermal boundary layer in adifferentially heated cavity. Int. J. Heat Mass Transfer, 51: 3803-3815.
    [155]
    Xu F, Patterson J C, Lei C. 2009a. Heat transfer through coupled thermal boundary layers induced by asuddenly generated temperature difference. Int. J. Heat Mass Transfer, 52: 4966-4975.
    [156]
    Xu F, Patterson J C, Lei C. 2009b. Transient natural convection flows around a thin fin on the sidewall ofa differentially heated cavity. J. Fluid Mech., 639: 261-290.
    [157]
    Xu F, Patterson J C, Lei C. 2009c. Transition to a periodic flow induced by a thin fin on the sidewall of adifferentially heated cavity. Int. J. Heat Mass Transfer, 52: 620-628.
    [158]
    Xu F, Patterson J C, Lei C. 2010a. A Pr < 1 intrusion flow induced by a vertical heated wall. Phys. Rev.E, 82: 350-359.
    [159]
    Xu F, Patterson J C, Lei C. 2010b. Temperature oscillations in a differentially heated cavity with andwithout a fine on the sidewall. Int. Comm. Heat Mass Transfer, 37: 350-359.
    [160]
    Xu F, Saha S. 2014. Transition to an unsteady flow induced by a fin on the sidewall of a differentially heatedair-filled square cavity and heat transfer. Int. J. Heat Mass Transfer, 71: 236-244.
    [161]
    Yewell R, Poulikakos D, Bejan A. 1982. Transient natural convection experiments in shallow enclosures. J.Heat Transfer, 104: 533-538.
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