Natural convection in a rectangular cavity heated from below and cooled from top as well as the sides

A three-dimensional, numerical simulation of Rayleigh–Benard convection in a cavity, having aspect ratios Ax=4 and Ay=4 has been performed using multigrid method, for Ra⩽1×104. The effect of the thermal boundary conditions of the vertical side walls on the flow bifurcations has been investigated by considering isothermal and conducting side wall cases. It has been found that the steady state flow patterns and the critical Rayleigh numbers for transition from one pattern to the other are completely different for each of the above mentioned boundary conditions. The local heat transfer distributions at the bottom and top plates are obtained and variations of the average Nusselt number for the isothermal and conducting side wall boundary conditions are compared for the range of Rayleigh numbers investigated.

[1]  M. P. Arroyo,et al.  Rayleigh-Bénard convection in a small box: spatial features and thermal dependence of the velocity field , 1992, Journal of Fluid Mechanics.

[2]  H. Q. Yang,et al.  Laminar natural-convection flow transitions in tilted three-dimensional longitudinal rectangular enclosures , 1987 .

[3]  M. Nansteel,et al.  Natural convection in rectangular enclosures heated from below and cooled along one side , 1987 .

[4]  Kwang-tzu Yang,et al.  Wavenumber selection for Rayleigh—Bénard convection in a small aspect ratio box , 1992 .

[5]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[6]  H. L. Stone.  ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS , 1968 .

[7]  Guy Lauriat,et al.  THE HORIZONTAL NATURAL CONVECTION BOUNDARY LAYER REGIME IN A CLOSED CAVITY , 1986 .

[8]  J. Maveety,et al.  Heat transfer in Rayleigh-Bénard convection with air in moderate size containers , 1998 .

[9]  S. Chandrasekhar.  Hydrodynamic and Hydromagnetic Stability , 1961 .

[10]  Luiz Fernando Milanez,et al.  Natural convection in rectangular enclosures heated from below and symmetrically cooled from the sides , 1995 .

[11]  M. Hortmann,et al.  Finite volume multigrid prediction of laminar natural convection: Bench-mark solutions , 1990 .

[12]  Stephen H. Davis,et al.  Convection in a box: linear theory , 1967, Journal of Fluid Mechanics.

[13]  B. P. Leonard,et al.  Why You Should Not Use 'Hybrid', 'Power-Law' or Related Exponential Schemes for Convective Modelling—There Are Much Better Alternatives , 1995 .

[14]  K. Stork,et al.  Convection in boxes: experiments , 1972, Journal of Fluid Mechanics.

[15]  Henk A. van der Vorst,et al.  Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems , 1992, SIAM J. Sci. Comput..

[16]  J. Gollub,et al.  Many routes to turbulent convection , 1980, Journal of Fluid Mechanics.

[17]  Kwang-Tzu Yang,et al.  Thermal convection in small enclosures: an atypical bifurcation sequence , 1995 .

[18]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[19]  S. G. Rubin,et al.  A diagonally dominant second-order accurate implicit scheme , 1974 .

[20]  B. P. Leonard,et al.  Beyond first‐order upwinding: The ultra‐sharp alternative for non‐oscillatory steady‐state simulation of convection , 1990 .

[21]  W. M. Coughran,et al.  Nonlinear pattern formation near the onset of Rayleigh-Bénard convection , 1982 .

[22]  Kwang-Tzu Yang,et al.  Rayleigh-Bénard Convection in a Small Aspect Ratio Enclosure: Part I—Bifurcation to Oscillatory Convection , 1993 .

[23]  Kwang-Tzu Yang,et al.  Rayleigh-Bénard Convection in a Small Aspect Ratio Enclosure: Part II—Bifurcation to Chaos , 1993 .