Multiple states, stability and bifurcations of natural convection in a rectangular cavity with partially heated vertical walls

نویسندگان

  • P. Z. BAR-YOSEPH
  • A. SOLAN
چکیده

The multiplicity, stability and bifurcations of low-Prandtl-number steady natural convection in a two-dimensional rectangular cavity with partially and symmetrically heated vertical walls are studied numerically. The problem represents a simple model of a set-up in which the height of the heating element is less than the height of the molten zone. The calculations are carried out by the global spectral Galerkin method. Linear stability analysis with respect to two-dimensional perturbations, a weakly nonlinear approximation of slightly supercritical states and the arclength path-continuation technique are implemented. The symmetry-breaking and Hopf bifurcations of the flow are studied for aspect ratio (height/length) varying from 1 to 6. It is found that, with increasing Grashof number, the flow undergoes a series of turning-point bifurcations. Folding of the solution branches leads to a multiplicity of steady (and, possibly, oscillatory) states that sometimes reaches more than a dozen distinct steady solutions. The stability of each branch is studied separately. Stability and bifurcation diagrams, patterns of steady and oscillatory flows, and patterns of the most dangerous perturbations are reported. Separated stable steady-state branches are found at certain values of the governing parameters. The appearance of the complicated multiplicity is explained by the development of the stably and unstably stratified regions, where the damping and the Rayleigh–Bénard instability mechanisms compete with the primary buoyancy force localized near the heated parts of the vertical boundaries. The study is carried out for a low-Prandtl-number fluid with Pr=0.021. It is shown that the observed phenomena also occur at larger Prandtl numbers, which is illustrated for Pr=10. Similar three-dimensional instabilities that occur in a cylinder with a partially heated sidewall are discussed.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Effects of an Imposed Magnetic Field on Natural Convection in a Tilted Cavity with Partially Active Vertical Walls:Numerical Approach

The effect of imposed magnetic field on natural convection in a tilted cavity with partially active walls was investigated numerically. The active part of the right side wall was at a higher temperature than the active part of the left side wall and were moving on vertical walls relative to each other. The top, the bottom and the remaining parts of the side walls were insulated. The magnetic fi...

متن کامل

Natural Convection at Different Prandtl Numbers in Rectangular Cavities with a Fin on the Cold Wall

The natural convection in differentially heated rectangular cavities with a fin attached to the cold wall was investigated numerically. The top and the bottom horizontal walls of the cavities were insulated while their left and the right vertical walls were maintained at a constant temperature Th and Tc, respectively with Th > Tc. The governing equations written in terms of the primitive variab...

متن کامل

Investigation of Natural Convection in a Vertical Cavity Filled with a Anisotropic Porous Media

In present paper, a numerical analysis for a rectangular cavity filled with a anisotropic porous media has been studied. It is assumed that the horizontal walls are adiabatic and impermeable, while the side walls of the cavity are maintained at constant temperatures and concentrations. The buoyancy force that induced the fluid motion are assumed to be cooperative. In the two extreme cases o...

متن کامل

Numerical Simulation of Mixed Convection Flows in a Square Double Lid-Driven Cavity Partially Heated Using Nanofluid

A numerical study has been done through an Al2O3–water in a double lid-driven  square  cavity with various  inclination  angles  and discrete heat sources. The top and right moving walls are at low temperature. Half of  the  left and bottom walls are  insulated and  the  temperatures of the other half are kept at high. A large number of simulations for a wide  range  of Richardson  number ...

متن کامل

Numerical Study of Natural Convection in an Inclined Cavity with Partially Active Side Walls Filled with Cu-water Nanofluid

The buoyancy-driven fluid flow and heat transfer in a square cavity with partially active side walls filled with Cu-water nanofluid is investigated numerically. The active parts of the left and the right side-walls of the cavity are maintained at temperatures Th and Tc, respectively, with Th>Tc. The enclosure’s top and bottom walls, as well as, the inactive parts of its side walls are kept insu...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003