Symmetric and asymmetric bifurcations of natural convection inside circular cavity in the route to chaos

We consider the two-dimensional problem of steady natural convection in a circular cavity with periodic heat generation filled with viscous fluid subject to cosine temperature variation on the boundary. The solution is expanded for low Rayleigh number and extended to 16 terms by computer. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small but pade approximation leads our result to be good even for higher value of the similarity parameter.

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COMPUTACIONAL SIMULATION OF NATURAL CONVECTION IN A SEMI-CIRCULAR CAVITY WITH A HEAT GENERATING FLUID

10.26678/abcm.encit2018.cit18-0117 ◽

2018 ◽

Author(s):

Wallthynay Ferreira ◽

Su Jian

Keyword(s):

Natural Convection ◽

Circular Cavity

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Numerical study of natural convection of nanofluid in a semi-circular cavity with lattice Boltzmann method

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-11-2018-0686 ◽

2019 ◽

Vol 30 (5) ◽

pp. 2625-2637 ◽

Cited By ~ 6

Author(s):

Hanieh Nazarafkan ◽

Babak Mehmandoust ◽

Davood Toghraie ◽

Arash Karimipour

Keyword(s):

Natural Convection ◽

Lattice Boltzmann Method ◽

Lattice Boltzmann ◽

Volume Fraction ◽

Numerical Study ◽

Solid Volume Fraction ◽

Circular Cavity ◽

Cu Nanoparticles ◽

Content Type ◽

Boltzmann Method

Purpose This study aims to apply the lattice Boltzmann method to investigate the natural convection flows utilizing nanofluids in a semicircular cavity. The fluid in the cavity is a water-based nanofluid containing Al2O3 or Cu nanoparticles. Design/methodology/approach The study has been carried out for the Rayleigh numbers from 104 to 106 and the solid volume fraction from 0 to 0.05. The effective thermal conductivity and viscosity of nanofluid are calculated by the models of Chon and Brinkman, respectively. The effects of solid volume fraction on hydrodynamic and thermal characteristics are investigated and discussed. The averaged and local Nusselt numbers, streamlines, temperature contours for different values of solid volume fraction and Rayleigh number are illustrated. Findings The results indicate that more solid volume fraction corresponds to more averaged Nusselt number for both types of nanofluids. It is also found that the effects of solid volume fraction of Cu are stronger than those of Al2O3. Originality/value Numerical study of natural convection of nanofluid in a semi-circular cavity with lattice Boltzmann method in the presence of water-based nanofluid containing Al2O3 or Cu nanoparticles.

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Symbolic Calculation for Free Convection in a Circular Cavity With Porous Material

Volume 2: Theory and Fundamental Research; Aerospace Heat Transfer; Gas Turbine Heat Transfer; Computational Heat Transfer ◽

10.1115/ht2009-88502 ◽

2009 ◽

Author(s):

Kamyar Mansour

Keyword(s):

Natural Convection ◽

Rayleigh Number ◽

Porous Material ◽

Dimensionless Parameter ◽

Circular Cavity ◽

Two Dimensional ◽

Dimensional Problem ◽

Similarity Parameter ◽

Symbolic Calculation ◽

Darcy Rayleigh Number

We consider the two-dimensional problem of steady natural convection in a circular cavity filled with porous material due to a cosine temperature variation on the boundary. We use Darcy’s law for this cavity filled with porous material. The solution is governed by dimensionless parameter Darcy-Rayleigh number. The solution is expanded for low Darcy-Rayleigh number and extended to 18 terms by computer. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small but Pade approximation leads our result to be good even for higher value of the similarity parameter.

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