## Abstract

A least-squares finite element method (LSFEM) has been developed to investigate the phenomenon of natural convection caused by temperature and concentration buoyancy effects in rectangular enclosures with different geometric aspect ratios. The time dependent Navicr-Stokes equations, the energy and the mass balance equations for an incompressible, constant property fluid in the Boussinesq approximation are reduced into a first-order velocity-pressure-vorticity-temperature-heat flux-concentration-mass flux (u-p-u-‘T-q-C-J) formulation. The coupled system is discretized by backward ditTerencing in time. For the case of heat and mass transfer from side walls, results for both augmenting and opposing flows are obtained with Prandtl number Pr — 0.7, Schmidt number Sc = 0.6 and 0.7 {Le= 1), Grashof number Gr up to 10^{6} buoyancy ratio = -0.2 to -5.0 and geometric aspect ratio of 1. For the case of heating from below, we test the LSFEM with two Raylcigh-Benard convection problems. Then the LSFEM algorithm is used to solve the doubly-difTusive convection in a horizontal rectangular cavity heated from below with Grashof number 5,5 x 10^{5}and geometric aspect ratio 7.

Original language | English |
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Pages (from-to) | 1-17 |

Number of pages | 17 |

Journal | International Journal of Computational Fluid Dynamics |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1994 |

## Keywords

- Least-squares Finite Element Method
- Rayleigh-Bénard
- doubly-diffusive convection
- heating from below
- side-wall diffusion

## ASJC Scopus subject areas

- Computational Mechanics
- Aerospace Engineering
- Condensed Matter Physics
- Energy Engineering and Power Technology
- Mechanics of Materials
- Mechanical Engineering