A finite element numerical solution of natural convection in enclosed cavities

Taylor, C.; Ijam, Abbas Z.

doi:10.1016/0045-7825(79)90069-0

Cited by 26 publications

(8 citation statements)

References 17 publications

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“…First, the fixed value conditions. If node i is on such a segment of boundary for variable a, the residual ra,i defined by (10) is deleted and replaced by, -ra,L = Qi -@, (11) 6i being the prescribed value. This treatment applies to the prescribed temperature boundaries.…”

Section: Formulationmentioning

confidence: 99%

“…There remains the stream function gradient condition which occurs in this formulation in place of any condition on the vorticity. The appropriate residuals ra,l are simply deleted and replaced by the residuals rT,l which, as already noted are displaced by residuals of type (11). Thus the residuals rq,l of type (1Oc) for boundary nodes are simply shifted in position in the system (and a change of sign is applied).…”

Section: Formulationmentioning

confidence: 99%

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Finite element, stream function–vorticity solution of steady laminar natural convection

Stevens

1982

Numerical Methods in Fluids

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SUMMARYStream function-vorticity finite element solution of two-dimensional incompressible viscous flow and natural convection is considered. Steady state solutions of the natural convection problem have been obtained for a wide range of the two independent parameters. Use of boundary vorticity formulae or iterative satisfaction of the no-slip boundary condition is avoided by application of the finite element discretization and a displacement of the appropriate discrete equations. Solution is obtained by Newton-Raphson iteration of all equations simultaneously. The method then appears to give a steady solution whenever the flow is physically steady, but it does not give a steady solution when the flow is physically unsteady. In particular, no form of asymmetric differencing is required. The method offers a degree of economy over primitive variable formulations. Physical results are given for the square cavity convection problem. The paper also reports on earlier work in which the most commonly used boundary vorticity formula was found not to satisfy the no-slip condition, and in which segregated solution procedures were attempted with very minimal success.

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Section: Formulationmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

Finite element, stream function–vorticity solution of steady laminar natural convection

Stevens

1982

Numerical Methods in Fluids

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“…Finite element methods are well established for solving the steady and transient Boussinesq equations and boundary conditionso. We use a method for mixed-order polynomial interpolation of velocities, temperature, and pressure that has been proposed before (see Zienkiewicz et al 1976, Huyakorn et al 1979, Taylor and Ijam 1979 The pressure is approximated by the expansion in terms of bilinear polynomials (ipJ (r,z) } as…”

Section: Calculation Of Steady Flowsmentioning

confidence: 99%

Multiple buoyancy-driven flows in a vertical cylinder heated from below

Yamaguchi

Chang

Brown

1984

Phil. Trans. R. Soc. Lond. A

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The structure of axisymmetric buoyancy-driven convection in a vertical cylinder heated from below is probed by finite-element solution of the Boussinesq equations coupled with computer-implemented perturbation techniques for detecting and tracking multiple flows and for determining flow stability. Results are reported for fluids with a Prandtl number of one and for cylinders with aspect ratio Λ (defined as the ratio of height to radius of the cylinder) between 0.5 and 2.25. Extensive calculations of the neutral stability curves for the static solution and of the nonlinear motions along the bifurcating flow families show a continuous change of the primary cellular motion from a single toroidal cell to two and three cells nested radially in the cylinder, instead of the sharp transitions found for a cylinder with shear-free sidewalls. The smooth transitions in flow structure with Rayleigh number and Λ are explained by nonlinear connectivity between the first two bifurcating flow families formed either by a secondary bifurcation point for Λ ⩽ Λ * ≃ 0.80 or by a limit point for Λ ⩽ Λ *. The transition between the two modes may be described by the theory of multiple limit point bifurcation.

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“…The study of natural convection in enclosures plays a vital role for the transport of heat energy in many engineering applications and naturally occurring processes as given in literature by many authors as Vahl Davis (1968), Ostrach (1972), Taylor and Ijam (1979), Ganzarolli and Milanez (1995) are done with either vertical or horizontal imposed heat flux or temperature difference. experimentally and numerically studied the convection of air in a vertical cylindrical enclosure, induced by a small hot spot centrally located on the floor.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of effect of magnetic field on combined surface tension and buoyancy driven convection in partially heated open enclosure

Nithyadevi

Öztop

Begum

et al. 2015

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose – The purpose of the paper is to investigate the effects of magnetic field on the flow driven by the combined mechanism of buoyancy and thermocapillary flow in an open enclosure with localized heating from below and symmetrical cooling from the sides. Design/methodology/approach – The governing equations are discretized by the control volume method with power-law scheme and solved numerically by SIMPLE algorithm for the pressure-velocity coupling together with under-relaxation technique. Findings – In this work, it is observed that, the average Nusselt number, decreases with an increase of Hartmann number Ha, and increases with increase of Prandtl and Grashof number. At large Marangoni number Ma, a prominent secondary eddies are observed at the top of the enclosure due to the effect of surface tension. Originality/value – The study combines many external forces on thermocapillary flow.

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A finite element numerical solution of natural convection in enclosed cavities

Cited by 26 publications

References 17 publications

Finite element, stream function–vorticity solution of steady laminar natural convection

Finite element, stream function–vorticity solution of steady laminar natural convection

Multiple buoyancy-driven flows in a vertical cylinder heated from below

Numerical analysis of effect of magnetic field on combined surface tension and buoyancy driven convection in partially heated open enclosure

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