Onset of natural convection in a cube

Hiller, W. J.; Koch, St.; Kowalewski, T. A.; Stella, F.

doi:10.1016/0017-9310(93)90008-t

Cited by 45 publications

(23 citation statements)

References 9 publications

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“…At each time step a series of three to ten RGB images are taken at a short time interval. Special acquisition and image analysis software has been developed and used to obtain 2-D flow pattern (particle tracks) and temperature and velocity fields ( [9][10][11]). …”

Section: Methodsmentioning

confidence: 99%

Phase change problems with free convection: fixed grid numerical simulation

1999

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Abstract.A numerical and experimental study of unsteady natural convection during freezing of water is presented. The mathematical model for the numerical simulations is based on the enthalpy-porosity method in vorticity-velocity formulation, equations are discretised on a fixed grid by means of a finite volume technique. A fully implicit method has been adopted for the mass and momentum equations. Experiments are performed for water in a differentially heated cube surrounded by air. The experimental data for natural convection with freezing in the cavity are collected to create a reference for comparison with numerical results. The method of simultaneous measurement of the flow and temperature fields using liquid crystal tracers is used. It allows us to collect transient data on the interface position, and the temperature and velocity fields. In order to improve the capability of the numerical method to predict experimental results, a conjugate heat transfer problem was solved, with finite thickness and internal heat conductivity of the non-isothermal walls. These results have been compared with the simulations obtained for the idealised case of perfectly adiabatic side walls, and with our experimental findings. Results obtained for the improved numerical model shown a very good agreement with the experimental data only for pure convection and initial time of freezing process. As time passes the discrepancies between numerical predictions and the experiment became more significant, suggesting a necessity for further improvements of the physical model used for freezing water.

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Section: Methodsmentioning

confidence: 99%

Phase change problems with free convection: fixed grid numerical simulation

1999

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“…It can also be used to compute mixed convection flow fields where part of the motion derives from the motion of a part of the boundary [10]. Although a referee has pointed out an an experimental work on natural convection in a cubical container driven by sidewall heating [3], we have not found any suitable work in the geometry considered here. So comparisons with experiments will have to wait.…”

Section: An Application: Three-dimensional Natural Convection In a Cymentioning

confidence: 68%

Axial eigenfunctions and inhomogeneous solutions for the three-dimensional Stokes system with an application to natural convection in a cylinder

Shankar

2005

Z. angew. Math. Phys.

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This paper presents two contributions to the analysis of three-dimensional slow viscous flows in cylinders of circular section. First the vector axial eigenfunctions for this geometry, namely those that satisfy homogeneous boundary conditions on the flat end walls, are derived. Secondly a method is presented to find particular solutions to the inhomogeneous Stokes equations in this geometry. These new results, together with some results obtained earlier, are used to analyse slow natural convection in a vertical cylinder completely filled with a viscous liquid. The fluid motion is generated by the differential heating of the walls of the cylinder. The natural convection flow field is shown to be a superposition of an inhomogeneous field, the fields generated by the vector eigenfunctions and a Stokes flow field. A by-product of this work has been the identification of constraints on the boundary data that have to be satisfied in order for the eigenfunction expansions to work; this knowledge will be useful when attempts are made to prove the completeness of these Stokes flow eigenfunctions.

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“…Application of TLC tracers to flow problems [4], combined with digital image analysis gave impact to quantitative and fully automatic temperature and velocity evaluation, based on DPIV [5] and DPIT [6]. In the present study use of both digital evaluation techniques, as initiated by Hiller et al [7], allows us simultaneous and fully automatic measurements of temperature and velocity fields for selected 2-D flow crosssection.…”

Section: Liquid Crystal Thermographymentioning

confidence: 91%