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International Heat Transfer Conference 13
Graham de Vahl Davis (open in a new tab) School of Mechanical and Manufacturing Engineering, University of New South Wales, Kensington, NSW, Australia
Eddie Leonardi (open in a new tab) Computational Fluid Dynamics Research Laboratory, School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney, Australia 2052

ISSN Online: 2377-424X

ISBN CD: 1-56700-226-9

ISBN Online: 1-56700-225-0

STABILITY OF GRAVITY DRIVEN CONVECTION IN A CYLINDRICAL POROUS LAYER SUBJECTED TO VIBRATION

page 10
DOI: 10.1615/IHTC13.p5.200
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RESUMO

In both pure fluids and porous media, the density gradient becomes unstable and fluid motion (convection) occurs when the Rayleigh number exceeds a critical value. The classical stability analysis no longer applies if the Rayleigh number is time dependant, as found in systems where the density gradient is subjected to vibration. The influence of vibrations on thermal convection depends on the orientation of the time dependant acceleration with respect to the thermal stratification.
The problem of a vibrating porous cylinder has numerous important engineering applications, the most important one being in the field of binary alloy solidification. In particular we may extend the above results to understanding the dynamics in the mushy layer (essentially a reactive porous medium) that is sandwiched between the underlying solid and overlying melt regions. Alloyed components are widely used in demanding and critical applications, such as turbine blades, and a consistent internal structure is paramount to the performance and integrity of the component. Alloys are susceptible to the formation of vertical channels which are a direct result of the presence convection, so any technique that suppresses convection/the formation of channels would be welcomed by the plant metallurgical engineer.
In the current study, the linear stability theory is used to investigate analytically the effects of gravity modulation on convection in a homogeneous cylindrical porous layer heated from below. The linear stability results show that increasing the frequency of vibration stabilizes the convection. In addition the aspect ratio of the porous cylinder is shown to influence the stability of convection for all frequencies analysed. It was also observed that only synchronous solutions are possible in cylindrical porous layers, with no transition to sub harmonic solutions as was the case in Govender (2005a) for rectangular layers or cavities. The results of the current analysis will be used in the formulation of a model for binary alloy systems that includes the reactive porous medium model.

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