Skip to main content
SpringerLink
Log in

On the stopping of thermal convection in viscoplastic liquid

  • Original Contribution
  • Published:
Rheologica Acta Aims and scope Submit manuscript

Abstract

The thermal convection in a square cavity filled in with a viscoplastic liquid is considered as a model example to illustrate the mechanism of convection termination. It is shown that at low Rayleigh numbers, the stopping of convection corresponds to a limit point in the parameter space. Using this observation, we propose a heuristic numerical approach to calculate the critical Rayleigh numbers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Balmforth NJ, Rust AC (2009) Weakly nonlinear viscoplastic convection. J Non-Newtonian Fluid Mech 158:36–45

    Article  CAS  Google Scholar 

  • Bayazitoglu Y, Paslay PR, Cernocky P (2007) Laminar Bingham fluid flow between vertical parallel plates. Int J Thermal Sci 46:349–357

    Article  CAS  Google Scholar 

  • Dean EJ, Glowinski R, Guidoboni G (2007) On the numerical simulation of Bingham visco-plastic flow: old and new results. J Non-Newtonian Fluid Mech 142:36–62

    Article  CAS  Google Scholar 

  • Derksen J, Prashant (2009) Simulations of complex flow of thixotropic liquids. J Non-Newtonian Fluid Mech 160:65–75

    Article  CAS  Google Scholar 

  • Drazin PG, Reid WH (2004) Hydrodynamic stability. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Dubash N, Frigaard I (2004) Conditions for static bubbles in viscoplastic fluids. Phys Fluids 12:4319–4330

    Article  Google Scholar 

  • Gershuni GZ, Zhukhovitskii EM (1976) Convective stability of incompressible fluids. Keter, New York

    Google Scholar 

  • Ginzburg I, Steiner K (2002) A free-surface lattice Boltzmann method for modelling the filling of expanding cavities by Bingham fluids. Philos Trans R Soc Lond Ser A 360:453–456

    Article  CAS  Google Scholar 

  • Jeffreys H (1952) The Earth, 3rd edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Kubichek M, Marek M (1979) Evaluation of limit and bifurcation points for algebraic equations and nonlinear boundary-value problems. Appl Math Comput 5:253–264

    Article  Google Scholar 

  • Lorenz EN (1963) Deterministic nonperiodic flow. J Atmos Sci 20:130–141

    Article  Google Scholar 

  • Sikorski D, Tabuteau H, de Bruyn JR (2009) Motion and shape of bubbles rising through a yield-stress fluid. J Non-Newtonian Fluid Mech 159:10–16

    Article  CAS  Google Scholar 

  • Vikhansky A (2008) Lattice–Boltzmann method for yield-stress liquids. J Non-Newtonian Fluid Mech 155:95–100

    Article  CAS  Google Scholar 

  • Vikhansky A (2009) Thermal convection of a viscoplastic liquid with high Rayleigh and Bingham numbers. Phys Fluids 21:103103

    Article  Google Scholar 

  • Vola D, Boscardin L, Latché JC (2003) Laminar unsteady flows of Bingham fluids: a numerical strategy and some benchmark results. J Comput Phys 187:441–456

    Article  Google Scholar 

  • Weinitschke H (1985) On the calculation of limit and bifurcation points in stability problems of elastic shells. Int J Solids Struct 21:79–95

    Article  Google Scholar 

  • Zhang J, Vola D, Frigaard IA (2006) Yield stress effects on Rayleigh–Bénard convection. J Fluid Mech 566:389–419

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering and Material Science, Queen Mary, University of London, Mile End Road, London, E1 4NS, UK

    Alexander Vikhansky

Authors
  1. Alexander Vikhansky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Vikhansky.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vikhansky, A. On the stopping of thermal convection in viscoplastic liquid. Rheol Acta 50, 423–428 (2011). https://doi.org/10.1007/s00397-010-0488-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00397-010-0488-z

Keywords

Search

Navigation