Transport in Porous Media

, Volume 110, Issue 1, pp 113–126 | Cite as

Unsteady Natural Convection with Temperature-Dependent Viscosity in a Square Cavity Filled with a Porous Medium

  • M. S. Astanina
  • M. A. Sheremet
  • J. C. Umavathi
Article
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Abstract

A numerical investigation is implemented on the unsteady natural convection with a temperature-dependent viscosity inside a square porous cavity. The vertical walls of the cavity are kept at constant but different temperatures, while the horizontal walls are adiabatic. The mathematical model formulated in dimensionless stream function, vorticity and temperature variables is solved using implicit finite difference schemes of the second order. The governing parameters are the Rayleigh number, Darcy number, viscosity variation parameter and dimensionless time. The effects of these parameters on the average Nusselt number along the hot wall as well as on the streamlines and isotherms are analyzed. The results show an intensification of convective flow and heat transfer with an increase in the viscosity variation parameter for the porous media, while in the case of pure fluid, the effect is opposite.

Keywords

Natural convection Unsteady regimes Temperature-dependent viscosity Porous media Square cavity  Numerical results Finite difference method 
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Notes

Acknowledgments

This work of M.S. Astanina and M.A. Sheremet was conducted as a government task of the Ministry of Education and Science of the Russian Federation, Project Number 13.1919.2014/K. The authors also wish to express their thank to the very competent Reviewers for the valuable comments and suggestions.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • M. S. Astanina
    • 1
  • M. A. Sheremet
    • 1
    • 2
  • J. C. Umavathi
    • 3
  1. 1.Department of Theoretical MechanicsTomsk State UniversityTomskRussia
  2. 2.Department of Nuclear and Thermal Power PlantsTomsk Polytechnic UniversityTomskRussia
  3. 3.Department of MathematicsGulbarga UniversityGulbargaIndia

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