Chaotic convection in couple stress liquid saturated porous layer‎

Subject Areas : International Journal of Industrial Mathematics

Vinod K‎. ‎Gupta‎ ¹ , A. K. ‎Singh‎ ² , B. S. Bhadauria‎ ³ , I. Hasim‎ ⁴ , J. M. Jawdat‎ ⁵

1 - Department of Mathematics, DIT University, Dehradun, India-$248009$.
2 - Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India.
3 - Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India.
4 - School of Mathematical Sciences, Faculty of Science,Universiti Kebangsaan Malaysia (UKM).
5 - Department of Applied Mathematics, University of Tabuk, Saudi Arabia.

Received: 2016-02-25 Accepted : 2016-02-25 Published : 2016-04-01

Keywords: Chaotic behavior‎, ‎Couple stress liquid, Porous media‎, ‎Lorenz equations,

Abstract :

‎In this paper‎, ‎we have investigated the chaotic behavior of thermal convection in couple stress liquid saturated porous layer subject to gravity‎, ‎heated from below and cooled from above‎, ‎based on theory of dynamical system‎. ‎A low dimensional Lorenz‎- ‎like model is obtained by using Galerkin-truncation approximation‎. ‎We found that there is proportional relation between scaled couple stress parameter and rescaled Rayleigh number‎. We analyzed that increase in level of couple stress parameter increases the level of chaos‎.