Linear and nonlinear stability of double diffusive convection in a couple stress fluid-saturated porous layer

I. S. Shivakumara, Jinho Lee, S. Suresh Kumar, N. Devaraju

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11 Citations (Scopus)

Abstract

The linear and nonlinear stability of double diffusive convection in a layer of couple stress fluid-saturated porous medium is theoretically investigated in this work. Applying the linear stability theory, the criterion for the onset of steady and oscillatory convection is obtained. Emphasizing the presence of couple stresses, it is shown that their effect is to delay the onset of convection and oscillatory convection always occurs at a lower value of the Rayleigh number at which steady convection sets in. The nonlinear stability analysis is carried out by constructing a system of nonlinear autonomous ordinary differential equations using a truncated representation of Fourier series method and also employing modified perturbation theory with the help of self-adjoint operator technique. The results obtained from these two methods are found to complement each other. Besides, heat and mass transport are calculated in terms of Nusselt numbers. In addition, the transient behavior of Nusselt numbers is analyzed by solving the nonlinear system of ordinary differential equations numerically using the Runge-Kutta-Gill method. Streamlines, isotherms, and isohalines are also displayed.

Original languageEnglish
Pages (from-to)1697-1715
Number of pages19
JournalArchive of Applied Mechanics
Volume81
Issue number11
DOIs
Publication statusPublished - 2011 Nov

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

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