Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer

doi:10.1007/s10483-018-2329-6

Abstract

Abstract:

The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffusivity is investigated with the perturbation method. A modified Darcy-Oldroyd model is used to describe the flow in a layer of an anisotropic porous medium. The results of the linear instability theory are delineated. The thresholds for the stationary and oscillatory convection boundaries are established, and the crossover boundary between them is demarcated by identifying a codimension-two point in the viscoelastic parameter plane. The stability of the stationary and oscillatory bifurcating solutions is analyzed by deriving the cubic Landau equations. It shows that these solutions always bifurcate supercritically. The heat transfer is estimated in terms of the Nusselt number for the stationary and oscillatory modes. The result shows that, when the ratio of the thermal to mechanical anisotropy parameters increases, the heat transfer decreases.

Key words: cubic Landau equation, Oldroyd-B fluid, elliptic, singular perturbation, difference scheme, uniform convergence, porous medium, convection

2010 MSC Number:

K. R. RAGHUNATHA, I. S. SHIVAKUMARA, SOWBHAGYA. Stability of buoyancy-driven convection in an Oldroyd-B fluid-saturated anisotropic porous layer. Applied Mathematics and Mechanics (English Edition), 2018, 39(5): 653-666.

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