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

作　　者：K.R.RACHUNATHA I.S.SHIVAKUMARA SOWBHAGYA 

机构地区：[1]Department of Mathematics,Bangalore University,Bangalore 560056,India

出　　处：《Applied Mathematics and Mechanics(English Edition)》2018年第5期653-666,共14页应用数学和力学（英文版）

基　　金：Project supported by the Innovation in Science Pursuit for the Inspired Research(INSPIRE)Program(No.DST/INSPIRE Fellowship/[IF 150253])

摘　　要：The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffu- sivity 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 de- marcated 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.The nonlinear stability of thermal convection in a layer of an Oldroyd-B fluid-saturated Darcy porous medium with anisotropic permeability and thermal diffu- sivity 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 de- marcated 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.

关 键 词：CONVECTION porous medium Oldroyd-B fluid cubic Landau equation 

分 类 号：O175.13[理学—数学] TQ021.3[理学—基础数学]