Coriolis effect on thermal convection in a couple-stress fluid-saturated rotating rigid porous layer

被引:10
|
作者
Shivakumara, I. S. [1 ]
Sureshkumar, S. [2 ]
Devaraju, N. [1 ]
机构
[1] Bangalore Univ, UGC Ctr Adv Studies Fluid Mech, Dept Math, Bangalore 560001, Karnataka, India
[2] Siddaganga Inst Technol, Dept Math, Tumkur 572103, India
关键词
Couple-stress fluid; Porous medium; Rotation; Hopf bifurcation; Nonlinear stability; DOUBLE-DIFFUSIVE CONVECTION; NONLINEAR STABILITY; LINEAR-STABILITY; SORET;
D O I
10.1007/s00419-010-0425-8
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Both linear and weakly nonlinear stability analyses are performed to study thermal convection in a rotating couple-stress fluid-saturated rigid porous layer. In the case of linear stability analysis, conditions for the occurrence of possible bifurcations are obtained. It is shown that Hopf bifurcation is possible due to Coriolis force, and it occurs at a lower value of the Rayleigh number at which the simple bifurcation occurs. In contrast to the nonrotating case, it is found that the couple-stress parameter plays a dual role in deciding the stability characteristics of the system, depending on the strength of rotation. Nonlinear stability analysis is carried out by constructing a set of coupled nonlinear ordinary differential equations using truncated representation of Fourier series. Sub-critical finite amplitude steady motions occur depending on the choice of physical parameters but at higher rotation rates oscillatory convection is found to be the preferred mode of instability. Besides, the stability of steady bifurcating equilibrium solution is discussed using modified perturbation theory. Heat transfer is calculated in terms of Nusselt number. Also, the transient behavior of the Nusselt number is investigated by solving the nonlinear differential equations numerically using the Runge-Kutta-Gill method. It is noted that increase in the value of Taylor number and the couple-stress parameter is to dampen the oscillations of Nusselt number and thereby to decrease the heat transfer.
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页码:513 / 530
页数:18
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