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Effect of rotation on the onset of double diffusive convection in a Darcy porous medium saturated with a couple stress fluid

机译：旋转对饱和应力流体达西多孔介质中双扩散对流的影响

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摘要

The effect of rotation on the onset of double diffusive convection in a horizontal couple stress fluid-saturated porous layer, which is heated and salted from below, is studied analytically using both linear and weak nonlinear stability analyses. The extended Darcy model, which includes the time derivative and Coriolis terms, has been employed in the momentum equation. The onset criterion for stationary, oscillatory and finite amplitude convection is derived analytically. The effect of Taylor number, couple stress parameter, solute Rayleigh number, Lewis number, Darcy-Prandtl number, and normalized porosity on the stationary, oscillatory, and finite amplitude convection is shown graphically. It is found that the rotation, couple stress parameter and solute Rayleigh number have stabilizing effect on the stationary, oscillatory, and finite amplitude convection. The Lewis number has a stabilizing effect in the case of stationary and finite amplitude modes, with a destabilizing effect in the case of oscillatory convection. The Darcy-Prandtl number and normalized porosity advances the onset of oscillatory convection. A weak nonlinear theory based on the truncated representation of Fourier series method is used to find the finite amplitude Rayleigh number and heat and mass transfer. The transient behavior of the Nusselt number and Sherwood number is investigated by solving the finite amplitude equations using Runge-Kutta method.
机译：利用线性和弱非线性稳定性分析，研究了旋转对水平耦合应力流体饱和多孔层中双扩散对流开始的影响，该层从下方加热并盐化，并进行了分析。动量方程中采用了扩展的达西模型，其中包括时间导数和科里奥利项。通过分析得出静止，振荡和有限振幅对流的起始准则。用图形显示了泰勒数，偶应力参数，溶质瑞利数，路易斯数，达西-普朗特数和归一化孔隙率对平稳，振荡和有限振幅对流的影响。发现旋转，耦合应力参数和溶质瑞利数对平稳，振荡和有限振幅对流具有稳定作用。 Lewis数在固定和有限幅值模式下具有稳定作用，在振荡对流的情况下具有稳定作用。 Darcy-Prandtl数和归一化孔隙率使振荡对流提前。基于傅立叶级数方法的截断表示的弱非线性理论被用来寻找有限振幅的瑞利数和传热传质。通过使用Runge-Kutta方法求解有限振幅方程，研究了Nusselt数和Sherwood数的瞬态行为。

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