Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifur...Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in- fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap- pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.展开更多
The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time.A perturbation method is used to compute the ...The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time.A perturbation method is used to compute the critical Rayleigh number and the wave number.The critical Rayleigh number is calculated as a function of the frequency of modulation,the temperature-dependent variable viscosity,the electric field dependent variable viscosity,the Prandtl number,and the electric Rayleigh number.The effects of all three cases of modulations are established to delay or advance the onset of the convection process.In addition,how the effect of variable viscosity controls the onset of convection is studied.展开更多
基金the University Grants Commission (UGC), New Delhi, India for supporting her research work with a Rajiv Gandhi National Fellowship
文摘Linear and weakly nonlinear analyses are made for the Rayleigh-Benard convection in two-component couple-stress liquids with the Soret effect. Conditions for pitchfork, Hopf, Takens-Bogdanov, and codimension-two bifurcations are presented. The Lorenz model is used to study the inverted bifurcation. Positive values of the Soret coefficient favor a pitchfork bifurcation, whereas negative values favor a Hopf bifurcation. Takens-Bogdanov and codimension-two bifurcations are not as much influenced by the Soret coefficient as pitchfork and Hopf bifurcations. The influence of the Soret coefficient on the inverted bifurcation is similar to the influence on the pitchfork bifurcation. The in- fluence of other parameters on the aforementioned bifurcations is also similar as reported earlier in the literature. Using the Newell-Whitehead-Segel equation, the condition for occurrence of Eckhaus and zigzag secondary instabilities is obtained. The domain of ap- pearance of Eckhaus and zigzag instabilities expands due to the presence of the Soret coefficient for positive values. The Soret coefficient with negative values enhances heat transport, while positive values diminish it in comparison with heat transport for the case without the Soret effect. The dual nature of other parameters in influencing heat and mass transport is shown by considering positive and negative values of the Soret coefficient.
文摘The linear Rayleigh-Bénard electro-convective stability of the Newtonian dielectric liquid is determined theoretically subject to the temperature modulation with time.A perturbation method is used to compute the critical Rayleigh number and the wave number.The critical Rayleigh number is calculated as a function of the frequency of modulation,the temperature-dependent variable viscosity,the electric field dependent variable viscosity,the Prandtl number,and the electric Rayleigh number.The effects of all three cases of modulations are established to delay or advance the onset of the convection process.In addition,how the effect of variable viscosity controls the onset of convection is studied.
