Perturbation Technique
Abbas Kosarineia
Abstract
The entropy generation analysis of non-Newtonian fluid in rotational flow between two concentric cylinders is examined when the outer cylinder is fixed and the inner cylinder is revolved with a constant angular speed. The viscosity of non-Newtonian fluid is considered at the same time interdependent ...
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The entropy generation analysis of non-Newtonian fluid in rotational flow between two concentric cylinders is examined when the outer cylinder is fixed and the inner cylinder is revolved with a constant angular speed. The viscosity of non-Newtonian fluid is considered at the same time interdependent on temperature and shear rate. The Nahme law and Carreau equation are used to modeling dependence of viscosity on temperature and shear rate, respectively. The viscous dissipation term is adding elaboration to the formerly highly associate set of governing motion and energy equations. The perturbation method has been applied for the highly nonlinear governing equations of base flow and found an approximate solution for narrowed gap limit. The effect of characteristic parameter such as Brinkman number and Deborah number on the entropy generation analysis is investigated. The overall entropy generation number decays in the radial direction from rotating inner cylinder to stationary outer cylinder. The results show that overall rate of entropy generation enhances within flow domain as increasing in Brinkman number. It, however, declines with enhancing Deborah number. The reason for this is very clear, the pseudo plastic fluid between concentric cylinders is heated as Brinkman number increases due to frictional dissipation and it is cooled as Deborah number increases which is due to the elasticity behavior of the fluid. Therefore, to minimize entropy need to be controlled Brinkman number and Deborah number.
Control
M. Zamanian; S. A. A. Hosseini
Abstract
This article studied static deflection, natural frequency and nonlinear vibration of a clamped-clamped microbeam under discontinues electrostatic actuation. The electrostatic actuation was induced by applying AC-DC voltage between the microbeam and electrode plate. In contrast to previous works, it was ...
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This article studied static deflection, natural frequency and nonlinear vibration of a clamped-clamped microbeam under discontinues electrostatic actuation. The electrostatic actuation was induced by applying AC-DC voltage between the microbeam and electrode plate. In contrast to previous works, it was assumed that length of the electrode plate was smaller than that of the microbeam. In addition, it was assumed that a layer whose length was equal to that of the electrode plate was deposited on the lower side of the microbeam. Equation of motion was derived using Newton's second law. The static deflection due to the DC electrostatic actuation and the natural frequency about this position were obtained using the Galerkin method. Nonlinear vibration of the system due to the AC electrostatic actuation was obtained using the multiple scale perturbation method. Variations of static deflection, pull-in voltage, natural frequency and frequency response of vibration about the static deflection of microbeam with respect to variations of second layer length, second layer thickness, electrode plate length and value of electrostatic actuation were also studied. It was shown that, depending on the value of these parameters, static deflection and natural frequency of vibration about static deflection increased or decreased. Moreover, it was demonstrated that, depending on the value of these system parameters, nonlinear vibration of the system due to the AC electrostatic actuation might be realized as a softening or hardening behavior.
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