Space-time decay rate for Navier–Stokes equations with power-law type nonlinear viscous fluid

2021 ◽  
Author(s):  
Jae-Myoung Kim
Keyword(s):  
Viscous Fluid ◽  
Decay Rate ◽  
Power Law ◽  
Stokes Equations ◽  
Space Time ◽  
Navier Stokes ◽  
Time Decay ◽  
Navier Stokes Equations ◽  
Time Decay Rate

scholarly journals Dynamic analysis of submerged microscale plates: the effects of acoustic radiation and viscous dissipation

2016 ◽  
Vol 472 (2187) ◽  
pp. 20150728 ◽  
Author(s):  
Zhangming Wu ◽  
Xianghong Ma
Keyword(s):  
Viscous Fluid ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Stokes Equations ◽  
Acoustic Radiation ◽  
Navier Stokes ◽  
Rectangular Plates ◽  
Fluid Loading ◽  
Navier Stokes Equations ◽  
Loading Impedance

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate–fluid interaction problem is developed on the basis of linearized Navier–Stokes equations and no-slip conditions. Analytical expression for the fluid-loading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers being mass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions.

The space-time CE/SE method for the Navier-Stokes equations in three spatial dimensions

2000 ◽  
Author(s):  
Zeng-Chan Zhang ◽  
S. Yu ◽  
Xiao-Yen Wang ◽  
Sin-Chung Chang ◽  
Philip Jorgenson
Keyword(s):  
Stokes Equations ◽  
Space Time ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Spatial Dimensions
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