Supersonic Rupture Pulses in an Earthquake Model

1994 ◽  
Vol 367 ◽  
Author(s):  
Michael Leibig
Keyword(s):  
Integral Equation ◽  
Viscous Dissipation ◽  
Friction Force ◽  
Interfacial Friction ◽  
Pulse Solution ◽  
Local Displacement ◽  
Dissipation Term ◽  
Slip Pulse ◽  
Earthquake Model ◽  
Held Back

In this work, I study the supersonicrupturepulse in a two dimensionalelastic sheet. There is a friction force acting at the edge of the sheet which is composed of a term that dependson the local displacement at the edge and a viscous dissipation term. I consider the case where the sheet is driven forward by a force acting in the bulk, but is held back by the interfacial friction. I present the equations which describe such a system and then look for solutions which describe a slip pulse propagatingthough a region which is uniformly stressed. Such a pulse will allow the entire interface to move forward and partially relieve the stress. I present the integral equation that such a pulse solution must satisfy, and then discuss the behavior observed in numericalsolutions of this equation.

Effect of viscous dissipation in stokes flow between rotating cylinders using BEM

2019 ◽  
Vol 30 (4) ◽  
pp. 2121-2136 ◽  
Author(s):  
Tomasz Janusz Teleszewski
Keyword(s):  
Nusselt Number ◽  
Temperature Distribution ◽  
Viscous Dissipation ◽  
Stokes Flow ◽  
Energy Equation ◽  
Outer Cylinder ◽  
Rotating Cylinders ◽  
Content Type ◽  
Dissipation Term ◽  
Cylinder Diameter

Purpose The purpose of this paper is to apply the boundary element method (BEM) to Stokes flow between eccentric rotating cylinders, considering the case when viscous dissipation plays a significant role and determining the Nusselt number as a function of cylinder geometry parameters. Design/methodology/approach The problem is described by the equation of motion of Stokes flow and an energy equation with a viscous dissipation term. First, the velocity field and the viscous dissipation term were determined from the momentum equation. The determined dissipation of energy and the constant temperature on the cylinder walls are the conditions for the energy equation, from which the temperature distribution and the heat flux at the boundary of the cylinders are determined. Numerical calculations were performed using the author’s own computer program based on BEM. Verification of the model was carried out by comparing the temperature determined by the BEM with the known theoretical solution for the temperature distribution between two rotating concentric cylinders. Findings As the ratio of the inner cylinder diameter to the outer cylinder diameter (r1/r2) increases, the Nusselt number increases. The angle of inclination of the function of the Nusselt number versus r1/r2 increases as the distance between the centers of the inner and outer cylinders increases. Originality/value The computational results may be used for the design of slide bearings and viscometers for viscosity testing of liquids with high viscosity where viscous dissipation is important. In the work, new integral kernels were determined for BEM needed to determine the viscous dissipation component.

scholarly journals Dynamically induced friction reduction in micro-structured interfaces

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
N. Menga ◽  
F. Bottiglione ◽  
G. Carbone
Keyword(s):  
Rigid Body ◽  
Friction Force ◽  
Friction Reduction ◽  
Interfacial Friction ◽  
Rigid Substrate ◽  
Regular Array ◽  
Elastic Supports ◽  
Frictional Behavior ◽  
Macroscopic Motion ◽  
Elastic Elements

AbstractWe investigate the dynamic behavior of a regular array of in-plane elastic supports interposed between a sliding rigid body and a rigid substrate. Each support is modelled as a mass connected to a fixed pivot by means of radial and tangential elastic elements. Frictional interactions are considered at the interface between the supports and the sliding body. Depending on the specific elastic properties of the supports, different dynamic regimes can be achieved, which, in turn, affect the system frictional behavior. Specifically, due to transverse microscopic vibration of the supports, a lower friction force opposing the macroscopic motion of the rigid body can be achieved compared to the case where no supports are present and rubbing occurs with the substrate. Furthermore, we found that the supports static orientation plays a key role in determining the frictional interactions, thus offering the chance to specifically design the array aiming at controlling the resulting interfacial friction force.

Viscous Dissipation Effect on Streamwise Entropy Generation of Nanofluid Flow in Microchannel Heat Sinks

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Tiew Wei Ting ◽  
Yew Mun Hung ◽  
Ningqun Guo
Keyword(s):  
Viscous Dissipation ◽  
Entropy Generation ◽  
Volume Fraction ◽  
Second Law Of Thermodynamics ◽  
Reynolds Numbers ◽  
Heat Sinks ◽  
Fluid Friction ◽  
Closed Form Solutions ◽  
Dissipation Effect ◽  
Dissipation Term

The effects of viscous dissipation on the entropy generation of water–alumina nanofluid convection in circular microchannels subjected to exponential wall heat flux are investigated. Closed-form solutions of the temperature distributions in the streamwise direction are obtained for the models with and without viscous dissipation term in the energy equation. The two models are compared by analyzing their relative deviations in entropy generation for different Reynolds numbers and nanoparticle volume fractions. The incorporation of viscous dissipation prominently affects the temperature distribution and consequently the entropy generation. When the viscous dissipation effect is neglected, the total entropy generation and the fluid friction irreversibility are nearly twofold overrated while the heat transfer irreversibility is underestimated significantly. By considering the viscous dissipation effect, the exergetic effectiveness for forced convection of nanofluid in microchannels attenuates with the increasing nanoparticle volume fraction and nanoparticle diameter. The increase in the entropy generation of nanofluid is mainly attributed to the intensification of fluid friction irreversibility. From the aspect of the second-law of thermodynamics, the widespread conjecture that nanofluids possess advantage over pure fluid associated with higher overall effectiveness is invalidated.

Energy Equation of Gas Flow With Low Velocity in a Micro-Channel

2014 ◽  
Author(s):  
Yutaka Asako
Keyword(s):  
Viscous Dissipation ◽  
Incompressible Flow ◽  
Gas Flow ◽  
Energy Equation ◽  
Outlet Temperature ◽  
Gas Temperature ◽  
Low Velocity ◽  
Dissipation Term ◽  
Pressure Term ◽  
Micro Channels

The energy equation for incompressible flow with the viscous dissipation term is often used for the governing equations of gas flow with low velocity in micro-channels. However, the results which are obtained by solving these equations do not satisfy the first law of the thermodynamics. In the case of ideal gas with low velocity, the inlet and the outlet temperatures of an adiabatic channel are the same based on the first law of the thermodynamics. However, the outlet temperature which is obtained by solving the energy equation for incompressible flow with the viscous dissipation term is higher than the inlet gas temperature, since the viscous dissipation term takes positive value. This inconsistency arose from wrong choice of the relation between the enthalpy and temperature that resulted in neglecting the substantial derivative of pressure term in the energy equation. In this paper the correct energy equation which includes the substantial derivative of pressure term is proposed. Some samples of physically consistent results which are obtained by solving the proposed energy equation are demonstrated.

PROPERTY SIMULATION FOR NANO-SCALE INTERFACIAL FRICTION BETWEEN TWO KINDS OF MATERIAL IN MEMS BASED ON AN ATOMISTIC SIMPLIFIED MODEL

2007 ◽  
Vol 21 (20) ◽  
pp. 3581-3590 ◽  
Author(s):  
PING YANG ◽  
NINGBO LIAO ◽  
DAOGUO YANG
Keyword(s):  
Molecular Dynamics ◽  
Friction Force ◽  
Computational Simulation ◽  
Research Work ◽  
Dynamics Simulation ◽  
Simplified Model ◽  
Dominant Factor ◽  
Interfacial Friction ◽  
Nano Scale ◽  
Peak Value

The objective of this research work is to provide a systematic method to perform molecular dynamics simulation or evaluation for nano-scale interfacial friction between different materials in MEMS. A simplified model to simulate surface sliding between different kinds of material by molecular dynamics [MD] is proposed because the surface property is a dominant factor for the performance between two kinds of material in MEMS. The Newton's equations of motion are established by using the Morse potential function. An improved Verlet algorithm is employed to solve atom trajectories. Comparing the results of the computer simulation with experimental results in Ref. 1, the validity of the model is confirmed. The simulation results show that the preliminary stage and the last stage, when no interface is formed, the friction force fluctuates periodly and its peak value is smaller relatively, while at the intermediate stage, where the interface is formed, the friction force fluctuates periodly and its peak value is relatively bigger. The friction force is approximately proportional to the contact area. In the meantime, Cu sliding along Al with uniform speed and accelerated motion was also investigated, the mechanical properties between two surfaces were analyzed and a tentative computational simulation on the effect of the driving force was developed. The results lay a basis for future work.

scholarly journals Numerical estimation of thermal load in a three blade vertically agitated mixer

2019 ◽  
Vol 128 ◽  
pp. 08004
Author(s):  
Anshul Singh Tomar ◽  
Harish K G ◽  
K Arul Prakash
Keyword(s):  
Angular Velocity ◽  
Viscous Dissipation ◽  
Temperature Rise ◽  
Solid Propellant ◽  
Maximum Velocity ◽  
Maximum Temperature ◽  
Fire Hazards ◽  
Dissipation Term ◽  
Clockwise Direction ◽  
Blade Mixer

The objective of this study is to understand the flow physics and resulting heat transfer behind the mixing of highly viscous solid propellant in a vertical three blade mixer. The mixer comprises a four-winged central agitator rotating in the counter-clockwise direction and two other two-winged agitators rotating in clockwise direction. The temperature rises due to the shearing of the solid propellant. Uncontrolled temperature rise may result in the self-ignition of the propellant and other fire hazards. Thus it becomes important to quantify the heat generated due to viscous dissipation to attain a controlled atmosphere for mixing. A detailed CFD analysis is carried out, and two-dimensional energy equation with viscous dissipation term is solved to quantify the temperature rise due to viscous dissipation. The effect of angular velocity of the agitator and viscosity of the propellant over temperature rise is studied quantitatively using the overset method in OpenFOAM. The maximum velocity of the propellant is observed at the tip of agitators, whereas maximum temperature rise is found around the vicinity of the blade profile. A correlation is proposed to predict the temperature rise with time due to the viscous effect for the given range of angular velocity.

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