Global Information Lookup Global Information

Viscous stress tensor information


The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed to the strain rate, the rate at which it is deforming around that point.

The viscous stress tensor is formally similar to the elastic stress tensor (Cauchy tensor) that describes internal forces in an elastic material due to its deformation. Both tensors map the normal vector of a surface element to the density and direction of the stress acting on that surface element. However, elastic stress is due to the amount of deformation (strain), while viscous stress is due to the rate of change of deformation over time (strain rate). In viscoelastic materials, whose behavior is intermediate between those of liquids and solids, the total stress tensor comprises both viscous and elastic ("static") components. For a completely fluid material, the elastic term reduces to the hydrostatic pressure.

In an arbitrary coordinate system, the viscous stress ε and the strain rate E at a specific point and time can be represented by 3 × 3 matrices of real numbers. In many situations there is an approximately linear relation between those matrices; that is, a fourth-order viscosity tensor μ such that ε = μE. The tensor μ has four indices and consists of 3 × 3 × 3 × 3 real numbers (of which only 21 are independent). In a Newtonian fluid, by definition, the relation between ε and E is perfectly linear, and the viscosity tensor μ is independent of the state of motion or stress in the fluid. If the fluid is isotropic as well as Newtonian, the viscosity tensor μ will have only three independent real parameters: a bulk viscosity coefficient, that defines the resistance of the medium to gradual uniform compression; a dynamic viscosity coefficient that expresses its resistance to gradual shearing, and a rotational viscosity coefficient which results from a coupling between the fluid flow and the rotation of the individual particles.[1]: 304  In the absence of such a coupling, the viscous stress tensor will have only two independent parameters and will be symmetric. In non-Newtonian fluids, on the other hand, the relation between ε and E can be extremely non-linear, and ε may even depend on other features of the flow besides E.

  1. ^ De Groot, S. R.; Mazur, P. (1984). Non-Equilibrium Thermodynamics. New York: Dover. ISBN 0-486-64741-2.

and 18 Related for: Viscous stress tensor information

Request time (Page generated in 0.8688 seconds.)

Viscous stress tensor

Last Update:

The viscous stress tensor is a tensor used in continuum mechanics to model the part of the stress at a point within some material that can be attributed...

Word Count : 2567

Stress tensor

Last Update:

continuum mechanics Viscous stress tensor, in continuum mechanics Stress–energy tensor, in relativistic theories Maxwell stress tensor, in electromagnetism...

Word Count : 86

Newtonian fluid

Last Update:

Newtonian. Fluid mechanics Non-Newtonian fluid Strain rate tensor Viscosity Viscous stress tensor Panton, Ronald L. (2013). Incompressible Flow (Fourth ed...

Word Count : 3037

Fluid mechanics

Last Update:

non-Newtonian manner.: 145  The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the viscosity. A simple equation...

Word Count : 2639

Viscosity

Last Update:

viscosity tensor that maps the velocity gradient tensor ∂ v k / ∂ r ℓ {\displaystyle \partial v_{k}/\partial r_{\ell }} onto the viscous stress tensor τ i j...

Word Count : 11380

Vorticity equation

Last Update:

ρ is the local fluid density, p is the local pressure, τ is the viscous stress tensor and B represents the sum of the external body forces. The first...

Word Count : 1490

Reynolds stress

Last Update:

In fluid dynamics, the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes...

Word Count : 2250

Fluid dynamics

Last Update:

fluctuation-dissipation theorem of statistical mechanics is added to the viscous stress tensor and heat flux. The concept of pressure is central to the study of...

Word Count : 4144

General equation of heat transfer

Last Update:

pressure and σ {\displaystyle \sigma } is the viscous stress tensor, with the components of the viscous stress tensor given by: σ i j = μ ( ∂ v i ∂ x j + ∂ v...

Word Count : 1893

Viscoelasticity

Last Update:

} (t)} is the Cauchy stress tensor as function of time t, p is the pressure I {\displaystyle \mathbf {I} } is the unity tensor M is the memory function...

Word Count : 5843

Einstein field equations

Last Update:

of a tensor equation which related the local spacetime curvature (expressed by the Einstein tensor) with the local energy, momentum and stress within...

Word Count : 5096

Computational fluid dynamics

Last Update:

relationships/equations: (a) constitutive relationships for the viscous stress tensor; (b) constitutive relationships for the diffusive heat flux; (c)...

Word Count : 8513

Aeroacoustics

Last Update:

{\boldsymbol {\tau }}} is the viscous stress tensor. Note that v v {\displaystyle \mathbf {v} \mathbf {v} } is a tensor (see also tensor product). Differentiating...

Word Count : 1711

Pressure

Last Update:

} . This tensor may be expressed as the sum of the viscous stress tensor minus the hydrostatic pressure. The negative of the stress tensor is sometimes...

Word Count : 5656

Reynolds stress equation model

Last Update:

individual components of the Reynolds stress tensor are directly computed. These models use the exact Reynolds stress transport equation for their formulation...

Word Count : 2883

Stokes flow

Last Update:

={\boldsymbol {0}}} where σ {\displaystyle \sigma } is the stress (sum of viscous and pressure stresses), and f {\displaystyle \mathbf {f} } an applied body...

Word Count : 3383

Boltzmann equation

Last Update:

\langle (v_{i}-V_{i})(v_{j}-V_{j})\rangle } is the pressure tensor (the viscous stress tensor plus the hydrostatic pressure). Letting A = m ( v i ) 2 2...

Word Count : 4961

Cauchy momentum equation

Last Update:

describes viscous forces; for incompressible flow, this is only a shear effect. Thus, τ is the deviatoric stress tensor, and the stress tensor is equal...

Word Count : 5375
PDF Search Engine © AllGlobal.net