Viscous energy dissipation rate

The last term is the rate of viscous energy dissipation to internal energy, dV, also called the rate of viscous losses. These... 

Turbulent velocity fluctuations ultimately dissipate their kinetic energy through viscous effects. MacroscopicaUy, this energy dissipation requires pressure drop, or velocity decrease. The ener dissipation rate per unit mass is usually denoted . For steady ffow in a pipe, the average energy dissipation rate per unit mass is given by... 

Majerus (61, 62) has approached the failure behavior of highly filled polymers by a thermodynamic treatment in which the ability to resist rupture is related to the propellant s ability to absorb and dissipate energy at a certain rate. An energy criterion which requires failure to be a function of both stress and strain was originally stated by Griffith (36) for brittle materials and later adapted to polymers by Rivlin and Thomas (80). Williams (115) has applied an energy criterion to viscoelastic materials such as solid propellants where appropriate terms are included for viscous energy dissipation. 

The last term is the rate of viscous energy dissipation to internal energy, Ev = jv <5 dV, also called the rate of viscous losses. These losses are the origin of frictional pressure drop in fluid flow. Whitaker and Bird, Stewart, and Lightfoot provide expressions for the dissipation function <5 for Newtonian fluids in terms of the local velocity gradients. However, when using macroscopic balance equations the local velocity field within the control volume is usually unknown. For such... 

From Eq. E2.5-17 we can calculate the total viscous dissipation between the parallel plates. The second invariant of the rate of strain tensor multiplied by the viscosity gives the viscous dissipation per unit volume. From Table 2.3 we find that, for the case at hand, the second invariant reduces to y2z therefore, the total viscous energy dissipation (VED) between the plates will be given by... 

Erj Energy dissipation rate due to purely viscous drag, W... 

Petrov, A. G., Energy dissipation rate in a viscous fluid with condition for shear stress ot the boundary stream line, Physics Doklady, Vol. 34, No. 2, 1989. 

The total energy dissipation rate, E tot (J/ml) is the sum of a network energy term (Em), a creep energy term (Ecr) to break the structural bonds, and a viscous energy term (Ev) to overcome the purely viscous drag. The corresponding shear stresses can be denoted as O, On, Ocr, andOv, respectively. Therefore, the stress (O) necessary to produce deformation at a constant shear rate is divided into three parts ... 

Viscous flow is accompanied by energy dissipation, which results in a conversion of all the work into heat. Energy dissipation rate, i.e. the power (energy per unit time) dissipated per unit volume, is given by... 

Similar to viscous flow, plastic flow is irreversible both thermodynamically and mechanically. The energy dissipation rate in the case... 

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