Energy viscous dissipation

Regardless of the viscometric technique, determination of the true, isothermal flow properties at high shear rates can be complicated by high rates of viscous energy dissipation, which make them hard to maintain isothermal conditions. If we divide both sides of Equation 13.3 by V Jt, we see that the rate of viscous energy dissipation per unit volume E is 

Example 14.4 Obtain an expression for the adiabatic rate of temperature rise in a polymer sample subjected to a shear stress t and shear rate y. 

Solution. In the absence of heat transfer, the rate of temperature rise T is given by the rate of energy dissipation per unit volume divided by the volumetric heat capacity, pcp, as follows  

Not only is temperature rise an important consideration in viscometry, where great care must be taken in the design of viscometers to permit adequate temperature regulation, but it 

Not only is this an important consideration in viscometry, where great care must be taken in the design of viscometers to permit adequate temperature regulation, but it also must be taken into account in the design of processing systems. In the steady-state operation of extruders, for example, virtually all the energy required to melt and maintain the polymer in the molten state is supplied by the mechanical drive. Here, however, we will limit our considerations to isothermal flows. 

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G is called the loss modulus. It arises from the out-of-phase components of y and T and is associated with viscous energy dissipation, ie, damping. The ratio of G and G gives another measure of damping, the dissipation factor or loss tangent (often just called tan 5), which is the ratio of energy dissipated to energy stored (eq. 16). 

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

The relation of hydraulic diameter to channel length and the Reynolds number are important factors that determine the effect of the viscous energy dissipation on flow parameters. 

Under certain conditions the energy dissipation may lead to an oscillatory regime of laminar flow in micro-channels. The relation of hydraulic diameter to channel length and the Reynolds number are important factors that determine the effect of viscous energy dissipation on flow parameters. The oscillatory flow regime occurs in micro-channels at Reynolds numbers less than Recr- In this case the existence of velocity fluctuations does not indicate change from laminar to turbulent flow. 

The subject of this chapter is single-phase heat transfer in micro-channels. Several aspects of the problem are considered in the frame of a continuum model, corresponding to small Knudsen number. A number of special problems of the theory of heat transfer in micro-channels, such as the effect of viscous energy dissipation, axial heat conduction, heat transfer characteristics of gaseous flows in microchannels, and electro-osmotic heat transfer in micro-channels, are also discussed in this chapter. 

At low speeds and high temperatures, viscous energy dissipation is minimized, and the tear strength approaches a lower limit Go of about 20 J/m (Figure 1.11). This is of the same order of... 

If the dominating domain is selected correctly, the error induced by the simplification will be no more than about 20%. However, even well into the viscous dissipation domain, the effects of the surface tension are still significant, while in the surface tension domain, the effects of viscous dissipation disappear far more rapidly as one moves away from the borderline. In other words, the viscous energy dissipation contribution to the spread factor rapidly declines within the surface tension-dominated domain, while significant residual surface tension effects extend well into the viscous energy dissipation domain. 

A7.2.2 Viscous Energy Dissipation for Screw Rotation for Channels... 

A7.3.1 Viscous Energy Dissipation for Barrel Rotation Generalized... 

Viscous Energy Dissipation and Temperature of the Resin in the Channei... 

The viscous energy dissipation is calculated using velocities in the laboratory (Eulerian) reference frame. As previously stated here and by Malvern [48], velocities are not frame indifferent. The Eulerian velocities and provided by... 

The absolute value of the pressure gradient is used for all dissipation calculations. Although the pressure-induced flow is in different directions for a positive- and negative-valued pressure gradient operation, the dissipation level, however, is identical. Viscous energy dissipation is always positive definite. 

This analysis starts with the assumption that melting occurs in all four melt films that surround the solid bed. The initial analysis will be carried out for Film C in Fig. A6.1. The film is located between the barrel and the solid bed interface. This analysis describes the viscous energy dissipation in the film and the energy conduction from the barrel wall and how they relate to the melting flux at the solid bed-melt interface. 

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