Energy dissipation, mechanical

Consider the mass, thermal and momentum balance equations. The key assumption of the present analysis is that the Knudsen number of the flow in the capillary is sufficiently small. This allows one to use the continuum model for each phase. Due to the moderate flow velocity, the effects of compressibility of the phases, as well as mechanical energy, dissipation in the phases are negligible. Assuming that thermal conductivity and viscosity of vapor and liquid are independent of temperature and pressure, we arrive at the following equations ... 

At the time of the writing of the first edition of this text (38), we wrote the following about mechanical energy dissipation in repeatedly deforming "active" compacted particulates and the evolution of their melting ... 

Frankel and Acrivos (1967) introduced a rather different type of cell model based on lubrication-theory-type arguments. First, the rate of mechanical energy dissipation in the small gap between adjacent sphere pairs is calculated,... 

As is well known, Einstein (1906, 1911) calculated the additional rate of mechanical energy dissipation engendered by the introduction of a single sphere into a homogeneous shear flow and ultimately obtained... 

For the worst case, calculation of temperature rise within the sample due to mechanical energy dissipation is about 1"C. With heat loss from the sample, this value should be lower. 

Conservative calculation of temperature rise within the sample due to mechanical energy dissipation is less than 1"C. 

For an isolated particle i.e., e —> 1, Eq. (223) reduces to Eq. (222). The buoyancy term represents the net force arising from the pressure distribution over the surface of the particle with the fluid at rest. The drag term represents the additional force exerted on the particle by a flowing fluid. Drag gives rise to mechanical energy dissipation. 

Two-phase pressure gradient is defined as the variation of the internal pressure per unit reactor length. The pressure gradient is related to the mechanical energy dissipation owing to the two-phase flow... 

The couple on the sphere vanishes unless it is restrained from rotating. If the sphere is also neutrally buoyant then F = 0, and only the last term in Eq. (147a) survives. By noting that the local rate of mechanical energy dissipation in the unperturbed flow is 2/iSjj Sjj, this ultimately leads to a simple proof of Einstein s law of suspension viscosity (Ela) for flow through cylinders (B17), provided that the spheres are randomly distributed over the duct cross section. 

FIGURE 3.26 The mechanical energy dissipated relative to the total input strain energy for four grades of NR, stretched at RT to various extent. Strain crystallization at ca. 250% or higher results in more marked hysteresis (Choi and Roland, 1997). 

As a result, most of the equipment heralded in process intensification not only intensifies chemical conversion per unit volume, but also intensifies the mechanical-energy dissipation per unit volume. This is the brute force of turbulence that the title alludes to most intensified technologies rely on turbulence to beat the fluids - in some way or other - into high contact area and thin boundary layers. 

As a result, a two-fold increase in the reactor productivity requires either a two-fold increase in the reactor volume or a two-fold decrease in the heat-transfer time. Since an increase in reactor volume is not compatible with the intensification objectives, only the second option (two-fold decrease in heat-transfer time) will be examined here. The following analysis is intended to quantify the variation in the mechanical energy dissipated in these reactors that would be required to accelerate heat transfer by a factor of two. 

Figure 11.7 shows the dynamic mechanical spectrum reported by Celli and Scandola [42] for PLLA after heating the sample at 200°C in order to erase the thermal history. The solid line refers to a sample quenched in a water-ice mixture after extrusion, while the broken line depicts an immediate rerun on the same sample, after cooling from 160°C. Below room temperature, no relaxation process is apparent in either curves, that is, the dynamic mechanical loss tangent is as low as 10 over the range —150-20°C [42]. The absence of any loss phenomena below Tg capable of mechanical energy dissipation is likely the reason for the observed brittleness of glassy PLLA and induces failure of lower molecular... 

The mechanical energy dissipated by the agitator is converted into viscous friction energy and finally altered into thermal energy. In most cases this term may be neglected when compared to the heat released by a chemical reaction. But with viscous reaction masses, as for example with polymerization reactions, this term must be integrated in the heat balance. It can be estimated from Equation (8). 

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