Viscosity effect temperature-jump

C. This figure is appropriate for adiabatic polymerization, which approximates reality in reactive processing of large articles with high volume-to-surface ratios. In this case, it is impossible to remove the heat effectively and to avoid intense local temperature jumps. Therefore, it is essential to know how to calculate temperature increase for reactions proceeding in non-isothermal conditions. The time dependence of viscosity in this situation can be written as... 

The earliest studies related to thermophysieal property variation in tube flow conducted by Deissler [51] and Oskay and Kakac [52], who studied the variation of viscosity with temperature in a tube in macroscale flow. The concept seems to be well-understood for the macroscale heat transfer problem, but how it affects microscale heat transfer is an ongoing research area. Experimental and numerical studies point out to the non-negligible effects of the variation of especially viscosity with temperature. For example, Nusselt numbers may differ up to 30% as a result of thermophysieal property variation in microchannels [53]. Variable property effects have been analyzed with the traditional no-slip/no-temperature jump boundary conditions in microchannels for three-dimensional thermally-developing flow [22] and two-dimensional simultaneously developing flow [23, 26], where the effect of viscous dissipation was neglected. Another study includes the viscous dissipation effect and suggests a correlation for the Nusselt number and the variation of properties [24]. In contrast to the abovementioned studies, the slip velocity boundary condition was considered only recently, where variable viscosity and viscous dissipation effects on pressure drop and the friction factor were analyzed in microchannels [25]. 

At low holdups, longitudinal dispersion due to continuous-phase velocity profiles controls the amount of mixing in the countercurrent spray column whereas at higher holdups the velocity profile flattens, and the shed-wake mechanism controls. Above holdups of 0.24, the temperature jump ratio is linearly proportional to the dispersed-to-continuous-phase flow ratio, and all mixing is caused by shed wakes into the bulk water and coalescence of drops. As column size decreases, it approaches the characteristics of a perfect mixer, and the jump ratio approaches unity (as compared with the value of zero for true countercurrent flow). It is interesting to note that changing the inlet temperature of dispersed phase by about 55°F hardly affected the jump ratio, probably due to the balancing effects of reduced viscosities and a decrease of drop diameter. 

When a shear stress is applied, the effect is to tilt the potential energy curve, as shown in Fig. 6.2(b), but for moderate shear stresses the tilt is quite small and the jump frequency is only slightly changed, though the spatial distribution of successful jumps is now biassed in the direction of the shear stress. Since the liquid viscosity will vary inversely as the jump frequency, it will show a temperature dependence of the form ... 

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