Heating viscous dissipation

The preceding equations are not applicable for highly viscous non-Newtonians such as molten polymers because of factors such as the materials compressibility or severe viscous heating effects. As an example of the latter, consider the processing of certain polymers in screw extruders where the shear heating (viscous dissipation) causes the fluid to rise significantly in temperature. 

The Br is a measure of the extent to which viscous heating is important relative to an impressed temperature difference. This can be of some concern in the scale-up design, v usually increasing, with other properties remaining constant. A comparison of the Br for a pilot scale (0.05-m screw) and an industrial (0.15-m screw) unit yields values of ca. 0.65, and 5.73, respectively, for the Br with A = 0.5 w/m K and rj = 500 Pa.s at 60 rpm. The numbers suggest that viscous dissipation will be important and will be much more pronounced in the case of an industrial unit. 

Celata et al. (2005) evaluated the effect of viscous heating on friction factor for flow of an incompressible fluid in a micro-channel. By integrating the energy equation over the micro-channel length, a criterion that determines conditions when viscous dissipation effect is signiflcant was obtained ... 

Judy J, Maynes D, Webb BW (2002) Characterization of frictional pressure drop for liquid flows through micro-channels. Int J Heat Mass Transfer 45 3477-3489 Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 Koo J, Kleinstreuer C (2004) Viscous dissipation effects in microtubes and microchannels. Int J Heat Mass Transfer 47 3159-3169... 

Equation (4.12) indicates the effect of viscous dissipation on heat transfer in micro-channels. In the case when the inlet fluid temperature, To, exceeds the wall temperature, viscous dissipation leads to an increase in the Nusselt number. In contrast, when To < Tv, viscous dissipation leads to a decrease in the temperature gradient on the wall. Equation (4.12) corresponds to a relatively small amount of heat released due to viscous dissipation. Taking this into account, we estimate the lower boundary of the Brinkman number at which the effect of viscous dissipation may be observed experimentally. Assuming that (Nu-Nuo)/Nuo > 10 the follow-... 

For the heating regime at small X+, the heat transferred from the wall to the cold fluid and the heat released due to viscous dissipation lead to an increase in... 

Koo J, Kleinstreuer C (2004) Viscous dissipation effects in micro-tubes and micro-channels. Int J Heat Mass Transfer 47 3159-3169... 

Q and R are generation terms for heat and chemical species respectively, while the pressure gradient Vp plays an analogous role for momentum generation. The heat generation arises from viscous dissipation and from reaction heating ... 

Figure 3 illustrates some additional capability of the flow code. Here no pressure gradient is Imposed (this is then drag or "Couette flow only), but we also compute the temperatures resulting from Internal viscous dissipation. The shear rate in this case is just 7 — 3u/3y — U/H. The associated stress is.r — 177 = i/CU/H), and the thermal dissipation is then Q - r7 - i/CU/H). Figure 3 also shows the temperature profile which is obtained if the upper boundary exhibits a convective rather than fixed condition. The convective heat transfer coefficient h was set to unity this corresponds to a "Nusselt Number" Nu - (hH/k) - 1. 

The third term on the right side of eq 68 represents viscous dissipation, the heat generated by viscous forces, where r is the stress tensor. This term is also small, and all of the models except those of Mazumder and Cole - neglect it. The fourth term on the right side comes from enthalpy changes due to diffusion. Finally, the last term represents the change in enthalpy due to reaction... 

Heating and cooling often take place while the polymer melt flows, making viscous dissipation an influencing factor during the process. However, since most plastic parts are thin, the conduction often occurs only across the thickness and the viscous heating is a result of shear within the narrow gap of a die or mold cavity. For such cases, the equations reduce to,... 

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