Viscous heat generation

Viscous heat generation is the dissipation of mechanical energy in a viscous fluid. The last term in the energy Eq. 5.5(d) shows the viscous dissipation in the most general case. In the simpler case of unidirectional shear, the viscous heat generation per unit volume is  

---

Within the viscous layer, all the viscous dissipation is taking place. The scale of viscous heat generation/unit volume (p) at any point is given by... 

This parameter appears to be the coefficient of the viscous term in the non-dimensionalized energy equation and determines the magnitude of the viscous heat generation. Since it is inversely proportional to the square of the system size, it shows the difference in viscous heating effects between a macro and a micro system. ... 

As described above, the temperature field is computed using the finite element formulation of the heat conduction equation, with the viscous heat generation being computed from the stress and velocity fields obtained during the first iteration of the problem. The temperature contours, normalized on the maximum centerline temperature Tc = v V2/3K expected for capillary Poiseuille... 

This is the net energy loss through viscous heat generation in material. 

The V term on the left hand side represents the movement of hot melt into an element, while the right hand side is a combination of thermal diffusion and viscous heat generation. If the computation shows that an element is solidified, the channel is narrowed at that position for the subsequent time step. 

Evidently, for the limiting case of a shear-thinning fluid (Newtonian fluid n = 1), the velocity gradient is a maximum and hence, the viscous heat generation is also maximmn. The effect of this process on the developing temperatme profile can be illustrated by considering the situation depicted in Figme 6.7. 

The steady-state heat convection between two parallel plates and in circular, rectangular, and annular channels with viscous heat generation for both thermally developing and fully developed conditions is solved. Both constant wall temperature and constant heat flux boundary conditions are crmsidered. The velocity and the temperature distributions are derived from the momentum and energy equations, and the proper slip-flow boundary conditions are considered. 

Equation 6 shows that the viscous dissipation term scales with the internal dimensions of the microchannel. In fact, for a fixed value of the volumetric flow rate (v) through a microtube with an inner diameter equal to D, the viscous heating generated per unit of length equals the pump power, and it can be written using Eq. 6 as follows ... 

Viscous dissipation (viscous-heat generation) n. In melt processing, wherever there is flow, the resistance of molecules to flow, i.e., viscosity causes heat to be generated within the melt. The rate of dissipation equals the product of shear stress times shear rate, or viscosity times the square of the shear rate. Because both the viscosity and shear rate are high in processes such as extrusion, injection and transfer molding, and intensive mixing, viscous dissipation is a principal mechanism of heating plastics in those processes. 

Equation 5.19 is a useful relationship. If specific heat and temperature changes are known, then the amount of heat required to accomplish this change in temperature can be determined. If the amount of heat and the specific heat are known, then the resulting change in temperature can be calculated. This relationship is indispensa-bie in the analysis of the extrusion process. For instance, if the amount of viscous heat generation in a certain amount of polymer is known, then the resulting adiabatic temperature rise can be determined if the specific heat of the polymer is known. 

The Brinkman number is a measure of the importance of viscous heat generation relative to the heat conduction resulting from the imposed temperature difference AT (= Tj-Tq) ... 

The melt flows from the melt film towards the active flight flank. Only a small fraction of the material can flow through the clearance. As a result, the majority of the melt will flow into the melt pool. A circulating flow will be set up in the melt pool as a result of the barrel velocity. Since most of the viscous heat generation occurs in the upper melt film, it is generally assumed that all melting takes place at the upper solid bed-melt film interface. As melting proceeds, the cross-sectional area of the solid bed will reduce and the cross-sectional area of the melt pool will tend to increase. The melt pool, therefore, will exert considerable pressure on the solid bed. This reduces the width of the solid bed, while the melt film between the solid bed... 

These equations can also explain why sometimes an increase in barrel temperature does not result in improved melting performance. When the barrel temperature T, is increased, the heat conduction term increases however, the viscous heat generation term wiii decrease because the viscosity in the melt film will decrease with increasing temperature of the melt film. If the reduction in the viscous heat generation is larger than the increase in heat conduction, the net result will be a reduced melting rate as shown in Fig. 7.39. 

The viscous heat generation per unit volume for a power law fluid can be written as ... 

---