Fluid flow Ellis model

Before closing this chapter, we feel that it is useful to list in tabular form some isothermal pressure-flow relationships commonly used in die flow simulations. Tables 12.1 and 12.2 deal with flow relationships for the parallel-plate and circular tube channels using Newtonian (N), Power Law (P), and Ellis (E) model fluids. Table 12.3 covers concentric annular channels using Newtonian and Power Law model fluids. Table 12.4 contains volumetric flow rate-pressure drop (die characteristic) relationships only, which are arrived at by numerical solutions, for Newtonian fluid flow in eccentric annular, elliptical, equilateral, isosceles triangular, semicircular, and circular sector and conical channels. In addition, Q versus AP relationships for rectangular and square channels for Newtonian model fluids are given. Finally, Fig. 12.51 presents shape factors for Newtonian fluids flowing in various common shape channels. The shape factor Mq is based on parallel-plate pressure flow, namely,... 

For flow in a narrow gap viscometer, the energy equation and the momentum balance are coupled together by the temperature-dependent viscosity. These equations have been solved for the equilibrium temperature profile and the effect on shear stress by Gavis and Laurence (1968) for a power-law fluid and by Turian (1969) with the Ellis model. For the power law model, the effect on torque in a narrow gap instrument can be expressed in terms of a power series in the Brinkman number (see Example 2.6.1, eq. 2.6.15). The first term of the series is helpful to the experimentalist to indicate where shear heating can affect data. 

B.3 Forced Convection Heat Transfer in Tubes-Short Contact Times. A polymeric fluid whose viscosity function is described by the Ellis model is flowing through the tube as shown in Figure 5.26. Determine the temperature profile and the wall heat flux for the... 

The shear-dependent viscosity of a commercial grade of polypropylene at 403 K can satisfactorily be described using the three constant Ellis fluid model (equation 1.15), with the values of the constants fiQ = 1.25 x lO Ea s, Ti/2 = 6900 Pa and a = 2.80. Estimate the pressure drop required to maintain a volumetric flow rate of 4cm /s through a 50 mm diameter and 20 m long pipe. Assume the flow to be laminar. 

Since we need the g — (—Ap) relation to solve this problem, such a relationship will be first derived using the generalised approach outlined in Section 3.2.4. For laminar flow in circular pipes, the Ellis fluid model is given as ... 

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