Parallel plate flow nonisothermal

Parallel-Plate Flow with Viscous Dissipation Consider the nonisothermal flow... 

Distributed Parameter Models Both non-Newtonian and shear-thinning properties of polymeric melts in particular, as well as the nonisothermal nature of the flow, significantly affect the melt extmsion process. Moreover, the non-Newtonian and nonisothermal effects interact and reinforce each other. We analyzed the non-Newtonian effect in the simple case of unidirectional parallel plate flow in Example 3.6 where Fig.E 3.6c plots flow rate versus the pressure gradient, illustrating the effect of the shear-dependent viscosity on flow rate using a Power Law model fluid. These curves are equivalent to screw characteristic curves with the cross-channel flow neglected. The Newtonian straight lines are replaced with S-shaped curves. 

Next, we explore some nonisothermal effects on of a shear-thinning temperature-dependent fluid in parallel plate flow and screw channels. The following example explores simple temperature dependent drag flow. 

Example 2.7 Nonisothermal Parallel Plate Drag Flow with Constant Thermophysical Properties Consider an incompressible Newtonian fluid between two infinite parallel plates at temperatures T(0) = T and T(H) — T2, in relative motion at a steady state, as shown in Fig. E2.7 The upper plate moves at velocity Vo (a) Derive the temperature profile between the plates, and (b) determine the heat fluxes at the plates. 

Parallel-Plate, Nonisothermal Newtonian Drag Flow with Constant Viscosity (a) Show that the temperature profile in steady drag flow of an incompressible Newtonian fluid between parallel plates at distance H apart, in relative motion Vo and different constant temperatures, T and T2, assuming constant thermophysical properties and temperature independent viscosity, is given by... 

Parallel-Plate, Nonisothermal Newtonian Drag Flow with Temperature-depen-dent Viscosity (a) Review the approximate linear perturbation solution given in Example 1.2-2 in R. B. Bird, R. C. Armstrong, and O. Hassager, Dynamics of Polymeric Fluids, Vol. 1, Wiley, New York, 1977. (b) Review an exact analytical solution in B. Martin, Int. J. Non-Newtonian Mech., 2, 285-301 (1967). 

Example 9.3 Nonisothermal Drag Flow of a Power Law Model Fluid Insight into the effect of nonisothermal conditions, on the velocity profile and drag flow rate, can he obtained by analyzing a relatively simple case of parallel-plate nonisothermal drag flow with the two plates at different temperatures. The nonisothermicity originates from viscous dissipation and nonuniform plate temperatures. In this example we focus on the latter. 

Fig. 10.48 Numerical simulation results of nonisothermal flow of HDPE, Melt Flow Index MFI = 0.1 melt obeying the Carreau-Yagoda model for a typical FCM model wedge of e/h — 3 and =15. (a) Velocity (b) shear rate and (c) temperature profiles [Reprinted by permission from E. L. Canedo and L. N. Valsamis, Non Newtonian and Non-isothermal Flow between Non-parallel Plate - Applications to Mixer Design, SPE ANTEC Tech. Papers, 36, 164 (1990).]...

In the model to be described, the gas is assumed to be in plug flow, whereas the liquid on the plate is completely mixed. It is an application of Section 14.2.3 to each plate of the column, but in addition nonisothermal and nonisobaric conditions are also accounted for. By way of example, the process consists of two parallel reactions of a gas-phase component with two components of the liquid phase. The stoichiometry is given by... 

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