Example. 1-D laminar flow of a shear-thinning polymer melt

Example. 1-D laminar flow of a shear-thinning polymer melt 

let us consider laminar flow between two parallel plates separated by a distance B, but now for simplicity we assume both plates to be stationary. Previously in Chapter 1, we employed finite differences to compute the velocity profile v (y) for a Newtonian fluid. We now consider the same problem, but for a nouNewtonian fluid whose viscosity decreases with increasing shear-rate, common behavior for many polymer solutions and melts. In this problem, the (y-dependent) shear-rate is 

A common model of shear-tiiinning behavior is that of Carreau and Yasuda (Yasuda et al, 1981), for which the shear-rate dependent viscosity t] y) is 

Abdel-Khalikgfo/. (1974) litthepoly(styrene)meltdataat453 KofBallengereta/. (1971) to obtain 

With this nonlinear dependence of the viscosity upon the local shear-rate, numerical solution of the equation of motion is now required. For 1-D laminar flow, the equation of motion 

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