Example Entry Flow of a Non-Newtonian Fluid

Next consider the entry flow of a non-Newtonian fluid, essentially the same problem as 

Once you know how to solve the problem for a Newtonian fluid (as in Fig. 10.2), there are two major changes you must make for a non-Newtonian fluid. One of those is to represent the viscosity, Eq. (10.14), in FEMLAB. The other is to be smart about how you obtain a converged solution. 

Step 1 Insert the parameters for the viscosity under the Options/Constants and the equation for viscosity, using those parameters, in Options/Expressions/Subdomain Expressions. Then the shear rate is defined in terms of the parameters of the problem. Here the variables are u in the radial direction and v in the axial direction. Making the appropriate conversions to Eq. (10.7) gives Eq. (10.9), which you type as a subdomain expression. 

Step 2 If the variable used for viscosity is eta, then under the Physics/Subdomain Settings, you insert the word eta is inserted in the box for 17. That is all that is required to set up the non-Newtonian problem. As the problem is being solved, when the viscosity 

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