Isothermal Flow in Channels Non-Newtonian Fluids

Referring to Fig. 5.4 and remembering that equilibrium of forces was the only condition necessary to derive (5.5) then this equation may be used as the starting point for the analysis of any fluid. 

Analysis of polymer melt flow So from above 

The shear rate at the wall is obtained by letting r — R and the equation is more convenient if Vq is replaced by Q from (5.33). In this case 

It is worth noting that since a Newtonian Fluid is a special case of the Power Law fluid when n = 1, then the above equations all reduce to those derived in Section 5.3(a) if this substitution is made. 

The flow rate, Q, may then be obtained from the expression 

It can be seen that in the special case of ra = I these equations reduce to those for Newtonian Flow. 

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