Calculating Shear Rate for Non-Newtonian Liquid Flow in Non-Circular Duct

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Calculating the shear rate for shear-thinning liquids in non-circular ducts involves using rheological equations that relate shear stress to shear rate. The power law model, T = k * j^n, is commonly referenced, where T is shear stress, k is a consistency index, and n is the flow behavior index. To determine viscosity for calculating the Reynolds number, the apparent viscosity must be derived from the shear rate, which complicates the process in complex duct geometries. The main challenge is accurately calculating the shear rate (j) within the duct to find the viscosity needed for further calculations. Understanding these relationships is crucial for effective analysis of non-Newtonian fluid flow in engineering applications.
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How to calculate the shear rate for the flow of a shear thinning liquid in a non circular duct
 
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With the constitutive equation relating viscosity (shear stress) to the shear rate. There are many models of shear thinning fluids; pick one.
 
Sorry Sir, I know for shear thinning fluids you have rheological equations linking share stress to shear rate. For example the power law model : T = k j^n. But when you have a shear thinning fluid flowing in a complex duct, you need a viscosity to calculate the Reynolds number. And to have the viscosity (apparent = T/j = kj^(n-1)) you need to calculat j in the duct ! It was the meening of my question. How to calculate the shear rate j ?
 

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