Often in liquid lubrication applications there is a heat generated that is transferred

Chapter 9, Problem 9.26

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Often in liquid lubrication applications there is a heat generated that is transferred across the lubricating layer. Consider a Couette flow with one wall at a higher temperature than the other. The temperature gradient across the flow affects the fluid viscosity according to the relationship. where f.l-o is the viscosity at y = 0 and L is the distance between the walls. Incorporate this expression into the Couette flow equation, integrate and express the shear stress in the fom1 Uf.l-o -r = c-- L where Cis a constant and U is the velocity of the moving wall. Analyze your answer. Should the shear stress be greater or less than that with uniform viscosity?

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