K. V. Gubareva, E. Yu. Prosviryakov, A. V. Eremin

AN EXACT ANALYTICAL SOLUTION FOR THE COUETTE–POISEUILLE FLOW OF A DILATANT POWER-LAW FLUID IN A PLANE CHANNEL

A study is presented of the steady flow of an incompressible dilatant fluid obeying a power-law model with a flow behavior index of two, in a plane channel. The flow is induced by a combination of the constant motion of the upper wall and a constant axial pressure gradient along the channel. A complete analytical solution to this nonlinear boundary value problem is derived for this nonlinear boundary value problem at all the values of the governing dimensionless parameter, which represents the ratio of the driving forces. It is shown that beyond a critical value of this parameter, the flow regime changes from monotonic to one featuring a region of backflow adjacent to the stationary wall. Closed-form expressions for the velocity and shear stress profiles are given for both regimes. The asymptotic analysis reveals that the flow reversal point approaches the channel centerline at large values of the governing parameter. The results contribute to the understanding of dilatant flow phenomena and provide a valuable benchmark for validating numerical methods.

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