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

STUDYING THE EFFECT OF WEAK CONVECTION ON THE COUETTE–POISEUILLE FLOW OF A POWER-LAW FLUID IN A PLANAR CHANNEL BY THE PERTURBATION METHOD

The paper studies the influence of weak convective effects on the steady flow of a non-Newtonian fluid in a planar channel with a moving upper wall and a longitudinal pressure gradient. The fluid is described by the Ostwald–de-Waele power-law model. To analyze the slow development of the profile along the channel, an asymptotic perturbation method is used, based on a small parameter equal to the ratio of the channel height to the characteristic longitudinal scale. A first-order analytical solution is obtained, including a correction to the primary velocity profile and the shear stress distribution. The flow features for pseudoplastic, Newtonian, and dilatant fluids are analyzed. It is shown that convection disrupts the linearity of the stress field, causes longitudinal evolution of the velocity profile, and modifies the conditions for the onset of reverse flow. The results are important for accurate modeling of processes in devices with combined action of the pressure gradient and wall motion.

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