This work is concerned with the influence of uniform suction or injection on unsteady incompressible Couette flow for the Eyring-Powell model. The resulting unsteady problem for horizontal velocity field is solved by means of homotopy analysis method (HAM). The characteristics of the horizontal velocity field and wall shear stress are analyzed and discussed. Pade approximants and Taylor polynomials are also found for velocity profile and are used to make the maximum error as small as possible. The graphs of the error for the Pade approximation and Taylor approximation are drawn and discussed. Convergence of the series solution is also discussed with the help of and interval of convergence is also found.-curve 

This study examines the turbulent flow field and heat transfer rate (HTR) of the non-Newtonian H2O-Al2O3-carboxymethyl (CMC) in a channel with vortex generators. The finite volume method and SIMPLE algorithm were employed for solving the partial differential equations. The mean Nusselt numbers (Num) and pressure drops were studied at angles of 30-60°, vortex generator depths of 1-3 mm, Reynolds numbers (Re) of 3000-30000, and nanoparticles volume fractions (φ) of 0.5% and 1.5%. According to the numerical results, the use of triangular vortex generators significantly incremented the Nusselt number (Nu) of the non-Newtonian nanofluid (NF), while it had a lower effect on the enhancement of pressure drop (DP). It was also indicated that a change in the vortex generator depth in the range of a few millimeters had no significant effects on the Nu and pressure drop. Moreover, a rise in the Re (i.e., more turbulent flow) significantly incremented HTR. An increase in the Re raised pressure drop; however, the Num incremented more than the pressure drop. Also, the variations of the local Nu indicated that the local Nu significantly incremented around vortex generators due to the formation of vortex flows. An enhancement in the volume fraction of the base fluid’s nanoparticles (NPs) from 0.5% to 1.5% significantly incremented HTR and the Nu.

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