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Viscoelastic fluid is an advanced fluid which exhibits both elastic and viscous properties. Whereas rotation of viscoelastic fluid is a very complex phenomenon and has an immense amount of applications in engineering and product making industries. Due to various applications in real life researchers are working to understand the rheology of viscoelastic fluids. Viscoelastic dusty fluids are used in gas cooling systems. In nuclear reactors, dusty fluids are used to lower the temperature of the system. Such fluids are also used in centrifugal separators, which separate solid particles from the liquid state, etc. Therefore, in the present study, viscoelastic dusty fluid is analyzed. More precisely free convective Couette flow under the influence of the transversely applied uniform magnetic field in a rotating frame is considered. The subject fluid is driven by the sine oscillations of the upper plate along with the effect of free convection. Due to rotation, the fluid and dust particles have complex velocities which is the sum of primary velocity and secondary velocity. The flow regime is modeled in terms of partial differential equations. To non-dimensionalize the system of governing equations, dimensionless variables have been derived through Buckingham-Pi theorem. The system of partial differential equations is solved through assumed periodic solutions (Poincare-Light Hill Technique). The expressions for skin friction (shear stresses at    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$y = 0$$\end{document}    y  =  0) and Nusselt number (the rate of heat transfer) are also calculated. Moreover, parametric influence on Nusselt number, and velocity profile of the fluid and the dust particles, is discussed. It is observed that increase in rotation parameter η causes retardation in the velocity of dust particles and the fluid. This is due to the fact that the increase in η enhances the Coriolis forces that are in fact inertial forces, causing a retardation in the velocity of the fluid phase and the dust phase.

Couette flow of viscoelastic dusty fluid in a rotating frame along with the heat transfer