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In this work a numerical investigation has been conducted to study the unsteady oscillatory flow of a viscous fluid induced by a swirling disk. The disk stretches radially with the time-based sinusoidal oscillations. The governing equations for the three-dimensional boundary layer-flow are normalized using a suitable set of similarity transformations. The normalized partial differential equations are then solved numerically using a finite difference scheme by altering the semi-infinite domain to a finite domain. The effects of various imperative parameters on the oscillatory flow are discussed with graphs and tables.

A complete thermal analysis is performed for the propulsion of cilia in an inclined channel. Coating around the channel walls is provided by a Carreau fluid under a uniform magnetic field. Uniformly grown cilia produce propulsive metachronal waves by moving in a coordinated rhythm along the channel surface and adapt an elliptic path along the direction of flow. Using lubrication approximations, the governing equations, formulated in the wave frame of reference, are solved by the perturbation method. Validation of the analytic solution is provided by computing the solution numerically with the shooting method. This study is concerned with the parametric consequences on pertinent flow and heat transfer quantities, such as streamlines, velocity profile, temperature profile, entropy lines and the Bejan number. The results reveal that large cilia propel the axial velocity near the channel wall but put hindrance to the axial velocity and the temperature profile in the central part of the channel. The entropy production in the channel reduces for large cilia and a high Hartmann number.