## Coriolis Effects on Air, Nanofluid and Casson Fluid Flow Over a Surface with Nonuniform Thickness

##### Abstract

The trajectories of moving objects in a rotating frame is usually deflected by Coriolis
force and this leads to many of the natural phenomena on Earth. Some of the natural
outcomes of Coriolis effect include the tropical storms, cyclones, and hurricanes.
Understanding the Coriolis effect on Newtonian and non-Newtonian fluid flow is
therefore vital in determining the right actions needed to forestall these natural
disasters. The invention of mass-flow meter to measure the density of fluid and the
rate of mass-flow in a tube and the invention of bioreactors are some of the many
practical uses of Coriolis force. The path followed by the air (Newtonian fluid) and
nanofluid (fluid suspending some nanoparticles) heated by the sun to reach the Earth
is usually deflected by the Coriolis force. It becomes worthwhile to investigate the
influence of Coriolis force on the flow of these fluids. Also, the effect of a rotating
frame of reference on the Brownian diffusivity and thermophoretic diffusivity of
nanofluids is important in industries for its role in cooling/heating processes. Casson
fluid possesses characteristics that closely agree with the nature of blood; with
applications in bioengineering. More so, the Earth’s surface is neither horizontal nor
vertical, and it is neither inclined. The Earth surface is geoid and so, a more
appropriate surface to model it is one with non-uniform thickness. This thesis
investigates and gives a comprehensive insight into the significance of rotational
force on the flow of Newtonian and non-Newtonian fluids over a surface with
non-uniform thickness. A suitable set of equations for the flow is obtained by
introducing the Coriolis force as a body force into the Navier-Stokes equations.
Appropriate similarity variables are used to reduce the set of governing partial
differential equations to a system of non-linear ordinary differential equations. The
transformed set of equations is numerically solved via shooting technique alongside
Runge-Kutta algorithm. The results are depicted graphically and in tables to show
the effects of pertinent parameters on the flow. It is observed that rotation enhances
primary flow velocity but impedes secondary flow velocity. Rotation also has an
increasing effect on temperature profiles but decreasing effects on the heat transfer
rate of Casson and Newtonian fluids.