Winifred N. MutukuSamuel, Oke Abayomi2022-09-142022-09-142022http://ir-library.ku.ac.ke/handle/123456789/24193A Research Submitted in Partial Fulfilment of the Requirements for the Award of the Degree of Doctor of Philosophy (Applied Mathematics) in the School of Pure and Applied Sciences of Kenyatta UniversityThe 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.enCoriolis EffectsAir,NanofluidCassonFluid FlowSurfaceNonuniform Thickness