Executive Summary : | This proposal aims to analyze the stability and transient energy growth of an incompressible fluid flow in pressure-driven narrow confinement under various conditions, including rotation, magnetic fields, porous media, and electro-thermal convection. Additionally, we will investigate the impact of geometrical factors such as curvature, bifurcation, and velocity slip in superhydrophobic microchannels. The study of hydrodynamic stability has significant applications in industrial, chemical, biological, and environmental processes. Our main objectives include analyzing linear instability for enhanced mixing phenomena to improve the compact and portable microfluidic devices, investigating instabilities and energy growth in curved microchannel or microtube flows. We will explore the effects of rotation, magnetic fields, electric fields, porous permeability, and sinusoidal varying wall conditions on linear instabilities and energy growth, examining stability characteristics of both Newtonian and non-Newtonian fluid flows. Chebyshev spectral collocation method will be adopted to simulate flow patterns and instability characteristics in microchannels. By achieving these objectives, this study aims to advance the field of microfluidics, improve the performance and sustainability of microfluidic devices. This will contribute to the development of mathematical models and techniques for investigating flow instability and mixing performance in microchannels. |