Study of Some Non Linear Partial Diffrential Equation of Fluid Dynamics

Abstract

This study investigates the behavior of fluid flow through cracked porous media with varying wetting abilities using the Integral Identity Method (IIM) and hypergeometric solution techniques. Non-linear partial differential equations govern the fluid dynamics in such complex systems, and understanding their behavior is crucial for numerous applications ranging from hydrology to petroleum engineering. The presence of cracks alters the flow characteristics significantly, particularly when the wetting abilities of the medium differ. By employing the IIM, a powerful tool for analyzing fluid dynamics problems, coupled with hypergeometric solution methods, we derive insights into the complex behavior of fluid flow in these heterogeneous environments. Our study aims to contribute to a better understanding of fluid flow through cracked porous media with different wetting abilities, shedding light on the underlying mechanisms governing such systems. Analytical Study of Instability Phenomenon using Fourier Transform and Laplace TransformThis research delves into the analytical investigation of instability phenomena in nonlinear partial differential equations of fluid dynamics. By employing Fourier and Laplace transforms, we analyze the instability behavior of the system under consideration. Instabilities are critical in understanding various fluid dynamics phenomena, such as turbulence and pattern formation, and their analytical study provides valuable insights into the underlying mechanisms driving these phenomena. Through our analytical approach, we aim to elucidate the intricate dynamics of instability and provide a deeper understanding of nonlinear behavior in fluid systems. newline