Problem of Fluctuating Fluid Flow in a Porous Medium
Shyambir Singh Chahar, Dharampal Singh · International Journal of Modern Trends in Engineering and Research · 2016
A mathematical solution and analysis of 2-D fluctuating flow of viscous, incompressible fluid through a porous medium bounded by a porous plate is presented as follows. Fluid dynamics is the science in which we study the properties of fluids (liquids and gases) in motion. The systematic study of fluid dynamics or hydrodynamics started only after the Euler's discovery of the equations of motion of an inviscid fluid. An attempt to describe the affect of fluid motion is made by Newton, who conceived the idea that the fluid consisted of a granulated structure of discrete particles. Later, some significant contributions to this subject were made by the following scientists. Langrange gave the concept of velocity potential stream function. The principle of resistance to flow in capillary tubes was given by Poiseuille. The credit for the equations of motion of viscous fluids goes to Navier and Stokes. Reynolds discovered the equations of turbulence motion. Prandtl put forward the boundary layer theory. The theories of turbulence and stabilities are the creations of G. I. Taylor and Lord Rayleigh. Still later, some other excellent contributions were given by many more famous scientists/mathematicians which include Benard, Kutta, Prandtl, Lord Kelvin, Orr, Sommerfield, Rayleigh, Zhukovski and Karman etc. Now-a-days fluid dynamics has become a very vast subject and has given birth to many other subjects like meteorology, gas dynamics, aerodynamics, non-Newtonian flows, magnetohydrodynamics etc. Fluid dynamics and its subdisciplines like aerodynamics, hydrodynamics and hydraulics have a wide range of applications. Examples include the design of aircraft, calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns and control of many industrial processes. Fluid dynamics is the key of our understanding some of the most important phenomena in our physical world like ocean currents, weather systems, convection currents such as motions of molten rocks inside the earth and the motion in the outer layer of the sun and the swirling of gases in galaxies. Classical (or Newtonian) mechanics and continuum hypothesis are going to act as the basis for study of fluid dynamics. Classical mechanics uses the concept of point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass and the forces applied to it. Classical mechanics is often referred to as Newtonian mechanics after Newton and his laws of motion.