Numerical modelling of unifom flow over a porous plane with suction perpendicular to the surface by using semi analytical numerical methods

In this thesis numerical modelling of uniform flow over a porous plane with suction in vertical direction to the plane by using semi analytical numerical methods were carried out. Semi analytical numerical methods are differential quadrature method and method of moments. In the first section purpose of the thesis and literature review were given. Then in the theory section, required theoretical information was given. Continuity equation, momentum equation and Biot's theory of poroelasticity were used as governing equations. Reynold and Darcy are dimensionless numbers. In the mathematical modelling section, firstly problem was defined. In this study the flow is 2 dimensional, incompressible, viscous and Newtonian. So density and viscosity are constant. By using equations in the theory section, dimensionless governing equations of the problem were found. After that employing the suggestion by Deng and Martinez, stream function was selected. Final form of the fluid layer equation and porous layer equation were found. Defining boundary conditions at the interface is the most important part of the mathematical modelling. In this study continuity of the velocity vector and shear stress were used as boundary conditions. In other sections, semi analytical numerical methods were explained and velocity distribution in the fluid layer and porous layer are found. In the result section, graphs were plotted and were interpreted in the section. Also approximate estimate of the error calculation was done. According to this, it is seen that error was reduced with increasing number of grid points. It is easily seen from the graphics that vertical velocity increases from top to the bottom because of the suction perpendicular to the surface. And at the bottom no horizontal velocity component exists. Thanks to this study alternative semi analytical solution to a two dimensional flow is derived. Without empirical constants meaningful solutions are obtained.