Laminar Flow Over a Flat Plate With MATLAB

Kevin Leatherman
HON 396
Abstract

The problem of my project is modeling the behavior of laminar, incompressible fluids that flow over a flat plate. As a fluid flows over a flat plate, a boundary layer forms. A boundary layer is a thin layer of fluid that is adjacent to the surface, caused by the viscosity of the fluid. Outside of this layer, fluid can be considered frictionless; therefore, it has a constant velocity. However, inside the boundary layer, the velocity of the fluid varies due to the drag. The velocity of the fluids can be represented by the Blasius equation. This is a non-linear ordinary differential equation that was simplified from a complex system of partial differential equations, and the final result is

f’’’+½ f f’’=0.

Using MATLAB, the ODE will be solved with different initial values and with different numerical methods. MATLAB should also allow several graphs to be made, in order to better understand what the fluid is doing with a visual aid, rather than trying to interpret the behavior only from the solution to a differential equation.