BLASIUS EQUATION Solution with Finite Difference Method

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SUMMARY

The discussion focuses on solving the Blasius equation using the Finite Difference Method (FDM) for a two-dimensional, incompressible flow over a flat plate. The boundary layer equations are expressed as 2f''' + ff'' = 0, with specific boundary conditions: f'(0) = 0, f(0) = 0, and f'(n) approaching 1 as n approaches infinity. Participants are tasked with obtaining a numerical solution for this equation and plotting f' and f as functions of n, as well as computing f''(0) to determine the shear stress on the wall.

PREREQUISITES
  • Understanding of the Blasius equation and boundary layer theory
  • Proficiency in numerical methods, specifically the Finite Difference Method
  • Familiarity with plotting functions using software tools like MATLAB or Python
  • Knowledge of boundary conditions in fluid dynamics
NEXT STEPS
  • Implement the Finite Difference Method for solving ordinary differential equations
  • Learn how to plot numerical solutions using MATLAB or Python libraries such as Matplotlib
  • Study the derivation and application of boundary layer equations in fluid dynamics
  • Explore the significance of shear stress in fluid flow and its calculation methods
USEFUL FOR

Fluid dynamics engineers, computational fluid dynamics (CFD) practitioners, and researchers focusing on boundary layer analysis and numerical methods in fluid mechanics.

antiochos
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1) Using a similarity variable, the boundary layer equations for a two-dimensional, incompressible flow over a flat plate can be written below:

2f'''+ff''=0


The boundary conditions are:

a) f ' (0) = 0, no slip at the wall
b) f(0)=0, solid wall
c) f ' (n) goes 1 as n goes infinity boundary layer solution merges into the inviscid solution.

I) using finite difference method, obtain a numerical solution of this equation. Plot f ' and f as a function n.
II) The shear stress on the wall requires f " (0) to be determined. From the numerical solution compute f " (0).
 
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