Numerical Investigation of the Classical Blasius Boundary Layer Equation Using Similarity Transformation

Abstract

This study investigates the classical Blasius boundary layer problem governing steady, 
incompressible, two-dimensional laminar flow over a stationary semi-infinite flat plate 
under zero pressure gradient conditions. The governing boundary layer equations are 
formulated from the Navier–Stokes equations by invoking the standard boundary layer 
approximations, which reduce the full fluid motion equations to a simplified system 
describing momentum transport within the viscous region adjacent to the plate. To 
facilitate numerical solution, the coupled partial differential equations are 
transformed into a nonlinear third-order ordinary differential equation through the 
application of the Blasius similarity transformation, thereby reducing the problem to a 
self-similar boundary value formulation. The resulting Blasius equation is solved 
numerically using the shooting technique in conjunction with the fourth-order Runge
Kutta integration scheme, enabling accurate determination of the unknown initial 
conditions that satisfy the far-field boundary constraints. Numerical simulations are 
performed to examine the dimensionless velocity profile, boundary layer growth, and 
wall shear characteristics along the flat plate. The computed results demonstrate 
smooth convergence of the velocity field toward the free-stream condition and exhibit 
excellent agreement with the well-established classical value of the skin-friction 
parameter, thereby validating the accuracy, stability, and reliability of the adopted 
numerical procedure. The findings reaffirm the effectiveness of similarity-based 
numerical techniques for solving nonlinear boundary layer problems and provide a 
robust computational framework for future investigations involving more complex 
transport phenomena, including coupled heat and mass transfer, magnetohydrodynamic 
flows, porous media, thermal radiation, viscous dissipation, chemical reactions, and non
Newtonian fluid models relevant to advanced engineering and industrial applications.