An Ultimate Combination of Physical Intuition with Experiments… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Boundary Layer Theory for Viscous Fluid Flows

Introduction of Boundary Layer Concept Based on his experimental observations, Prandtl found that effect of the viscosity is confined to a thin viscous layer that he called, the boundary layer.

Analytical Proof of Prandtls Intuition & Experiments Consider non-dimensional of NS Equations Steady State non-dimensional of NS Equations Steady State Incompressible non-dimensional of NS Equations

Equivalent ODE to NS A selected property of any fluid flow field can be approximated as:

General Response of A Second Order System y y

Toward Creeping y y

Response of Flow Field towards Boundary Effects y

The limit of Very large Re Flow over a Wedge

Prandtls Large Reynolds Number 2-D Incompressible Flow The free-stream velocity will accelerate for non-zero values of β: where L is a characteristic length and m is a dimensionless constant that depends on β:

The condition m = 0 gives zero flow acceleration corresponding to the Blausius solution for flat-plate flow. The Measure of Wedge Angle The boundary layer is seen to grow in thickness as x moves from 0 to L.

Two-dimensional Boundary Layer Flows In dimensionless variables the steady Navier-Stokes equations in two dimensions may be written: The boundary layer is seen to grow in thickness as x moves from 0 to L.