Boundary layer

In physics and fluid mechanics, the boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. In the atmosphere the boundary layer is the air layer near the ground affected by diurnal heat, moisture or momentum transfer to or from the surface. On an aircraft wing the boundary layer is the part of the flow close to the wing. The Boundary layer effect occurs at the field region in which all changes occur in the flow pattern. The boundary layer distorts surrounding nonviscous flow. It is a phenonomen of viscous forces. This effect is related to the Leidenfrost effect and the Reynolds number.

Boundary layer equations

The deduction of the boundary layer equations was perhaps one of the most important advances in aerodynamics. Using an order of magnitude analysis, the well-known governing Navier-Stokes equations of viscous fluid flow can be greatly simplified within the boundary layer. Notably, the characteristic of the partial differential equations (PDE) becomes parabolic, rather than the elliptical form of the full Navier-Stokes equations. This greatly simplifies the solution of the equations. By making the boundary layer approximation, the flow is divided into an inviscid portion (which is easy to solve by a number of methods) and the boundary layer, which is governed by an easier to solve PDE.

Related Topics:
Navier-Stokes equations - Viscous - Fluid - Flow - Characteristic - Partial differential equations (PDE)

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The approximation states that, for a sufficiently high Reynolds number the flow over a surface can be divided into an outer region of inviscid flow unaffected by viscosity (the majority of the flow), and a region close to the surface where viscosity is important (the boundary layer). For a two-dimensional fluid flow, let u_0 be the fluid velocity outside the boundary layer and u and v be streamwise and transverse velocities respectively inside the boundary layer, where u and u_0 are parallel. Then the equation of motion for an incompressible fluid is given by

Related Topics:
Reynolds number - Incompressible

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: u{partial u over partial x}+v{partial u over partial y}=u_0{partial u_0 over partial x}+{ u}{partial^2 uover partial x^2}

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where

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: u is the kinematic viscosity of the fluid at a point;

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with the boundary condition

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: {partial uoverpartial x}+{partial voverpartial y}=0

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For a flow in which the static pressure p does not change in the direction of the flow then

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: {partial poverpartial x}=0

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so u_0 remains constant.

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Therefore, the equation of motion simplifies to become

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: u{partial u over partial x}+v{partial u over partial y}={ u}{partial^2 uover partial x^2}

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This approximation is used in a variety of practical flow problems of scientific and engineering interest.

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