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Unformatted text preview: Module 13 ME 6302 ME 6302 Integral MethodI Professor S.M. Ghiaasiaan G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 303320405 Module 13 ME 6302 ME 6302 2 Integral Method • The integral method is a simple and powerful technique for the approximate solution of many boundary layer problems. • The method is based on the integration of boundary layer momentum and energy conservation equations across a boundary layer, assuming simple and welldefined velocity, temperature, or mass fraction distributions that satisfy the major boundary conditions for the boundary layer. As a result, the boundary layer partial differential equations are replaced with ordinary differential equations, often with boundary layer thickness as the dependent variable. • The method has been applied extensively in the past, and has led to many widelyused correlations. Module 13 ME 6302 ME 6302 3 Integral Equations for a 2D Boundary Layer on a Flat Plate: Hydrodynamics • Consider a slice of the boundary layer and its surroundings, where Y is a finite and fixed height, chosen so that Y> . δ x y Y y Y x ( ) , v i ρ , ( , , , ) x dx y u v i ρ + ( ) , s s v i ρ , ( , , , ) x y u v i ρ δ U ∞ Module 13 ME 6302 ME 6302 4 Integral Equations for a 2D Boundary Layer on a Flat Plate: Hydrodynamics • Apply to both sides of the continuity equation • Derive the integral momentum equation by direct momentum balance on the boundary layer slice Y dy ∫...
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 Spring '10
 MostafaGhiaasiaan
 Mechanical Engineering, Heat Transfer, Incompressible Flow, flat plate, integral momentum equation

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