13-Integral_1-1

13-Integral_1-1 - Module 13 ME 6302 ME 6302 Integral...

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Unformatted text preview: Module 13 ME 6302 ME 6302 Integral Method-I Professor S.M. Ghiaasiaan G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0405 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 well-defined 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 widely-used correlations. Module 13 ME 6302 ME 6302 3 Integral Equations for a 2-D 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> . x y Y y Y x ( ) , v i , ( , , , ) x dx y u v i + ( ) , s s v i , ( , , , ) x y u v i U Module 13 ME 6302 ME 6302 4 Integral Equations for a 2-D 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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13-Integral_1-1 - Module 13 ME 6302 ME 6302 Integral...

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