5-sim_solutions1

5-sim_solutions1 - Module 5 Similarity Solutions to the...

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Module 5 ME 6302 Similarity Solutions to the Forced Laminar Boundary Layers-I Professor S.M. Ghiaasiaan G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0405
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Module 5 ME 6302 2 Laminar Boundary Layers Laminar boundary layers (BLs) have velocity and temperature profiles that remain unchanged with respect to their shapes. Similarity solution methods attempt to define an independent variable that transforms the boundary layer partial differential equations into ordinary differential equations. Similarity solutions, when possible, provide exact solutions to problems. Some important and classical solutions are discussed here.
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Module 5 ME 6302 3 Incompressible, Steady-State, 2-D Flow Flat Plate: Hydrodynamics (Blasius, 1908) 2 2 v (1) 0 (2) 0 at (3) at (4) uu u u xy y uv y uU y ν ∂∂ += == = =→ U ν u δ x y
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Module 5 ME 6302 4 Incompressible, Steady-State, 2-D Flow In view of the fact that velocity profile is expected to be self-similar, let’s use , as the independent variable. Also, assume, for stream function: Equation (6) satisfies the continuity equations and gives η ν = (5) U y x ψν = f( ) (6) xU ψ ψη ψψ ∂∂ == = −= = () v= 1 ( ) 2 uU f yy xx x U ff x
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Module 5 ME 6302 5
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5-sim_solutions1 - Module 5 Similarity Solutions to the...

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