7-sim_solutions3 - Module 7 1 Similarity Solutions to the...

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Module 7 ME 6302 1 Similarity Solutions to the Forced Laminar Boundary Layers-III Professor S.M. Ghiaasiaan G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0405
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Module 7 ME 6302 2 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Heat Transfer with Viscous Dissipation 2 2 2 2 2 0 () p uv xy uu u y TT T u x yy C y ν α ∂∂ += + s 0, T=T , at 0 , T=T , at y uU y ∞∞ == = =→ y x δ , UT s T
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Module 7 ME 6302 3 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Heat Transfer with Viscous Dissipation • To solve, use Blasius’s similarity parameter • Blasius’s solution for hydrodynamics applies '( ) 1 (') 2 U y x uU f vU vf f x η ν = = =
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Module 7 ME 6302 4 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Heat Transfer with Viscous Dissipation • The thermal energy equation, in terms of Blasius’s similarity parameter, is: 22 2 2 Pr Pr ( ") 2 , at y=0(constant wall temperature) at y=0, 0(adiabatic wall) at T=T s dT U ff dd C p TT T y y ηη += = = →∞
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Module 7 ME 6302 5 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Heat Transfer with Viscous Dissipation • To solve, assume: s TT θ = 2 12 Homogeneous Solution Particular Solution T( ) T ( ) 2 U C Cp η θη −= + ±²³ ±´² ´³
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Module 7 ME 6302 6 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Heat Transfer with Viscous Dissipation The homogeneous solution is the same as the solution without dissipation The particular solution must satisfy: Pr 0 1 Pr 0 (" ) 1 ) f d f d η θ =− 2 2 22 2 2 2 1 Pr 2Pr " 2 0 at y 0 at y=0 dd f f d d θθ ηη += =→ = 11 (0) 1, and ( ) 0 are satisfied.
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This note was uploaded on 05/22/2010 for the course ME 6302 taught by Professor Mostafaghiaasiaan during the Spring '10 term at Georgia Institute of Technology.

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7-sim_solutions3 - Module 7 1 Similarity Solutions to the...

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