6-sim_solutions2_revised Feb 04

6-sim_solutions2_revised Feb 04 - Module 6 1 Similarity...

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Module 6 ME 6302 1 Similarity Solutions to the Forced Laminar Boundary Layers-II Professor S.M. Ghiaasiaan G.W. Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332-0405
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Module 6 ME 6302 2 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Mass Transfer • The problem and its solution are very similar to heat transfer 2 11 1 12 2 , 1 1, 1 1 (17) 1 at y 0 0 at y s mm m uv D xy y m m m ∗∗ ∂∂ += = == =→ y x v u m m 1,S
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Module 6 ME 6302 3 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Mass Transfer • Assume 11 () , a n d d e r i v e mm η ∗∗ = "' 1 1 12 1 f0 2 1 at 0 0 at where mS c m m m v Sc D + = == = →∞ =
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Module 6 ME 6302 4 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Mass Transfer • The formal solution is: Sc 0 1 Sc 0 (f ") () 1 (f ") d m d η =−
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Module 6 ME 6302 5 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Mass Transfer • From the definition of Sherwood number, Sh x : • The final solution is: 1 12 1, 12 12 0 1 0 () / ( ) xs y gx x m Sh D m m DD y xd m d vx U η ρ ρρ = = == =− 0 1 2 f 2 0 Re (18) x x Sc d Sh de =
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Module 6 ME 6302 6 Incompressible, Steady-State, 2-D Flow Past a Flat Plate: Mass Transfer • Numerical solution results over the 1 1 3 2 x 0.5 15 range can be correlated as: Sh 0.332 Re (19) x Sc Sc << = ±±
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6-sim_solutions2_revised Feb 04 - Module 6 1 Similarity...

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