Heat_Transfer_with_Phase_Change_Notes

Heat_Transfer_with_Phase_Change_Notes - Film Condensation...

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g A Film Condensation – on a vertical wall T s < T sat < T T Ts T T T s T T sat T Ts < T ρ l u u,v,T u l ,v l ,T l Without Phase Change With Phase Change Governing Differential Equations and Boundary Conditions Momentum : () 2 g 2 uu uv g xy y    ∂∂ ρ+ = ρ ρ + µ u AA A Continuity : 0 += Thermal Energy : 2 2 2 TT u T Cp u v k y y = + µ A A Boundary Conditions : At y = 0: u = 0, v = 0, T = T w < T sat At ( ) yx :u u max,T T sat = δ= = Further approximation : The film moves very slowly Therefore, inertia and dissipation are neglected. Reduced Equations Continuity Equation remains unchanged. Momentum : ( ) 2 g 2 g u y −ρ −ρ = µ A A (10.16) 1
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Thermal Energy : 2 2 T 0 y = The Momentum and Thermal Energy equations are linear and uncoupled and, hence, can be solved analytically. Solution of Thermal Energy Equation to obtain T(y) 2 2 w T 0w i t h T ( 0 ) T , T ( ) T sat y == δ = . Integrating twice gives ( ) Tx ,y Cy C 12 =+ The constants C 1 and C 2 are determined by using the boundary conditions. T(0) T T C ww 2 =⇒ = TT w sat T( ) T T C T C w sat sat 11 δ= = δ+ = δ () w sat y T w    δ (G4) Note: Temperature varies linearly with y in the condensation film.
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Heat_Transfer_with_Phase_Change_Notes - Film Condensation...

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