2 heat transfer across the liquid film is by pure

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Unformatted text preview: ed above was first developed by Nusselt in 1916 under the following simplifying assumptions: 1. Both the plate and the vapor are maintained at constant temperatures of Ts and Tsat, respectively, and the temperature across the liquid film varies linearly. 2. Heat transfer across the liquid film is by pure conduction (no convection currents in the liquid film). 3. The velocity of the vapor is low (or zero) so that it exerts no drag on the condensate (no viscous shear on the liquid–vapor interface). 4. The flow of the condensate is laminar and the properties of the liquid are constant. 5. The acceleration of the condensate layer is negligible. Then Newton’s second law of motion for the volume element shown in Figure 10–24 in the vertical x-direction can be written as Fx max 0 since the acceleration of the fluid is zero. Noting that the only force acting downward is the weight of the liquid element, and the forces acting upward are the viscous shear (or fluid friction) force at the left and the buoyancy force, the force balance on the volume element becomes Weight l g( Fdownward ↓ Fupward ↑ Viscous shear force Buoyancy force du y)(bdx) (bdx) g( y)(bdx) l dy Canceling the plate width b and solving for du/dy gives du dy g( l )g( l y) Weight ρl g(δ – y) (bdx) Buoyancy force ρv g(δ – y) (bdx) y 0 x δ dx =0 at y = 0 y Idealized velocity profile No vapor drag Idealized temperature profile Ts g Liquid, l Tsat Linear FIGURE 10–24 The volume element of condensate on a vertical plate considered in Nusselt’s analysis. cen58933_ch10.qxd 9/4/2002 12:38 PM Page 536 536 HEAT TRANSFER Integrating from y 0 where u 0 (because of the no-slip boundary condition) to y y where u u(y) gives g( u(y) )g l y2 2 y l (10-12) The mass flow rate of the condensate at a location x, where the boundary layer thickness is , is determined from · m (x) l u(y)dA A l u(y)bdy y0 (10-13) Substituting the u(y) relation from Equation 10–12 into Eq. 10–13 gives gb l( · m (x) ) l 3 3 2 d dx (10-14) l whose derivative with respect to x is · dm dx gb l( ) l l (10-15) which represents the rate of condensation of vapor over a vertical distance dx...
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This note was uploaded on 01/28/2010 for the course HEAT ENG taught by Professor Ghaz during the Spring '10 term at University of Guelph.

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