Condensation of Flowing Vapors

Abstract

Nusselt already extended the film condensation theory and took into consideration the fact that the vapor flowing along the condensate film influences the velocity in the condensate. The boundary condition to Eq. (2.5) then no longer reads ∂w/∂=0 at y=δ but rather the velocity has a finite gradient at the free film surface corresponding to the shear stress exerted by the flowing vapor. Accordingly, in Eq. (2.5) for the velocity profile

$$w = - \frac{{{\varrho _L}g}}{{2{\eta _L}}}{y^2} + {c_1}y + {c_0}$$

the coefficients c ₁ and c ₀ are to be so determined that the boundary conditions

$$w\left( {y = 0} \right) = 0and{\eta _L}{\left( {\partial w/\partial y} \right)_{y = \delta }} = \pm {\tau _\delta }$$

(4.1)

are fulfilled, whereby the positive sign holds for downward flowing vapor and the negative one for vapor flowing upward. For the calculation of the shear stress at the phase interface, one assumes equality of pressure and friction forces in the vapor space. Let the pressure drop along the flow path dx be dp. Then

$${\tau _\delta }d\pi = \frac{{{d^2}\pi }}{4}\frac{{dp}}{{dx}}$$

(4.2)

holds for the tube flow. On the other hand, there holds for the pressure drop

$$\frac{{dp}}{{dx}} = \zeta \frac{{{\varrho _G}w_G^2}}{d}$$

(4.3)

Herewith we obtain

$${\tau _\delta } = \zeta \frac{{{\varrho _G}w_G^2}}{4}$$

(4.4)