Similarity Solution for Free-Convection Condensation of Binary Vapors

Abstract

The basic equations, boundary conditions, and compatibility conditions for free-convection condensation of a binary vapor mixture correspond to Eqs. (2.1)–(2.7), (2.14)–(2-19), and (2–20)–(2-27), respectively, where U _{v ∞} in Eq. (2-17) is set to zero. Prior to performing similarity transformation to these equations, it is necessary to express ρ _{V ∞}/ρ _V in Eq. (2-5) as a function of concentration and temperature. Since the total pressure is invariable through the vapor boundary layer, the following equation is valid under the assumption that each component vapor is an ideal gas:

$$ \frac{{{\rho _{V\infty }}}}{{{\rho _V}}} = \frac{{{M_{V\infty }}{T_V}}}{{{M_V}{T_{V\infty }}}}, $$

(4-1)

where

$$ {M_v} = \frac{{{M_1}{M_2}}}{{{M_1} - \left( {{M_1} - {M_2}} \right){W_{1V}}}}. $$

(4-2)