Condensation of Vapors: Heat exchanger-coefficients for situations where phase change occurs (condensation) depend on the orientation of heat transfer surface (vertical, horizontal). Simplified correlations are developed for film type condensation. If a phase is condensing (steam), then heat transfer coefficient for a steam inside a circular tube assuming film-type condensation is given as a group, f_D, a function of both Reynolds number and Prandtl number. Figure 5.3 (Figure 7.17 Chopey) presents Dukler's results. In this Figure f_D given by

and is plotted against Reynolds number with Prandtl number as a parameter. In this equation, h_o is heat transfer coefficient without any shear. In order to account for interfacial shear, Dukler demonstrated that a ratio h/h_o is a function of Re_T and A_D, where Re_T is terminal Reynolds number (Chopey, Table 7.3) The parameter A_D is given as

Where subscripts L and G stand for liquid and vapor.

Example 5.12: Calculate the condensing coefficient for a vertical tube with an inside diameter of 0.62 in if steam is condensing on the inside of the tube at a rate of 50 lb/h.

Use the following data:

Condensate:

Density, ρ_L = 60 lb/ft³,

Specific heat, c_L = 1.0 Btu/(lb·°F),

Absolute viscosity, μ_L = 0.72 lb/(ft·h),

Thermal conductivity, k = 0.395 Btu/(h·ft·°F),

Condensation rate, W = 50 lb/h

Vapor:

Density, ρ_G = 0.0372 lb/ft³,

Viscosity, μ_G = 0.0313 lb/(ft·h)

Inside diameter of the tube, d_i = 0.62 in, number of tubes, n = 1, g_c = 4.18´10⁸ ft/h²

Solution: The condensate rate per unit periphery, Γ, can be calculated as

And the terminal Reynolds number can be found to be

And the Prandtl number for the condensate can be calculated to be 1.82. We can find f_D to be 0.21. The heat transfer coefficient, h_o, is found as

Dukler parameter, A_D, can be found to be

Using the value of terminal Reynolds number and Dukler parameter, we see that

(Table on Page 7-50 Chopey) and corrected heat transfer coefficient, h, can be calculated to be