Nearly a century ago, heat-transfer pioneer, Willhelm Nusselt, proposed a model to predict the magnitude of a condensing coefficient for a special geometric situation1. Nusselt envisioned the condensation of vapor on a cold vertical plate, Fig. 7.2, as a process where vapor condenses on the plate and the condensate drains downward, with the condensate film becoming progressively thicker as it descends. The local condensing coefficient is taken to be the conductance through the condensate film—the conductivity of the liquid divided by the film thickness at that point. Nusselt developed the expression for the mean condensing coefficient as
The immediate question is where, if at all, does condensation occur on a vertical plate in industrial practice? Actually, a very old condenser design oriented the tubes vertically and water flowed by gravity down the inside of the tubes to ease their cleaning. The refrigerant in the shell condensed on the outside of the vertical tubes.
A slight modification of Eq. 7.1 applies to the widely used horizontal shelland-tube condenser, Fig. 7.1b. The product of the number of tubes in a vertical row multiplied by the diameter of the tubes replaces the vertical length of the plane L. White found by experimental tests that the coefficient is 0.63 and Goto measured 0.65, so the equation for N tubes of diameter D in a vertical row is:
Before leaving the condensing equations, an interesting comparison of the condensing coefficients of various refrigerants can be made. As Table 7.1 shows, the condensing coefficients of ammonia condensing on the outside of tubes far surpasses the coefficients of the other refrigerants shown. Experimental tests also show ammonia to have a higher condensing coefficient—five times that of the halocarbons in one study.