Latent heat models were developed to calculate heat-transfer coefficients in agitated vessels for two cases : (1) heating with a condensable fluid flowing through coils and jackets; (2) vacuum reflux cooling with an overhead condenser. In either case the mathematical treatment, based on macroscopic balances, requires no iterative schemes. In addition to providing heat-transfer coefficients, the models predict flow rates of service fluid through the coils and jackets, estimate the percentage of heat transfer due to latent heat, and compute reflux rates.