Abstract
Analytical equations are developed for heating and cooling of liquid batches, where the volume changes with time. Both reacting and nonreacting batches, as well as isothermal and nonisothermal exchange media, are considered. The operations of evaporation and exothermic chemical reaction are discussed as typical examples of batch heating and batch cooling. Previous effort at modeling varying-heat-transfer-area batch processes involved the use of a chart, and the calculations required graphical/numerical integration in the case of a nonisothermal exchange medium; here, analytical solutions are presented for the lime dependence of the batch volume and the heat transfer rate. Furthermore, the previously made assumption of the arithmetic mean for the temperature driving force is shown to be unnecessary, as the log-mean temperature difference leads to a simple, appropriate analysis.
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