Discuss the following problem:
Q: Batch processes are often used in chemical and pharmaceutical operations to achieve a desired chemical composition for the final product. Related heat transfer processes are typically transient, involving a liquid of fixed volume that may be heated from room temperature to a desired process temperature, or cooled from the process temperature to room temperature. Consider a batch process for which a pharmaceutical (the cold fluid, c) is poured into an insulated, highly agitated vessel (a stirred reactor) and heated by passing a hot fluid (h) through a submerged heat exchanger coil of thin-walled tubing and surface area As. The flow rate, mh, mean inlet temperature, Th,i, and specific heat. cp,K of the hot fluid are known, as are the initial temperature, Tc,i < th,i="" the="" volume="" vc,="" mass="" density,="" pc'="" and="" specific="" heat,="" cvc="" of="" the="" pharmaceutical.="" heat="" transfer="" from="" the="" hot="" fluid="" to="" the="" pharmaceutical="" is="" governed="" by="" an="" over-all="" heat="" transfer="" coefficient="">
