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, , mean inlet temperature, T_h,i, and specific heat, c_p,h, of the hot fluid are known, as are the initial temperature, T_{c,i h,i}, the volume, V_c, mass density, c, and specific heat, c_v,c, of the pharmaceutical. Heat transfer from the hot fluid to the pharmaceutical is governed by an overall heat transfer coefficient U.

 

(a) Starting from basic principles, derive expressions that can be used to determine the variation of Tc and T_h,o with time during the heating process.

(b) Consider a pharmaceutical of volume V_c = 1m³, density ρ_c = 1100 kg/m³, specific heat c_v,c = 2000 J/kg∙ K, and an initial temperature of T_c,i = 25°C. A coiled Coiled