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Q: Batch processes are often used in chemical and pharmaceutical operations to achieve a desired chemical composition for the final product and typically involve a transient heating operation to take the product from room temperature to the desired process temperature.
Consider a situation for which a chemical of density p = 1200 kg/m3 and specific heat c = 2200 J/kg · K occupies a volume of V = 2.25 m3 in an insulated vessel. The chemical is to be heated from room temperature, Tj = 300 K, to a process temperature of T = 450 K by passing saturated steam at Th = 500 K through a coiled, thin-waned, 20-mm-diameter tube in the vessel. Steam condensation within the tube maintains an interior convection coefficient of hi = 10,000 W/m2 · K, while the highly agitated liquid in the stirred vessel maintains an outside convection coefficient of h n = 2000 W/m2 · K. If the chemical is to be heated from 300 to 450 K in 60 minutes, what is the required length L of the submerged tubing?
