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, T_j = 300 K, to a process temperature of T = 450 K by passing saturated steam at T_h = 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?

Steam Coiled tubing (D, L, h, h) Stirred liquid T1), V, p, c Containment vessel