Chapter 3, Problem 3.158P

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 $\rho =1200kg/m^3$ and specific heat $c=2200J/kg\cdot K$ occupies a volume of $V=2.25m^3$ in an insulated vessel. The chemical is to be heated from room temperature. $T_i=300K$, to a process temperature of $T=450K$ by passing saturated steam at $T_h=500K$ through a coiled, thin-walled, 20-mm-diameter tube in the vessel. Steam condensation within the tube maintains an interior convection coefficient of $h_i=10,000W/m^2\cdot K$, while the highly agitated liquid in the stirred vessel maintains an outside convection coefficient of $h_o=2000W/m^2\cdot K$ .