Consider a batch process in which 200 liters of a pharmaceutical are heated from 25°C to 70°C by saturated steam condensing at 2.455 bars as it flows through a coiled tube of 15-mm diameter and 15-m length. At any time during the process, the liquid may be approximated as an infinite, quiescent medium of uniform temperature and may be assumed to have constant properties of p = 1100 kg/m³, c = 2000 J/kg ∙ K, k = 0.25 W/m ∙ K, v = 4.0 x 10^-6 m²/s, Pr = 10, and (3 = 0.002 K^-1. The thermal resistances of the condensing steam and tube wall may be neglected.

(a) What is the initial rate of 'heat transfer to the pharmaceutical?

(b) Neglecting heat transfer between the tank and its surroundings, how long does it take to heat the pharmaceutical to 70°C? Plot the corresponding variation with time of the fluid temperature and the convection coefficient at the outer surface of the tube. How much steam is condensed during the heating process?

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Saturated steam, Pt Coiled tubing L, D Quiescent liquid, T) - Containment vessel, v Insulation