Consider a batch process in which $300$ L of a pharmaceutical are heated from $20C$ to $80C$ by saturated steam condensing at $2\mathrm{.}455$ bars as it flows through a coiled tube of $12-$mm diameter and $16-$m length. At any time during the process, the liquid $($the pharmaceutical$)$ may be approximated as an infinite, quiescent medium of uniform temperature and may be assumed to have constant properties of $=1100k\frac{g}{m^3},c=568\mathrm{.}182\frac{J}{k}g*K,k=0\mathrm{.}25\frac{W}{m}*K,v=4\mathrm{.}0{10}^{-6}\frac{m^2}{s},Pr=10,$ and $=0\mathrm{.}002K^{-1}.$ The thermal resistances of the condensing steam and tube wall may be neglected.

What is the initial rate of heat transfer in W to the pharmaceutical?

HINT: The steam condenses at the saturation temperature.

BONUS $(+4$ points extra credit$)$: Show that it takes $602$ seconds for the pharmaceutical to reach $80C.$

Correct Answer: $30986$