Heating the Contents of a Stirred Tank:

A well$-$mixed cylindrical tank filled with liquid is surrounded by a steam$-$fed heating jacket as shown

in the figure below. The specifications regarding the tank and liquid are summarized next to the

figure. The walls are so thin compared to the tank and jacket dimensions that they can be treated as

a flat plate. Determine how long it will take to heat tank contents of the tank from $25C$ to $70C.$

Liquid mass: $4000kg$

Liquid density: $1000k\frac{g}{m^3}$

Heat capacity: $4\mathrm{.}3{10}^{3}W-\frac{s}{k}gC$

Tank wall thickness $()$: $1\mathrm{.}2cm$

Tank wall thermal conductivity $($k$)$: $20\frac{W}{m}C$

Steam temperature $($constant$)$: $100C$

Steam heat transfer coefficient $h_0$:$10,000$

$\frac{W}{m^{2**}}C$

Liquid heat transfer coefficient h$$: $5500$

$\frac{W}{m^{2**}}C$

Wall area available for heat transfer: $13m^2.$

Hint: You do not need to develop a model from scratch. Consider expressing the rate of heat

transfer using an overall heat transfer coefficient we already developed that would be relevant for

this geometry.