A cylinder is suddenly submerged in a hot liquid to increase the cylinder's temperature. The initial temperature of the cylinder is $293$

$K,$ and the temperature of the large bath is $600K.$ The bath temperature is maintained at $600K$ by recirculating the liquid through an

external heat exchanger. What will the center temperature in the cylinder be after $10$ minutes for a cylinder made from:

Note: Be sure to use the circular ends and the side of the cylinder when calculating the area.

Important Information:

Outside diameter of the cylinder $=4cm$

Length of the cylinder $=10cm$

Convective heat transfer coefficient for the liquid, $h=20\frac{W}{m^2}K$

a$.$ aluminum, $k=229\frac{W}{m}K$

Density of the aluminum, $=2700k\frac{g}{m^3}$

Heat Capacity, $Cp=0\mathrm{.}91k\frac{J}{k}gK$

b$.$ asbestos, $k=0\mathrm{.}2\frac{W}{m}K$

Density of asbestos, $=580k\frac{g}{m^3}$

Heat Capacity of asbestos, $Cp=1\mathrm{.}05k\frac{J}{k}gK$

Note that a W is a J$/$s and a $kJ$ is a $1000J.$