Question $1$

A long iron $,$ and $\{$:$=23\mathrm{.}1{10}^{-6}\frac{m^2}{s})$ with a

diameter of $25$ mm is initially heated to a uniform temperature of $700C.$ The iron rod is then quenched in

a large water bath that is maintained at constant temperature of $50C$ and convection heat transfer

coefficient of $128\frac{W}{m^2}*K.$ Assume heat transfer is one dimensional.

i$.$ Use the relevant Heisler Charts for long cylinders to determine the time required for the centre

temperature of the iron rod to cool to $200C($s$).$

ii$.$ Determine the temperature at the surface of the rod when the centre is at $200C(C).$

iii. If you assume that the lumped capacitance model applies, determine the time it takes for the

temperature of the iron rod to cool to $200C($s$).$

iv$.$ Compare the result with that obtained in $($i$)$ and discuss.