Question points $=7\mathrm{.}5\%$

A cylindrical rod with an outer diameter of $3$ cm is initially at $30C.$ It is heated in a furnace with

hot air maintained at $120C.$ When the temperature at the center of the rod reaches $110C,$ the rod

is removed from the furnace and cooled in ambient air at $20C$ until the center temperature drops

back to $30C.$ Assume the convection heat transfer coefficients for the heating and cooling

processes are $400\frac{W}{m^2}*K$ and $15\frac{W}{m^2}*K,$ respectively. Properties of the rod are $=1500k\frac{g}{m^3},$

$c($specific heat$)=1800\frac{J}{k}gK,k=1\mathrm{.}2\frac{W}{m}*K.$ Determine the time required for both the heating

and cooling stages.