Unsteady$-$State Conduction in a Short Cylinder. An aluminum cylinder is initially heated, so it is at a uniform temperature of $204\mathrm{.}4C.$ Then it is plunged into a large bath held at $93\mathrm{.}3C,$ where $h=568\frac{W}{m^2.K}.$ The cylinder has a diameter of $50\mathrm{.}8mm$ and is $101\mathrm{.}6mm$ long. Calculate the center temperature after $60$s$.$ The physical properties are $=9\mathrm{.}44{10}^{-5}\frac{m^2}{s}$ and $k=207\mathrm{.}7\frac{W}{m*K}.$