$1-(35$ pts $)$ Bearing ball made of stainless steel $($AISI$304)$ that was heated to the temperature of $850C$ is to be annealed in an oil bath maintained at a temperature of $40C.$ The diameter of the bearing ball is $20$ mm and heat transfer coefficient in the oil bath is $1100\frac{W}{m^2}K.$

a$)$ Find the center temperature of the bearing ball at $t=50s.$

b$)$ Determine heat transfer from the bearing ball in this time range.

Properties: AISI$304,(T$~~$500C)$;$k=22\mathrm{.}2\frac{W}{m}.K$;$c_p=579\frac{J}{k}g.K$;

$=7900k\frac{g}{m^3}$;$=4\mathrm{.}85{10}^{-6}\frac{m^2}{s}.$