$(30$ pts$.)$ A solid sphere $($d$=0\mathrm{.}111$m $)$ is initially at a uniform temperature of $555C.$ It is suddenly submerged in a fluid $(999C)$ flow with a convection coefficient of $22\mathrm{.}22\frac{W}{m^{2**}}K.$ Determine the time required for the temperature at a radial distance halfway between the center of the sphere and its outer surface to reach $560C.$

Solid Material Properties: $=8765\frac{kg}{m^3},Cp=951\frac{J}{kg}*K,k=45\mathrm{.}67\frac{W}{m}*K,$