In a manufacturing facility $8$ mm diameter brass $($density $8900k\frac{g}{m^3},k=14687\frac{W}{m}C,Cp=385\frac{J}{k}gC)$ ball initially at $900C$ is cooled using a water bath at $25C$ for a period of $2$ min $.$ Determine a$)$ temperature at the center of the ball. If $100$ balls are added at $t=0$ and stayed for $2$ min in bath find out b$)$ the heat needs to be removed from water to maintain it at constant temperature. Assume convection heat transfer coefficient is $75\frac{W}{m^2}C5+5$