Problem Statement

A $8cm$ diameter sphere made of Aluminium $($pure$)$ was initially

at $34C$ and then suddenly put in a pre$-$heated oven maintained

at $170C$ for $35$ minutes. The convection coefficient is $559$

$\frac{W}{m^2}.K$ The task is considered complete if center of the sphere

has reached $65C,$ Answer the following;

Was the $35$ min sufficient to reach the $65C$

How long should be left in the oven to reach the $65C$

What was the total amount of energy transferred to the

sphere in the $35$min $?$

Solve in exact method $($ analytical solution$)$