A $600$ mm long pump shaft of stainless steel $($k $=20$ W$/$mK$)$ is $30$ mm in

diameter. The heat transfer coefficient for the outside surface of the shaft to

the cooling air at $30\backslash$deg C is $30$ W$/$m$2$K$.$ Calculate:

A At what distance the bearing must be placed so that the maximum temperature at the bearing is not greater than $80\backslash$deg C$?$

B If the shaft is hollow with di $=20$ mm$,$ what will be the temperature at

the bearing location determined above? The shaft is not cooled from the

inner surface.