$2\mathrm{.}10$ As shown in the below figure, circular circumferential fins of rectangular profle have been added to an engine cylinder. The tins have a conductivity of $180$ w$/$miC$-$ The engine cylinder has an outer diameter of $10$ cm $.$ The fins are attached to this outer surface that is at $550$ C $.$ The fins have a thickness of $2$ mm and an outer diameter of $12$ cm $.$ The surrounding air is at $40$ C and the convective coellicient is $45\frac{W}{m}2C.$ There are $30$ fins on the engine cylinder, with a center to$-$center spacing of $5$ mm $-$

What is the heat transfer from the cylinder to the surrounding air $($W$)?$ Include heat transfer from both the fins and the unfinned areas between the fins.