$2\mathrm{.}10$ As shown in the below figure, circular circumferential fins of rectangular profile have

been added to an engine cylinder. The fins have a conductivity of $180$ W$/$m C$.$ 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 coefficient is $45$ W$/$m$2$ C$.$ There are $30$ fins on the engine

cylinder, with a center$-$to$-$center spacing of $5$ mm$\mathrm{.}2\mathrm{.}10$ As shown in the below figure, circular circumferential fins of rectangular profile have

been added to an engine cylinder. The fins have a conductivity of $180$ W$/$m C$.$ 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 coefficient is $45$ W$/$m$2$ C$.$ 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.