Hot engine oil is being transported in a horizontal pipe $($k $=15$ W$/$m$$K$,$ Di $=5$ cm$)$ with a wall thickness of $5$ mm$.$ The pipe is covered with a $5-$mm$-$thick layer of insulation $($k $=0\mathrm{.}15$ W$/$m$$K$).$ A length of $2$ m of the outer surface is exposed to cool air at $10\backslash$deg C$.$ If the pipe inner surface temperature is at $90\backslash$deg C$,$ determine the outer surface temperature in $\backslash$deg C$.$ Begin the calculations by using a film temperature of $50\backslash$deg C$.$

Given: The properties of air at Tf $=50\backslash$deg C$.$

k $=0\mathrm{.}02514$ W$/$m$$K$,$

v $=1\mathrm{.}516$ x $105$ m$2/$s$,$

Pr $=0\mathrm{.}7309$