A straight Duralumin $($k $=221$ W$/$m K$)$ fin has a parabolic profile y $=($t$/2)(1-$x$/$L$)2,$ with t $=5$ mm and L $=35$ mm$.$

Determine the heat dissipation by length of the fin when its base temperature is $486$ K and it is exposed to fluid at $320$ K with a heat transfer coefficient of $3200$ W$/$m$2$K