$5.$ A fin is made of aluminum and has a thickness of $3$ mm$,$ length of $50$ mm$,$ and a rectangular cross$-$section of $10$ mm x $20$ mm$.$ The temperature of the fins base is maintained at $100\backslash$deg C$,$ while the surrounding air temperature is $20\backslash$deg C$.$ Calculate the heat transfer rate through the fin, assuming the thermal conductivity of aluminum to be $220$ W$/$m$$K$,$ and the convective heat transfer coefficient between the fin surface and surrounding air to be $50$ W$/$m$^2$K$.$