$[20$pt$]$ A $100-mm-$long $5-mm-$diameter copper $)=(400\frac{W}{m}*K$ is attached to the $2020m{m}^2$ isothermal wall at $T_s=60C.$ The rod is in an air environment with $T_{}=20C$ and $h=50\frac{W}{m^2}*K.$

a$.$ Determine the heat transfer rate from the rod to the surroundings. Use Case A solution or Case B solution with a corrected fin length $L_c.$

b$.$ Determine the efficiency of the rod.

c$.$ Determine the total heat transfer from the finned surface $($the rod and the wall$)$ to the surroundings.

d$.$ Determine the overall efficiency of the finned surface $($the rod and the wall$).$