A stainless steel $($k$=50$W$//$m$.$K$)$ fin has a circular cross$-$sectional area with a diameter of $2$ cm and a length of $10$ cm $.$ The fin is attached to a wall that has a temperature of $200^($@$)$C$.$ The fluid surrounding the fin has an ambient temperature of $20^($@$)$C and the heat transfer coefficient is $30$W$//$m$^(2)$K$.$ The end of the fin is subjected to convection cooling. By numerically $($Solve with the Thomas Algorithm$)$ solving the fin equation determine:

a$.$ rate of heat dissipated from the fin,

b$.$ the temperature at the end of the fin? Plot the temperature distribution.

c$.$ heat dissipated from the fin if the stainless steel fin is replaced by a fictitious fin with infinite thermal conductivity.