Consider a circular fin with rectangular profile as shown

The steady conduction along the radial direction in the fin is described by the following

equation

$\frac{1}{A}\frac{d}{dr}(Ak\frac{dT}{dr})+\frac{hP}{A}(T_{}-T)=0$

where $,A$ is the cross section area $(A=2rt)$

$P$ is the wetted perimeter of the cross section $(P=4r),$

Let $r_1=5mm,r_2=20mm,t=0\mathrm{.}2mm,k=205\frac{W}{m}K,T_{}=300K,h=8\mathrm{.}2\frac{W}{m^2}K$

and $T(r_1)=380K.$

$($a$)$ Draw a detailed $1$D diagram of the fin having a spatial discretization of $10$ nodes

$($b$)$ Use the Finite Volume Method to discretize the fin equation.

$($c$)$ Apply the discretized fin equation to the boundary and central nodes in order to obtain

equations of the form

$a_P{T}_P=a_W{T}_W+a_E{T}_E+S_u$ and Complete the table given