Q$1.$ Solve $\frac{d^{2}T}{d{x}^2}+\frac{(q^{})}{k}=0,$ with given boundary conditions as

B$.$C

$Atx=0$;$,T=100C,$

Free convection boundary with

$T_f=27C,$ and$\frac{h}{k}=50.(ifR=0)$

$x=1$;

Insulated boundary with $T_f={27}^{0}C,\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{x}}=0$

and$\frac{h}{k}=50.(ifR=1)$

$R=$ rem$($last two digit of your roll number, $2)$

A$,$ B $=$ represents the location of the discrete heat source $(\frac{q}{k}=5000)$ at a distance of N$1($last

two digits of your roll number$)$ grid points from the boundary.

Solve and plot the temperature across the length of the rod including boundary temperatures

using TDMA. Also, evaluate the temperature at the location of heat source. $($Note: take $49$

internal grid points$)$Wr$.$