Apply ADI methods to two dimensional heat equation and find $T^{n+1}$ at the internal grid points in the mesh shown in figure. Also, find the length a and $b,$ initial condition are:

$T^n=1-\frac{x}{3x}$ along $y=0$

$T^n=1-\frac{y}{3y}$ along left side

$\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{t}}=[\frac{de{l}^2(T)}{del{x}^2}+\frac{de{l}^2(T)}{del{y}^2}]$

Where: $T^n=0$ everywhere else, and the boundary conditions remain fixed at these initial value. $k=240\frac{W}{m}.C,=2700K\frac{g}{m^3},Cp=920\frac{J}{k}g.k,R=1cm.$