Problem #$1$

Steady$-$State Conduction in$.$ Two Dimensional slab figure shown below at steady$-$state conditions can be represented by the following equation:

$0=k\{\frac{de{l}^{2}T}{del{x}^2}+\frac{de{l}^{2}T}{del{y}^2}\}*T_1=r$

$($a$)$ Develop a code using MATLAB inbuilt functions and plot the temperature contour plots as per the boundary conditions mentioned in the figure. Use two different grid points: $1212$ and $4848$ in both directions.

$B(n,n)=(T1+T4)$

$Bv=$reshape$(B,1,n^2)$;

$\%$Temperature profile

$T=B\frac{v}{A}$;

Tmatrix$=$reshape $(T,n,n)$;

contour$($Tmatrix$)$;

$($b$).$ Develop a code using your own logical code $($such as nested for loops$)$ and plot the temperature contour plots as per the boundary conditions mentioned in the figure. Use two different grid points: $1212$ and $4848$ in both directions.

$0=$k$+$T$1=30\backslash$deg CT$4=40\backslash$deg CT$2=90\backslash$deg CT$3=60\backslash$deg C explain and show all work write out the matlab code