The concept of thermal resistance can be used to find the temperature distribution in a flat

square plate shown in the following figure. The plate's edges are insulated so that no heat can

escape, except at two points where the edge temperature is heated to $T_a$ and $T_b$ respectively.

Modeling the temperature distribution in the flat square plate by using the finite difference

approach, results in the following set of linear equations.

$T_1-\frac{1}{3}(T_a+T_2+T_3)=0$

$T_2-\frac{1}{2}(T_1+T_4)=0$

$T_3-\frac{1}{2}(T_1+T_4)=0$

$T_4-\frac{1}{3}(T_2+T_3+T_b)=0$

$T_a$

b

Solve the set of equations for the case where $T_a$ and $T_b$ are $150$ and $20C,$ respectively. $($Analyze in matlab$)$