In a grid of wires the temperature at exterior mesh poins is

In a grid of wires, the temperature at exterior mesh poins is maintained at constant values as shown in the figure. When the grid is in thermal equilibrium, the temperature at each interior mesh point is the average of the temperatures at the four adjacent points. For instance, T1=T2+T3+0?1704. T1=T2+T3+0?1704. Find the temperatures T1,T1, T2,T2, T3,T3, T4,T4, when the grid is in thermal equilibrium.

I tried turning this into an augmented matrix and solving, I got T1 = 15, T2 = 50, T3 = 60 and T4 = 25 but this is not correct. Whats the correct method, how do you do this? Please show your work.

(1 point) In a grid of wires, the temperature at exterior mesh poins is maintained at constant values as shown in the figure. When the grid is in thermal equilibrium, the temperature at each interior mesh point is the average ofthe temperatures at the four adjacent points. For instance, T2 T3 0 170 Find the temperatures T, T2, T3, T4, when the grid is in thermal equilibrium. T 15 50 50 25

Solution

4(T1+T2+T3+T4) = 2(T1+T2+T3+T4)+370-170*3+160*2;

2(T1+T2+T3+T4) = 180;

(T1+T2+T3+T4) = 90;

NOW;

4T1 + 170 = (T2+T3);

(T1+ 4T1 + 170 +T4) = 90;

(5T1 +T4) = -80; eq 1

Now,

4T4 + 10 = (T2+T3);

(T1+ 4T4 + 10 +T4) = 90;

(T1+ 5T4 ) = 80; eq 2

Eq 1 + eq2;

T1+T4 = 0;

so,

T4 = 20;

T1 = -20;

So now,

T2 + T3 = 90;

Also;T3 = (T1+T4+370-170)/4

T3 = 50;

T2 = 40;

Ans

T1 = -20;

T2 = 40;

T3 = 50;

T4 = 20;