An important concern in the study of heat transfer is to determine the steady-state temperature distribution of the thin plate when the temperature around the boundary is known. Assume the plate shown...

An important concern in the study of heat transfer is to determine the steady-state temperature distribution of the thin plate when the temperature around the boundary is known. Assume the plate shown in the figure represents the cross section of metal beam with negligible heat flow in the direction perpendicular to the plate. Let denotes the temperature at the four interior nodes of the mesh in the figure. The temperature in the node is approximately equal to the average of the four nearest nodes-to the left, above, to right and below.

Write the system of four equations whose solution gives the estimate for the temperature

Solve the system for four equations to calculate .T1,T2,T3,T4.