MTH501 Linear Algebra GDB Solution Fall 2013

Topic Detail

“An important in the study of heat transfer is to determine steady state temperature distribution of a thin plate when the temperature on boundary is known. Assume the plate shown in the figure (Click on Picture to see the figure) represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T1, T2, T3, T4 denote the temperatures at the four interior nodes of the mesh in the figure. The temperature at a node is approximately equal to the average of the four nearest nodes that is “to the left, above, to the right, and below”.

So, using above information, write a system of four equations whose solution gives estimates for the temperaturesT1,T2, T3,T4”