An important concern in the study of heat transfer is to determine the steady-state temperature distribution of
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Question:
An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. Assume that the plate in the figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T 1 ; T 2 ; T 3 ; T 4 denote the temperature at the four interior nodes of the mesh in the figure. The temperature at a node is equal to the average of the four nearest nodes- the left, right, above and below. For instance,
T 1 = (10 + 20 +T 2 + T 4 ) = 4.
(a) Find a system of four equations whose solution will giveT 1 ; T 2 ; T 3 ; T 4 .
(b) Solve the above system.
Expert Answer:
a The equation of the following systems are by standard formula T 1 10 20 T ... View the full answer
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