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. The figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T,, ., L, denote the temperatures at the four interior nodes of the figure. The temperature at a node is approximately equal to the average of the four nearest nodes to the left, above, to the right, and below. Solve the system of equations below to find the temperatures T. .. T4 25° 25° 4T, - T2 -T, +4T2 - T3 - T2 +4T3 - T4 = 75 - T4 = 40 1 2 150 45° = 70 15° 4 13 45° -T, T3 + 4T4 = 45 30° 30° Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The unique solution of the system is ( D. (Type integers or decimals rounded to the nearest thousandth as needed.) O B. The system has infinitely many solutions. O C. The system has no solution.
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. The figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T,, ., L, denote the temperatures at the four interior nodes of the figure. The temperature at a node is approximately equal to the average of the four nearest nodes to the left, above, to the right, and below. Solve the system of equations below to find the temperatures T. .. T4 25° 25° 4T, - T2 -T, +4T2 - T3 - T2 +4T3 - T4 = 75 - T4 = 40 1 2 150 45° = 70 15° 4 13 45° -T, T3 + 4T4 = 45 30° 30° Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The unique solution of the system is ( D. (Type integers or decimals rounded to the nearest thousandth as needed.) O B. The system has infinitely many solutions. O C. The system has no solution.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text: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. The figure
represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T1,.
The temperature at a node is approximately equal to the average of the four néarest nodes to the left, above, to the right, and below. Solve the system of equations below to find the
temperatures T1, .., T4-
T denote the temperatures at the four interior nodes of the figure.
25° 25°
4T, - T2
-T, +4T2 - T3
- T4 = 40
= 70
%3D
15°
1
2
T2 +4T3 - T4 = 75
450
4
15°
3
450
- T1
- T3 +4T4 = 45
%3D
30° 30°
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
A. The unique solution of the system is (,
(Type integers or decimals rounded to the nearest thousandth as needed.)
B. The system has infinitely many solutions.
C. The system has no solution.
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