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,, ..., T4 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, .., 25° 25° T4. 4T, - T2 T4 = 40 15° 1 450 -T, + 4T2 - T3 = 70 15° 4 3 T2 +4T3 - T4 =80 450 T3 + 4T4 = 50 35° 35° 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.) O B. The system has infinitely many solutions. O C. The system has no solution. 2.
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,, ..., T4 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, .., 25° 25° T4. 4T, - T2 T4 = 40 15° 1 450 -T, + 4T2 - T3 = 70 15° 4 3 T2 +4T3 - T4 =80 450 T3 + 4T4 = 50 35° 35° 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.) O B. The system has infinitely many solutions. O C. The system has no solution. 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 T,, ..., T4 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, ..,
25° 25°
T4.
4T, - T2
T4 = 40
15°
1
450
-T, + 4T2 - T3
= 70
15°
4
3
T2 +4T3 - T4 =80
450
T3 + 4T4 = 50
35° 35°
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.)
O B. The system has infinitely many solutions.
O C. The system has no solution.
2.
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