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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,..., 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 T₁,..., T4. 4T₁ T₂ T4 = 35 -T₁ +4T₂ - T3 = 75 - T₂+4T3 T4=85 -T₁ - T3 + 4T4 = 45 10° 10° 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 (T₁, T2, T3, T4) =(1-1-1-1- (Type integers or decimals rounded to the nearest thousandth as needed.) OB. The system has infinitely many solutions. OC. The system has no solution. 25° 25° 1 2 4 3 35° 35° 50° 50°

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,..., 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 T₁,..., T4. 4T₁ T₂ T4 = 35 -T₁ +4T₂ - T3 = 75 - T₂+4T3 T4=85 -T₁ - T3 + 4T4 = 45 10° 10° 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 (T₁, T2, T3, T4) =(1-1-1-1- (Type integers or decimals rounded to the nearest thousandth as needed.) OB. The system has infinitely many solutions. OC. The system has no solution. 25° 25° 1 2 4 3 35° 35° 50° 50°

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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,..., 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 T₁,..., T4. 4T₁ T₂ T4 = 35 -T₁ +4T₂ - T3 = 75 T4 = 85 -T₁ - T3 +4T4 = 45 T₂+4T3 - 10° 10° 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 (T₁, T2, T3, T4) =(1-1-1-1- (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. 25° 25° 1 2 4 3 35° 35° 50° 50°
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,..., 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 T₁,..., T4. 4T₁ T₂ T4 = 35 -T₁ +4T₂ - T3 = 75 T4 = 85 -T₁ - T3 +4T4 = 45 T₂+4T3 - 10° 10° 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 (T₁, T2, T3, T4) =(1-1-1-1- (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. 25° 25° 1 2 4 3 35° 35° 50° 50°
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