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°

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.45P

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An important concern in the study of heat transfer is to determine the steady-state temperature distribution of the thin plate when the temperature around the boundary is known. Assume the plate shown in the figure represents the cross section of metal beam with negligible heat flow in the direction perpendicular to the plate. Let denotes the temperature at the four interior nodes of the mesh in the figure. The temperature in the node is approximately equal to the average of the four nearest nodes-to the left, above, to right and below. Write the system of four equations whose solution gives the estimate for the temperature Solve the system for four equations to calculate .T1,T2,T3,T4.
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