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 -T₁+4T2 T3 T₂+4T3 -T₁ - T₁ = 35 = 70 T4 = 80 - T3 +4T4 =45 H 10° 10° 25° 25° 1 4 2 3 35⁰ 35° 45 45
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 -T₁+4T2 T3 T₂+4T3 -T₁ - T₁ = 35 = 70 T4 = 80 - T3 +4T4 =45 H 10° 10° 25° 25° 1 4 2 3 35⁰ 35° 45 45
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 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
- T₁ +4T₂ - T3
T2 +4T3
-T₁
wwny
-
- T4 = 35
= 70
T4 = 80
- T3 + 4T4 = 45
-
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
10°
10°
25° 25°
1 2
4 3
35° 35°
45°
45°
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