01: 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. Assume the plate shown in the figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T₁, ..., T denote the temperatures at the four interior nodes of the mesh in 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.³ For instance, T₁ = (10 + 20 + T2 + T4)/4, or 4T₁-T₂-T₁ = 30 10° 10° 20° 20° 1 2 4 3 40° 40° 30° 30° Write a system of four equations whose solution gives esti- mates for the temperatures T₁,..., T4.
01: 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. Assume the plate shown in the figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T₁, ..., T denote the temperatures at the four interior nodes of the mesh in 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.³ For instance, T₁ = (10 + 20 + T2 + T4)/4, or 4T₁-T₂-T₁ = 30 10° 10° 20° 20° 1 2 4 3 40° 40° 30° 30° Write a system of four equations whose solution gives esti- mates for the temperatures T₁,..., T4.
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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