A simple model for estimating the temperature distribution on a square plate gives rise to a linear system of equations. To construct the appropriate linear system, we use the following information: The square plate is perfectly insulated on its top and bottom so that the only heat flow is through the plate itself. The four edges are held at various temperatures. To estimate the temperature at an interior point on the plate, we use the rule that it is the average of the temperatures at its four compass-point neighbors, to the west, north, east and south Estimate the temperatures Find the temperatures T1, T2, T3, T4 of the four evenly spaced interior points of the plate shown in the figure below, using the triangular matrix method. (When solving, equations that give average temperature should be written as homogeneous linear equations.) 100 T2 21 08 T3 0°

A simple model for estimating the temperature distribution on a square plate gives rise to a linear system of equations. To construct the appropriate linear system, we use the following information: The square plate is perfectly insulated on its top and bottom so that the only heat flow is through the plate itself. The four edges are held at various temperatures. To estimate the temperature at an interior point on the plate, we use the rule that it is the average of the temperatures at its four compass-point neighbors, to the west, north, east and south Estimate the temperatures Find the temperatures T1, T2, T3, T4 of the four evenly spaced interior points of the plate shown in the figure below, using the triangular matrix method. (When solving, equations that give average temperature should be written as homogeneous linear equations.) 100 T2 21 08 T3 0°

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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Question

A simple model for estimating the temperature distribution on a square plate gives rise to a linear system of
equations. To construct the appropriate linear system, we use the following information: The square plate is
perfectly insulated on its top and bottom so that the only heat flow is through the plate itself. The four edges are
held at various temperatures. To estimate the temperature at an interior point on the plate, we use the rule that
it is the average of the temperatures at its four compass-point neighbors, to the west , north, east and south
Estimate the temperatures
Find the temperatures T1, T2, T3, T4 of the four evenly spaced interior points of the plate shown in the figure
below, using the triangular matrix method. (When solving, equations that give average temperature should be
written as homogeneous linear equations.)
100
T
T2
80
21
T3
T
0°

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