A thin square metal plate has a uniform temperature of 80°C on two opposite edges, a temperature of 120°C on the third edge, and a temperature of 60°C on the remaining edge. A mathematical procedure to approximate the temperature at six uniformly spaced interior points results in the following equations:13

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A thin square metal plate has a uniform temperature of 80°C on two opposite edges, a
temperature of 120°℃ on the third edge, and a temperature of 60°C on the remaining
edge. A mathematical procedure to approximate the temperature at six uniformly
spaced interior points results in the following equations:13
=
4T₁-T₂-T6 = 200
-T₁ + 4T₂-T3-T5 = 80
-T₂ + 4T3-T4 = 140
-T3 + 4T4 T5 = 140
-T₂-T4+ 4T5-T6 = 80
-T₁-T5+ 4T6 = 200
What is the value of T1, T2, T3, T4, T5 and T6?
Transcribed Image Text:A thin square metal plate has a uniform temperature of 80°C on two opposite edges, a temperature of 120°℃ on the third edge, and a temperature of 60°C on the remaining edge. A mathematical procedure to approximate the temperature at six uniformly spaced interior points results in the following equations:13 = 4T₁-T₂-T6 = 200 -T₁ + 4T₂-T3-T5 = 80 -T₂ + 4T3-T4 = 140 -T3 + 4T4 T5 = 140 -T₂-T4+ 4T5-T6 = 80 -T₁-T5+ 4T6 = 200 What is the value of T1, T2, T3, T4, T5 and T6?
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