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0°C Figure 1: A heated plate where boundary temperatures are held at constant levels (a) Determine the values of: T10 = T20 = T30 = T14 = T24 = T34 =

0°C Figure 1: A heated plate where boundary temperatures are held at constant levels (a) Determine the values of: T10 = T20 = T30 = T14 = T24 = T34 =

Advanced Engineering Mathematics
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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Use Liebmann's method to solve for the temperature of the heated plate (Figure 1), but with the upper boundary condition is increased to 120 °C and the left boundary condition is decreased to 60 °C. Use an overrelaxation factor of 1.2 and iterate to three iterations. 100°C (1, 3) (2, 3) (3, 3) (1, 2) (2, 2) (3, 2) 75°C 50°C (1, 1) (2, 1) (3, 1) 0°C Figure 1: A heated plate where boundary temperatures are held at constant levels (a) Determine the values of: T10 = T20 = T30 = T14 = T24 = T34 = To1 = To2 = To3 = T41 = T42 = T43 = (b) Write equation for node (1,1) (i = 1, j = 1) and solve for T1
Transcribed Image Text:Use Liebmann's method to solve for the temperature of the heated plate (Figure 1), but with the upper boundary condition is increased to 120 °C and the left boundary condition is decreased to 60 °C. Use an overrelaxation factor of 1.2 and iterate to three iterations. 100°C (1, 3) (2, 3) (3, 3) (1, 2) (2, 2) (3, 2) 75°C 50°C (1, 1) (2, 1) (3, 1) 0°C Figure 1: A heated plate where boundary temperatures are held at constant levels (a) Determine the values of: T10 = T20 = T30 = T14 = T24 = T34 = To1 = To2 = To3 = T41 = T42 = T43 = (b) Write equation for node (1,1) (i = 1, j = 1) and solve for T1
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