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29.3 Compute the fluxes for Prob. 29.2 using the parameters from Example 29.3.

29.3 Compute the fluxes for Prob. 29.2 using the parameters from Example 29.3.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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solve question 29.3 only by hand and explain step by step please

 

29.3 Compute the fluxes for Prob. 29.2 using the parameters from Example 29.3. O 29.2 Use Liebmann's method to solve for the temperature of the square heated plate in Fig. 29.4, but with the upper boundary condition increased to 150°C and the left boundary decreased to 50°C. Use a relaxation factor of 1.2 and iterate to & = = 1%. 75°C (1, 3) (1, 2) (1, 1) 100°C (2,3) (2, 2) (2,1) (3, 3) (3, 2) (3, 1) 50°C
Transcribed Image Text:29.3 Compute the fluxes for Prob. 29.2 using the parameters from Example 29.3. O 29.2 Use Liebmann's method to solve for the temperature of the square heated plate in Fig. 29.4, but with the upper boundary condition increased to 150°C and the left boundary decreased to 50°C. Use a relaxation factor of 1.2 and iterate to & = = 1%. 75°C (1, 3) (1, 2) (1, 1) 100°C (2,3) (2, 2) (2,1) (3, 3) (3, 2) (3, 1) 50°C
4 −1 - 1 -1 4 −1 −1_4 T₁ ㅗ - To = 71.91 72.81 11 −1 = = T12 76.01 T13 = 83.41 -2 4 -1 −1 -2 747 -2 -1 −1 -1 4 -1 T20 = 67.01 T21 T2] = 68.31 -1 T22 T22 = 72.84 T23 = 82.63 747 -1 -1 - 747 −1 -−1 4 −1 1 T30 = 59.54 T31 = 60.57 T32 = 64.42 T33 = 74.26 4 -1 T - −1 −1 Note that because of the derivative boundary condition, the matrix is increased to 12 × 12, in contrast to the 9 x 9 system in Eq. (29.10), to account for the three unknown tem- peratures along the plate's lower edge. These equations can be solved for −1 4 −1 4 - To 75 T 20 0 T30 50 Tu 75 0 50 75 0 T21 T31 T12 T22 T32 T13 T23 T33. 50 175 100 150
Transcribed Image Text:4 −1 - 1 -1 4 −1 −1_4 T₁ ㅗ - To = 71.91 72.81 11 −1 = = T12 76.01 T13 = 83.41 -2 4 -1 −1 -2 747 -2 -1 −1 -1 4 -1 T20 = 67.01 T21 T2] = 68.31 -1 T22 T22 = 72.84 T23 = 82.63 747 -1 -1 - 747 −1 -−1 4 −1 1 T30 = 59.54 T31 = 60.57 T32 = 64.42 T33 = 74.26 4 -1 T - −1 −1 Note that because of the derivative boundary condition, the matrix is increased to 12 × 12, in contrast to the 9 x 9 system in Eq. (29.10), to account for the three unknown tem- peratures along the plate's lower edge. These equations can be solved for −1 4 −1 4 - To 75 T 20 0 T30 50 Tu 75 0 50 75 0 T21 T31 T12 T22 T32 T13 T23 T33. 50 175 100 150
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