Fig 2 (II) [60 Points] Using centered finite difference approximation as done in class, solve the equation: 020 020 + მx2 მy2 +0.0150+Q=0 subject to the boundary conditions shown in the stencils below. Do this for two values of Q: (a) Q = 0.3, and (b) Q = 10.5x² + 1.26 * 1.5 x 0.002 0.008. For Case (a) (that is, Q = 0.3) use Fig 3. For Case (b), use both Fig. 3 and Fig 4. For all the three cases, show a table as well as the contour plots of versus (x, y), and the (x, y) heat flux values at all the nodes on the boundaries x = 1 and y = 1. Discuss your results. Use MATLAB and hand in the MATLAB codes. (Note that the domain is (x, y)e[0,1] x [0,1].) 0=0 0=0 4 8 12 16 10 Ꮎ0 15 25 9 14 19 24 3 11 15 0=0 8-0 0=0 3 8 13 18 23 2 6 сл 5 0=0 10 14 6 12 17 22 1 6 11 16 21 13 e=0 Fig 3 Fig 4 Textbook: Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, Eighth Edition (2021).
Fig 2 (II) [60 Points] Using centered finite difference approximation as done in class, solve the equation: 020 020 + მx2 მy2 +0.0150+Q=0 subject to the boundary conditions shown in the stencils below. Do this for two values of Q: (a) Q = 0.3, and (b) Q = 10.5x² + 1.26 * 1.5 x 0.002 0.008. For Case (a) (that is, Q = 0.3) use Fig 3. For Case (b), use both Fig. 3 and Fig 4. For all the three cases, show a table as well as the contour plots of versus (x, y), and the (x, y) heat flux values at all the nodes on the boundaries x = 1 and y = 1. Discuss your results. Use MATLAB and hand in the MATLAB codes. (Note that the domain is (x, y)e[0,1] x [0,1].) 0=0 0=0 4 8 12 16 10 Ꮎ0 15 25 9 14 19 24 3 11 15 0=0 8-0 0=0 3 8 13 18 23 2 6 сл 5 0=0 10 14 6 12 17 22 1 6 11 16 21 13 e=0 Fig 3 Fig 4 Textbook: Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, Eighth Edition (2021).
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.7P
Related questions
Question
![Fig 2
(II) [60 Points] Using centered finite difference approximation as done in class, solve the equation:
020 020
+
მx2 მy2
+0.0150+Q=0
subject to the boundary conditions shown in the stencils below. Do this for two values of Q: (a) Q = 0.3,
and (b) Q = 10.5x² + 1.26 * 1.5 x 0.002 0.008. For Case (a) (that is, Q = 0.3) use Fig 3. For Case (b),
use both Fig. 3 and Fig 4. For all the three cases, show a table as well as the contour plots of versus
(x, y), and the (x, y) heat flux values at all the nodes on the boundaries x = 1 and y = 1. Discuss your
results. Use MATLAB and hand in the MATLAB codes. (Note that the domain is (x, y)e[0,1] x [0,1].)
0=0
0=0
4
8
12
16
10
Ꮎ0
15
25
9
14
19
24
3
11
15
0=0
8-0
0=0
3
8
13
18
23
2
6
сл
5
0=0
10
14
6
12
17
22
1
6
11
16
21
13
e=0
Fig 3
Fig 4
Textbook: Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, Eighth
Edition (2021).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fece3d40f-e8f0-464a-aada-c18e494e1994%2F2b20204d-00b6-4918-87b0-37a09f783697%2Ffzdoukj_processed.png&w=3840&q=75)
Transcribed Image Text:Fig 2
(II) [60 Points] Using centered finite difference approximation as done in class, solve the equation:
020 020
+
მx2 მy2
+0.0150+Q=0
subject to the boundary conditions shown in the stencils below. Do this for two values of Q: (a) Q = 0.3,
and (b) Q = 10.5x² + 1.26 * 1.5 x 0.002 0.008. For Case (a) (that is, Q = 0.3) use Fig 3. For Case (b),
use both Fig. 3 and Fig 4. For all the three cases, show a table as well as the contour plots of versus
(x, y), and the (x, y) heat flux values at all the nodes on the boundaries x = 1 and y = 1. Discuss your
results. Use MATLAB and hand in the MATLAB codes. (Note that the domain is (x, y)e[0,1] x [0,1].)
0=0
0=0
4
8
12
16
10
Ꮎ0
15
25
9
14
19
24
3
11
15
0=0
8-0
0=0
3
8
13
18
23
2
6
сл
5
0=0
10
14
6
12
17
22
1
6
11
16
21
13
e=0
Fig 3
Fig 4
Textbook: Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, Eighth
Edition (2021).
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