Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 29, Problem 13P
Develop a user-friendly computer program to implement Liebmann's method for a rectangular plate with Dirichlet boundary conditions. Design the program so that it can compute both temperature and flux. Test the program by duplicating the results of Examples 29.1 and 29.2.
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An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. The figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate.
Suppose you fit the first-order model y = Po + B, x, + B2x2 + B3X3 + B,x4 + B5X5 + ɛ to n=28 data points and obtain SSE = 0.33 and R = 0.94. Complete
parts a and b.
a. Do the values of SSE and R suggest that the model provides a good fit to the data? Explain.
A.
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provides a good fit.
B. There is not enough information to decide.
No. Since R = 0.94 is close to 1, this indicates the model does not provide a good fit. Also, SSE = 0.33 is fairly small, which indicates the
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Test the null hypothesis Ho: B, = B2 = ... = B5 = 0 against the alternative hypothesis: At least
of the
%3D
parameters B1, B2,
B5 is nonzero. Use a = 0.05.
The test statistic is
(Round to two decimal places as needed.)
Need help with parts d and k.
Data:
TSERofReturn
AcmeRofReturn
1
0.42478
-0.48194
2
1.61213
-0.73284
3
-0.98754
-2.28445
4
-0.30013
-1.55312
5
1.41215
0.68674
6
0.68725
-1.31132
7
0.03733
-0.83295
8
-1.72494
-1.71975
9
0.33729
1.14443
10
-1.07502
-1.79885
11
0.86222
0.89736
12
1.17468
1.66664
13
-0.38761
-0.02658
14
1.66212
0.9086
15
1.09969
1.99935
16
-0.06266
0.46148
17
-1.96241
-1.41004
18
-1.32499
-0.38086
19
-1.51247
-1.90904
20
0.74974
0.91873
21
-0.38761
-0.49714
22
-0.17514
-1.31385
23
-3.41222
-1.15681
24
-0.01266
2.11718
25
0.16231
1.78766
26
-0.82506
1.30344
27
-0.41261
-0.43377
28
0.2623
-1.70274
29
-1.16251
0.4692
30
-1.05003
0.27671
31
-0.65008
-0.63741
32
0.62475
2.9895
33
-0.68758
1.3613
34…
Chapter 29 Solutions
Numerical Methods for Engineers
Ch. 29 - 29.1 Use Liebmann’s method to solve for the...Ch. 29 - 29.2 Use Liebmann’s method to solve for the...Ch. 29 - 29.3 Compute the fluxes for Prob. 29.2 using the...Ch. 29 - Repeat Example 29.1, but use 49 interior nodes...Ch. 29 - Repeat Prob. 29.4, but for the case where the...Ch. 29 - 29.6 Repeat Examples 29.1 and 29.3, but for the...Ch. 29 - Prob. 7PCh. 29 - 29.8 With the exception of the boundary...Ch. 29 - Write equations for the darkened nodes in the grid...Ch. 29 - 29.10 Write equations for the darkened nodes in...
Ch. 29 - Apply the control-volume approach to develop the...Ch. 29 - Derive an equation like Eq. (29.26) for the case...Ch. 29 - 29.13 Develop a user-friendly computer program to...Ch. 29 - Employ the program from Prob. 29.13 to solve...Ch. 29 - Employ the program from Prob. 29.13 to solve Prob....Ch. 29 - Use the control-volume approach and derive the...Ch. 29 - 29.17 Calculate heat flux for node in Fig. 29.13...Ch. 29 - 29.18 Compute the temperature distribution for...Ch. 29 - 29.19 The Poisson equation can be written in...
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