Consider the hot rod problem. Assume L=10m, h=0.01 m² and Ta= 20°C. dᎢ dx dz dx = Z =h(T-Ta) The boundary conditions are T(x = 0) = 40°C and T(x=L) = 200°C. Use a range of z values as your guesses to test in the loop. 1. In Matlab, input the right hand side of the ODEs as a function named RHS=@() _____ _____ ]- 2. Define x, and the initial condition (also as a matrix). One of the initial conditions will be a guess value of z(x = 0) = 5. 3. Use the ode45() command to evaluate the solution for the x range given. Plot the solution and check your boundary condition at the end. 4. Now add a loop that evaluates each value of zg given above, running ode45() each time. Create a matrix of test values where you subtract the calculated condition at x=L each time. Then use the min() command to find the best value of zg. 5. Run ode45() one last time. This time use the best value of zg and name your final solution "Tfinal" (should be the matrix output from ode45 that is two columns and includes both y1 and y2). Plot your final temperature and make sure it matches your expectations well. 1 % Constants L = 10; %m 3 h = 0.01; %m2 4 Ta = 20; %C 5 6 % To solve we need to guess a value of z 7 zg= linspace (5,15,10); 8 9 % x range |18|xin = 0:0.01:10; 11 12 13 % Set up the right hand side of the ODE as a matrix function 14 RHS = 15 16 % Set up a for loop to test each value of z. Don't forgot to change the initial condition inside the loop. 17 for i=1:length(zg) 18 19 end 20 21 % Find the best solution by looking at the minimium test value 22 23 bestz = %best value of z guess 24 25 % Re-run ODE45 with the best value of z 26 27 Tfinal - 28 29 30 % Plot to make sure the final solution matches the boundary conditions 31 32
Consider the hot rod problem. Assume L=10m, h=0.01 m² and Ta= 20°C. dᎢ dx dz dx = Z =h(T-Ta) The boundary conditions are T(x = 0) = 40°C and T(x=L) = 200°C. Use a range of z values as your guesses to test in the loop. 1. In Matlab, input the right hand side of the ODEs as a function named RHS=@() _____ _____ ]- 2. Define x, and the initial condition (also as a matrix). One of the initial conditions will be a guess value of z(x = 0) = 5. 3. Use the ode45() command to evaluate the solution for the x range given. Plot the solution and check your boundary condition at the end. 4. Now add a loop that evaluates each value of zg given above, running ode45() each time. Create a matrix of test values where you subtract the calculated condition at x=L each time. Then use the min() command to find the best value of zg. 5. Run ode45() one last time. This time use the best value of zg and name your final solution "Tfinal" (should be the matrix output from ode45 that is two columns and includes both y1 and y2). Plot your final temperature and make sure it matches your expectations well. 1 % Constants L = 10; %m 3 h = 0.01; %m2 4 Ta = 20; %C 5 6 % To solve we need to guess a value of z 7 zg= linspace (5,15,10); 8 9 % x range |18|xin = 0:0.01:10; 11 12 13 % Set up the right hand side of the ODE as a matrix function 14 RHS = 15 16 % Set up a for loop to test each value of z. Don't forgot to change the initial condition inside the loop. 17 for i=1:length(zg) 18 19 end 20 21 % Find the best solution by looking at the minimium test value 22 23 bestz = %best value of z guess 24 25 % Re-run ODE45 with the best value of z 26 27 Tfinal - 28 29 30 % Plot to make sure the final solution matches the boundary conditions 31 32
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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27.1
please complete the code
![Consider the hot rod problem. Assume L=10m, h=0.01 m² and Ta= 20°C.
dᎢ
dx
dz
dx
= Z
=h(T-Ta)
The boundary conditions are T(x = 0) = 40°C and T(x=L) = 200°C.
Use a range of z values as your guesses to test in the loop.
1. In Matlab, input the right hand side of the ODEs as a function named RHS=@() _____ _____ ]-
2. Define x, and the initial condition (also as a matrix). One of the initial conditions will be a guess value of z(x = 0) = 5.
3. Use the ode45() command to evaluate the solution for the x range given. Plot the solution and check your boundary condition at the end.
4. Now add a loop that evaluates each value of zg given above, running ode45() each time. Create a matrix of test values where you subtract the calculated condition at x=L each time. Then use the min() command to find the
best value of zg.
5. Run ode45() one last time. This time use the best value of zg and name your final solution "Tfinal" (should be the matrix output from ode45 that is two columns and includes both y1 and y2). Plot your final temperature and
make sure it matches your expectations well.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd20dfe5a-a4c1-4793-9f05-a80ad59a67d4%2Fb42fdee3-8f67-4178-b101-26cdf680c556%2Fyll1b4_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the hot rod problem. Assume L=10m, h=0.01 m² and Ta= 20°C.
dᎢ
dx
dz
dx
= Z
=h(T-Ta)
The boundary conditions are T(x = 0) = 40°C and T(x=L) = 200°C.
Use a range of z values as your guesses to test in the loop.
1. In Matlab, input the right hand side of the ODEs as a function named RHS=@() _____ _____ ]-
2. Define x, and the initial condition (also as a matrix). One of the initial conditions will be a guess value of z(x = 0) = 5.
3. Use the ode45() command to evaluate the solution for the x range given. Plot the solution and check your boundary condition at the end.
4. Now add a loop that evaluates each value of zg given above, running ode45() each time. Create a matrix of test values where you subtract the calculated condition at x=L each time. Then use the min() command to find the
best value of zg.
5. Run ode45() one last time. This time use the best value of zg and name your final solution "Tfinal" (should be the matrix output from ode45 that is two columns and includes both y1 and y2). Plot your final temperature and
make sure it matches your expectations well.
Transcribed Image Text:1 % Constants
L = 10; %m
3 h = 0.01; %m2
4 Ta = 20; %C
5
6 % To solve we need to guess a value of z
7 zg= linspace (5,15,10);
8
9 % x range
|18|xin = 0:0.01:10;
11
12
13
% Set up the right hand side of the ODE as a matrix function
14 RHS =
15
16 % Set up a for loop to test each value of z. Don't forgot to change the initial condition inside the loop.
17 for i=1:length(zg)
18
19 end
20
21 % Find the best solution by looking at the minimium test value
22
23 bestz = %best value of z guess
24
25 % Re-run ODE45 with the best value of z
26
27 Tfinal -
28
29
30 % Plot to make sure the final solution matches the boundary conditions
31
32
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