Write a program in MATLAB to numerically solve for the concentration distribution in a duct of length l = 10 m with insulated sides and with the boundary and initial conditions given in problem 1. Plot the concentration distribution in the duct at t = 100 s and at the steady-state value. Be sure to indicate your method used, time step, spatial grid size and Courant number and how you decided which values (This will likely involve plots, tables or other means of justification.) You may let co = 3 g/m³ and D = 0.008 m²/s. Compare your results with the analytical solution (found in problem 1) by plotting the analytical result on the same graph. to use. For this problem, you may use either the explicit or the implicit method. Be sure to indicate which you used. For extra credit, you can try it using both methods. In order to get the extra credit: (a) Clearly present the solutions for each method, both in your discussion (how you did it, how you picked your Courant number, how you picked your spatial grid size), and in showing the results. (b) Show SOMETHING that is different in the results.
Write a program in MATLAB to numerically solve for the concentration distribution in a duct of length l = 10 m with insulated sides and with the boundary and initial conditions given in problem 1. Plot the concentration distribution in the duct at t = 100 s and at the steady-state value. Be sure to indicate your method used, time step, spatial grid size and Courant number and how you decided which values (This will likely involve plots, tables or other means of justification.) You may let co = 3 g/m³ and D = 0.008 m²/s. Compare your results with the analytical solution (found in problem 1) by plotting the analytical result on the same graph. to use. For this problem, you may use either the explicit or the implicit method. Be sure to indicate which you used. For extra credit, you can try it using both methods. In order to get the extra credit: (a) Clearly present the solutions for each method, both in your discussion (how you did it, how you picked your Courant number, how you picked your spatial grid size), and in showing the results. (b) Show SOMETHING that is different in the results.
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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Transcribed Image Text:2. Write a program in MATLAB to numerically solve for the concentration distribution in a duct of length
l = 10 m with insulated sides and with the boundary and initial conditions given in problem 1. Plot the
concentration distribution in the duct at t = 100 s and at the steady-state value. Be sure to indicate
your method used, time step, spatial grid size and Courant number and how you decided which values
to use. (This will likely involve plots, tables or other means of justification.) You may let co = 3
g/m³ and D = 0.008 m²/s. Compare your results with the analytical solution (found in problem 1)
by plotting the analytical result on the same graph.
For this problem, you may use either the explicit or the implicit method. Be sure to indicate which
you used. For extra credit, you can try it using both methods. In order to get the extra credit:
(a) Clearly present the solutions for each method, both in your discussion (how you did it, how you
picked your Courant number, how you picked your spatial grid size), and in showing the results.
(b) Show SOMETHING that is different in the results.
Transcribed Image Text:1. The concentration of pollutants in a long, thin air duct (of length, ) is governed by the diffusion
equation:
əc
Ət
D (DOC)
dx
where c(x, t) is the concentration at a given location and time and D, the diffusion coefficient, may or
may not be a constant. When the pollutants are discovered, the duct is sealed on both ends so that
no pollutants can escape. The correct boundary conditions for this situation are:
əc
ax (0, t) = 0
əc
-(l, t) = 0
= 0
əx
If the initial concentration of pollutants in the duct is given as
2πα
(1-cos ²72)
c(x,0) = Co
find the solution for c(x, t) if D is a constant. (Note that n = 0 does give a non-trivial and valid
solution for this case and so should be included in your series.)
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