MATLAB PARTIAL DIFFERENTIAL EQUATION TOOLBOX 1 Manuale Utente Scaricare il pdf (Pagina 18)

4. Using the PDE toolbox solve for the temperature distribution with variable thermal

conductivity (make sure to change your function for k to the polynomial fit given for steel in the

function k_SS) for the case given in Lab 3, Part 4. Include a figure of the PDE toolbox solution.

Include a figure plotting temperature at x = 0.5 m and y = 0.9 m versus total number of elements

for both the PDE toolbox solution and FD method. For both methods obtain data for at least 4

different meshes. Determine the number of elements required by both methods to get agreement

within 0.01% of the converged solution of 1299.3 K.

5. Using the PDE toolbox solve for the temperature distribution as a function of space and time

for the case given in Lab 3, Part 5. Include a figure of the PDE toolbox solution at time

t = 90,000 s (25 hours). Include a figure plotting temperature at x = 0.5 m and y = 0.9 m versus

total number of elements for both the PDE toolbox solution and FD method. For the PDE

toolbox solution use 10 time steps of 9,000 s. For the FD method, use a time step of 50 s (check

that this is a stable time step for your node spacing). Determine the number of elements required

by both methods to get agreement within 0.01% of the converged solution of 71.576 ˚C.

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MATLAB PARTIAL DIFFERENTIAL EQUATION TOOLBOX 1 Manuale Utente Pagina 18