This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ( bAT ) The value of κ as I’ve written it depends on the lattice spacing. You can take it to be κ = p 2 10 . 1 a. Let T s be the steady state solution as computed in Homework 2. That is AT s = b verify that if we write T ( t ) = T s + W ( t ) then dW dt =κAW, W (0) = T (0)T s b. Use eig to compute the eigenvalues of A for p = 10. What do you conclude about the convergence of the temperature to the steady state value? c. Suppose the sample is intially heated to a temperature of 80. Use expm to compute the temperature at times t = . 5 : . 5 : 5 and use surf to plot it. (Note you are solving for W so you need to add in T s to get the total temperature ﬁeld. Use p = 10.) 2...
View
Full Document
 Fall '09
 Hagstrom
 Linear Algebra, Algebra, matlab, Thermodynamics, Matrices, Heat, Heat Transfer, matrix form dT, T. Hagstrom, random similarity transforms

Click to edit the document details