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# hw5 - 3 Use the Rayleigh-Ritz method with the trial form y...

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Department of Chemical Engineering University of California, Santa Barbara ChE 230A Fall 2006 Instructor: Glenn Fredrickson Homework #5 Homework Due: Thursday, November 2, 2006 1. Consider a problem of one-dimensional heat conduction along a semi-inﬁnite rod that is insulated along its length, x [0 , ]. In dimensionless form, the heat equation is T t = T xx . Solve for the temperature ﬁeld T ( x,t ) if the rod is initially at T = 0, the left boundary is subject to a variable heat ﬂux, T x (0 ,t ) = 1+5 t , and the boundary at inﬁnity is subject to lim x →∞ T, T x = 0. 2. Solve the following problems in your RHB text: 22.1, 22.2, 22.10, 22.20.
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Unformatted text preview: 3. Use the Rayleigh-Ritz method with the trial form y ≈ x + x (1-x )( c 1 + c 2 x ) to obtain an approximate solution of the boundary value problem [ xy ( x )] + y ( x ) = x, y (0) = 0 , y (1) = 1 Notice that this is not an eigenvalue problem, but because of the self-adjoint form of the diﬀerential operator, the variational method can still be applied! Explain why this is the case and how you would go about reﬁning your approx-imate solution....
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