problem_set8 - 10.34 Fall 2006 Homework #8 Due Date:...

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10.34 – Fall 2006 Homework #8 Due Date: Wednesday, November 1 st , 2006 – 9 AM Problem 1: Solve 6.B.1 in Beers’ (pg. 432) by GMRES, using sparse representation of the large matrix. Note that you may have to restart GMRES after a few iterations, and also things may work better if you pre-condition the matrix. Your Matlab program should take T 0 ,T 1 , lambda, rho, C P , Re, mu, and R as inputs. Please run your program for the case (you do not need to answer specific questions ask in Beers’ book, only the ones asked here): T 0 = 300 K T 1 = 400 K λ = 0.6 W/m-K ρ = 1 g/cm 3 C P = 4 J/g-K Re = 100 μ = 0.5 cP = 0.5 x 10 -3 N-s/m 2 R = 5 cm Generate following plots (over a range that shows all dynamics): - A 3-D surface plot and 2-D contour/pcolor plot of the velocity field - A plot showing the T(z) for r = 0, 1, 2, 3, 4 cm (all on the same figure) Hints and notes: The flow in the problem and the ambiguous boundary conditions in the z- direction create a problem: how can we define the axial boundary conditions? This is a place where the scaling analysis you have learned in transport can be important. We know that at -
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problem_set8 - 10.34 Fall 2006 Homework #8 Due Date:...

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