HW #4 - BIOE604 1. Consider Problem #4 in HW#3. The solution can be written as C A ( x) C w NA 2 D AB w 2 2 x2 where x is measured from the centerline. Verify that this solution satisfies the problem statement. 2. Consider a plane wall diffusion problem with no source. Assume the wall surface concentrations are Cs1 = 100 mM and Cs2 = 50 mM. Further, assume w = 1 mm & DAB = 2 x 10-5 cm2/s. At the centerline, determine the flux. Note that the net diffusion term is d 2C dx 2 0 Reconcile these two pieces of information. 3. Solve the following problem using pdepe in Matlab. Plane wall diffusion with sink. DAB = 2.4 x 10-5 cm2/s; Sink = 25 x 10-6 M/s; w = 40 x 10-6 m. Assume the left wall is impermeable and the right wall has a known concentration, Cw = 4 x 10-8 mol/cm3. Assume the initial concentration is 4 x 10-8 mol/cm3 throughout the domain. Suggest to modify the pdepe example problem line by line Steps: a. Choose m = 0 (Cartesian) b. Define pde through specification of c, f & s in the function called pdepb c. Define the initial conditions d. Define the boundary conditions e. Check all of the input values – is anything missing? f. Think about the limits on the independent variables – these are problem dependent and may be off by many orders of magnitude. g. Run the program and plot the results 4. Using the code you developed in Problem 3, examine the effect of DAB and N’’’. Make a series of runs to examine these variables and come up with a way to summarize the results 5. Using the code you developed in Problem 3, examine the effect of initial conditions. Make a run with initial condition set to the wall value. Make a run with a half sinusoidal initial condition with zero at each end and the wall value at the centerline. One of the things to look for here is that the steady state solution should be independent of the initial conditions. 6. Using the code you developed in Problem 3, examine the effect of boundary conditions. Learn how to specify b.c. in pdepe. Make a series of runs with different boundary conditions and summarize the results. Make sure you learn how to plot the results from pdepe. The plotting capabilities in Matlab are pretty powerful but you need to work with it to learn the features. You should document your HW efforts with plots. However, there is no extra credit for color or number of pages. The whole point here is to learn the useful features and to document your capability (in summary form).
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