HW #6 - BIOE604 1. Consider a transient pipe flow convection problem with constant mass flux on the wall (out of the tube) equal to 2.5 x 10-9 mol/s-m2. Consider a 1D approximation to this setup. Assume the fluid velocity is 2 x 10-8 m/s, DAB = 2 x 10-5 cm2/s, Cin = 100 mM and tube diameter is 1 mm and the length is 10 cm. 1.a. Solve the steady state problem analytically. 1.b. Perform a macroscopic mass balance. Be sure to include the diffusive flux at the inlet. The objective is to see if the mass balance is satisfied. 1.c. Now, switch the sign on the wall mass flux and redo a & b. Carefully observe the signs on the fluxes in this new case. 1.d. Solve the transient problem using pdepe in a dimensionless form. Now, take the dimensionless solution and transform it into a dimensional solution. Plot concentration vs time and space. 2. Modify the code from Prob 1.d. to examine effects of initial conditions. Set the wall flux equal to zero. Set the initial condition to a slug at the inlet of width ΔX = 0.1 and magnitude ψ = 1. Set the inlet concentration to zero. Track the progress of the slug down the tube. Run a series of Pe cases Pe = 1, 10, 100 and tabulate the width of the slug and the maximum height at T = 1 as well as plotting the concentration profiles. 3. Run the same cases as in Prob 2 only set the inlet concentration to 1. Plot all three cases on the same plot at T=1 to allow comparison of shape of the concentration front vs. X. Note: I think it should be possible to solve these problems in about an hour each. Whatever time you spend beyond that should be running the resulting codes to learn something about mass transfer.
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