Question

Use the separation of variables method to solve the following problem. Consider a long, narrow

tube connecting two large, well-mixed reservoirs containing a small concentration of N2 in another

inert gas. The tube length is L = 100 cm. To establish an initial concentration profile in the

tube, each reservoir is held at a fixed concentration: Reservoir 1 contains no N2 and reservoir 2 has

2 × 10−6 mol/cm3 of N2.

(a) At t = 0, the concentrations of the reservoirs are rapidly (instantaneously) switched. Solve

for the concentration in the tube as a function of position and time. The diffusion coefficient of N2

is D = 0.2 cm2/s.

(b) Plot the concentration c(z, t) as a function of the position along the tube at four different

times (initial, early, intermediate, and long times). Use software to plot enough terms of the series

solution to have a reasonable representation of the solution. As always, be sure to clearly label

your axes.

(c) Repeat part (b), but plot the transient part of the solution, ct(z, t).

Answer 1

c)