Suppose you have a plate, with length of 1 mm. One end of the plate is exposed source of diffusing atoms with a concentration of atomic fraction equal to 1. The diffusivity is 0.01 mm2 /s. You wonder how the distribution changes inside the plate as a function of time. You decide to use the FDM method to solve your problem numerically and you assume it is a 1D problem.

(a) To ensure stability, How would you choose the time and spatial increments for approximations to be valid?

(b) Make a table in a spread sheet program with the appropriate FDM equations. The plate initially has a concentration of zero. The boundary conditions are fixed concentration. At the far end of the plate is held at 0 concentration.

(c) Plot the concentration vs. position at 2, 5 and 10 s on the same plot.

(d) Repeat problems b) and c) with new boundary conditions. Leave one end at concentration and change the far end to a no flux (no diffusion) boundary condition.

Answer rating: 100% (QA)

a To ensure stability in the Finite Difference Method FDM we need to satisfy the CourantFriedrichsLewy CFL stability condition In the case of diffusio... View the full answer