bethel-physics / hw_diffusion

Homework for Garcia Ch. 6

hw_diffusion

Homework for Garcia Ch. 6

• Problem 1 (in-class)
• Problem 2 (homework)

Problem 1 (in-class)

Complete the diffusion_exercise.m program to implement the FTCS, Richardson, and DuFort-Frankel algorithms for solving the 1D heat diffusion equation along a bar of length L from x = -L/2 to +L/2.

Problem 2 (homework)

Modify the diffusion_hw.m program to solve the 1D heat diffusion equation along a bar of length L, from x = -L/2 to +L/2, for the following conditions:

• Initial conditions:
  • T = 1 for x < -L/4
  • T = 0 for x ≥ -L/4
• Run the computation for 500 steps with a step size of τ = 0.0001
• Run the computation for 3 different boundary conditions:
  • Case 1: Dirichlet conditions with T(-L/2) = 1 and T(L/2) = 0
  • Case 2: Neumann conditions for insulation with dT/dx = 0 at x = ±L/2
  • Case 3: Mixed conditions with dT/dx = 0 at x = -L/2 and T = 0 at x = L/2

Plot:

• Temperature vs. time at x = 0 for each boundary case, labeling each case.
• T(x, t) as a surface plot like the one shown below (plot for one boundary condition).