Thermal Diffusivity, Backwards Differencing, and Von Neumann Stability Analysis

[che-4071-hw2]
Part B:
1. Derive the time dependent heat diffusion equation for a uniform linear bar assuming constant thermal diffusivity.
2. Express the heat diffusion equation from Part B1 as an algebraic equation via backward (explicit) differencing.
3. Simulate the time dependent response of a uniform bar initially at 50C after its ends are raised then maintained at 40 and 80C respectively. Discretize the bar into 20 sections and show the simulated result for r=
=0.495 and r=0.505
4. Using von Neumann stability analysis explain why simulation results are unstable when r is set larger than 0.5