Project
Objective: To apply principles of numerical methods covered in this course to model the heat transfer and temperature distribution in a one-dimensional time-dependent system.
Description: A cylindrical rod of length L and cross-sectional area A is insulated along its circumference so that there is no heat transfer or temperature variation in the radial direction. Temperature varies only along its length (x-direction) and as a function of time. The ends of the rod are exposed to surrounding temperatures at x=0 (left side) and x=L (right side). The rod is initially at a uniform temperature Ti and in equilibrium with its surroundings.
Deliverables: Prepare a short write-up that includes a brief description of your method, a listing of your code (MATLAB or other software), and a short discussion of results, to include:
1. Plots of T vs. x at times t = 1, 2, 5, 10, 20, 50, 100, and 10000 seconds. Note that the 10000s case should correspond to the steady state result.
2. Plot of Eu vs. t for 0 < t < 100s and 0 < t < 10000s.
Bonus 1: In addition to the above, implement functionality to use either the Euler explicit method, the RK2 method, or the classical RK4 method to perform the time stepping. Comment on differences in error order and their impact on the results. (This is required if taking the course for Honors credit.)
Bonus 2: In addition to the above, implement an O(h4) for computing the second-derivative ∂2T/∂x2 during each time step. Comment on differences in error order and their impact on the results.
Attachment:- Project Assignment.rar