Problem 46084. Parabolic Partial Differential Equations: Explicit Method

  • Created by A C
I got this example from numericalmethodsguy youtube video. He solves the problem step by step.
A rod of steel is subjected to a temperature of 100°C on the left end and 25°C on the right end. If the rod is of length 0.05m, use the explicit method to find the temperature distribution in the rod from t = 0 and t = 9 seconds. Use ∆x = 0.01m , ∆t = 3s . Given: k =-54 W/(m*K) , ρ = 7800 kg/m^3, C = 490 J/(kG*K) . The initial temperature of the rod is 20°C.
Make a matrix of all Temperatures in °C. The first column is the initial conditions at time 0 second, the middles columns are the unknow tempertures, and the final column is the linear path from the intial conditions to the final conditions.
On the second test: I varied the length of rod and the final time.
rod is of length 0.10m and ∆x = 0.02m
from t = 0 and t = 102 seconds

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33.33% Correct | 66.67% Incorrect
Last Solution submitted on May 27, 2024

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