The module heateq can be used to solve the heat equation in 1D.
This module solve the partial differential (PDE) equation describing, for instance, the heat diffusion fenomena. The equation is as follows:
The boundary condition is , where
is the size of the sample.
Make sure you have installed numpy and scipy in your systems or environment. It is suggested to install via pip:
pip install numpy
pip install scipy
In example bellow, the defalt sample is initiated: 10 mm linear sample (with spacing 0.1mm - equivalent to 100 points), heated at 100°C (372 K) and smoothly cooled down until both edges at 20ºC (296 K). The choosen material is iron (D = 23 mm²/s).
import heateq as heq
import matplotlib.pyplot as plt
D = 23 # for iron
dx = 0.1
u0, t, xscale = heq.initiate(dx=dx)
k = heq.kappa(u0, dx) # The FFT frequencies (wavenumbers)
u = heq.solve(dudt, u0, t, D, k)
plt.figure(figsize=(8, 8))
plt.contourf(xscale, t, u, 100)
plt.colorbar()
plt.show()Here's the sample image:
- Vagner Bessa - Initial work - bessava or bessavagner
This project is licensed under the MIT License - see the LICENSE.md file for details
- IFCE - Instituto Federal de Ciência, Tecnologia e Educação do Ceara - Brazil
- Inspiration: Steve Brunton See his chanel