HEAT 2D

#How to create a heat map
#Why are we doing it , it's just a nice partial derivative to solve

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation


#Just like all numerical problem we must descritise our problem
#We can choose a small dx for better precision, but we must choose dt to resepct certain parameters , namely
#dt <= 0.5 * dx^2/alpha

a = 110
length = 10 #mm
time = 4 #seconds
nodes = 50


#Need to define the temperature at the boundaries of our rod
#When prefomrming in 2D we simply just add another y dimension partial derivative

dx = length / nodes
dy = length / nodes
dt = 0.3 * dx*dy/a
u = np.zeros((nodes, nodes)) +20  #PLate is initially at 20 degrees C

#Boundary conditions (This gives all the corners equal to 100)
u[0, :]= 100
u[-1, :] = 100

#Visualisng the sim

fig, axis = plt.subplots()

pcm  = axis.pcolormesh(u, cmap=plt.cm.jet, vmin=0 , vmax=100)
plt.colorbar(pcm, ax=axis)
#simulating

counter = 0
while counter < time :
    w = u.copy()

    for i in range(1, nodes - 1):
        for j in range(1, nodes -1 ):

            dd_ux = (w[i-1, j] - 2*w[i, j] +w[i+1, j])/dx**2
            dd_uy = (w[i, j-1] - 2 * w[i, j] + w[i, j+1]) / dy ** 2

            u[i, j] = dt * a * (dd_ux + dd_uy) + w[i, j]

    counter += dt

    pcm.set_array(u)
    axis.set_title("Distribution at t: {:.3f} [s].".format(counter))
    plt.pause(0.01)

plt.show()