2D_HeatTransfer

import matplotlib.pyplot as plt
import numpy as np
# Adam Grendys 
# 10/30/2024

# INPUT PARAMETERS
a = 111 # Thermal Diffusivity (mm^2/s)
length_x = 100 # Length (mm)
length_y = 100 # Length (mm)
time = 100 # Time (s)
nodes = 50 # Node Count (Resolution)

# INITIALIZATION
dx = length_x / nodes
dy = length_y / nodes
dt = min(dx**2/(4*a), dy**2/(4*a))
t_nodes = int(time / dt)
temp = np.zeros((nodes, nodes)) + 20 # Starting Temp (C)

# BOUNDARY CONDITIONS
temp[0, :] = 20 # Bottom start temp (C)
temp[-1, :] = 20 # Top start temp (C)
temp[:, 0] = 100 # Left End start temp (C)
temp[:, -1] = 100 # Right End start temp (C)

# Figure
fig, axis = plt.subplots()
pcm = axis.pcolormesh(temp, cmap=plt.cm.jet, vmin=0, vmax=100)
plt.colorbar(pcm, ax=axis)

# Simulation
counter = 0

while counter < time : 
    new_temp = temp.copy()

    for i in range(1, nodes - 1) :
        for j in range(1, nodes - 1):
            dd_tempx = (new_temp[i-1, j] - 2*new_temp[i, j] + new_temp[i+1, j])/dx**2
            dd_tempy = (new_temp[i, j-1] - 2*new_temp[i, j] + new_temp[i, j+1])/dy**2

            temp[i, j] = dt * a * (dd_tempx + dd_tempy) + new_temp[i, j]

    counter += dt

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

axis.set_xlabel("Length X (mm)")
axis.set_ylabel("Length Y (mm)")
plt.show