# CRANK_01.py
# Calculation of Dynamic Heat Flow
# Example 1 in Bagda, Dlabal, Öztürk
# Calculation of temperature change in a wall of cellular concrete
# at 20 °C, if one side is cooled down to 0 °C.
# System design by Engin Bagda, Python programming by Erkam Talha Öztürk
# Version 2020_07_03
import numpy as arr # to set up arrays
# Crank Nicolson function
def CrankNicolson():
e[0] = 0
f[0] = Temp[0]
for i in range(1, n - 1, 1): # n-1 because string has to run until i=19
r = Lambda[i] * dTime / (Wkap[i] * Rho[i] * x[i] * x[i])
K1 = Lambda[i - 1] * x[i] / (Lambda[i] * x[i - 1])
K2 = Lambda[i] * x[i + 1] / (Lambda[i + 1] * x[i])
a = r
b = 2 + (2 * r)
c = r
d = (a * Temp[i - 1]) + (2 - (2 * r)) * Temp[i] + (c * Temp[i + 1])
e[i] = c / (b - (a * e[i - 1]))
f[i] = (d + a * f[i - 1]) / (b - a * e[i - 1])
# Thomas algorithm
def ThomasAlgorithm():
for i in range(n - 2, 0, -1): # n-1 because string has to start i=18
Temp[i] = (e[i] * Temp[i + 1]) + f[i]
# Definitions
global e, f, r, K1, K2, a, b, c, d # in Ctank Nicolsen function
global dTemp # in Thomas algorithm
global n, x, Temp, Lambda, Rho, Wkap, dTime # in main run
n = 20 # index for layers from i=0 to i=20
x = arr.empty(n)
e = arr.empty(n)
f = arr.empty(n)
Temp = arr.empty(n)
Lambda = arr.empty(n)
Rho = arr.empty(n)
Wkap = arr.empty(n)
# Setup of conditions and material properties
dTime = 60.00 # s, duration of the time steps
for i in range(0, n, 1): # string stops at i=n-1
x[i] = 0.010 # thickness of each element
Lambda[i] = 0.160 # thermal conductivity (W/m/K)
Rho[i] = 550 # density (kg/m3)
Wkap[i] = 1000 # heat capacity (oule/m3)
Temp[i] = 20 # °C, primary definition
# Main run
for Time in range(0, 1440, 1): # ammount of time steps 24 hours x 60 minutes
Temp[n - 1] = (
0 # °C new temperature after 1 minute (boundary condition in elemnt i=n-1
)
CrankNicolson()
ThomasAlgorithm()
print(
"%4.0f, %6.1f, %8.1f, %8.1f, %8.1f, %8.1f, %8.1f, %8.1f, %6.1f "
% (
Time,
Temp[0],
Temp[1],
Temp[2],
Temp[3],
Temp[n - 4],
Temp[n - 3],
Temp[n - 2],
Temp[n - 1],
)
)
# End of run