Solucion analitica 1d

analitico

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


L      = 0.1         # 10 cm
Nx     = 100
xi     = 0.0
xf     = L
dx     = (xf-xi)/Nx
x      = np.zeros(Nx+1)
T      = np.zeros(Nx+1)
T0     = 1.0
k      = math.pi/L

for ix in range(0,Nx+1):
 x[ix]  = xi + ix*dx
 T[ix]  = T0*math.sin(k*x[ix])

plt.plot(x,T)
plt.show()

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

D      = 9.7e-5
L      = 0.1         # 10 cm
alfa   = D*(math.pi/L)**2
Nx     = 100
xi     = 0.0
xf     = L
dx     = (xf-xi)/Nx
x      = np.zeros(Nx+1)
TT0      = np.zeros(Nx+1)
TT1      = np.zeros(Nx+1)
TT2      = np.zeros(Nx+1)
TT3      = np.zeros(Nx+1)

T0     = 1.0
k      = math.pi/L

t0 = 0.0
t1 = 1.0
t2 = 2.0
t3 = 3.0

for ix in range(0,Nx+1):
 x[ix]  = xi + ix*dx
 TT0[ix]  = T0*math.sin(k*x[ix])*math.exp(-alfa*t0)
 TT1[ix]  = T0*math.sin(k*x[ix])*math.exp(-alfa*t1)
 TT2[ix]  = T0*math.sin(k*x[ix])*math.exp(-alfa*t2)
 TT3[ix]  = T0*math.sin(k*x[ix])*math.exp(-alfa*t3)
plt.plot(x,TT0,'-k',label='0 segundos')
plt.plot(x,TT1,'-b',label='1 segundos')
plt.plot(x,TT2,'-g',label='2 segundos')
plt.plot(x,TT3,'-r',label='3 segundos')
plt.xlabel("x")
plt.ylabel("T(x)")
plt.title('Decaimiento de temperatura')
plt.legend()
plt.grid()
plt.show()

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

D      = 9.7e-5
L      = 0.1         # 10 cm
alfa   = D*(math.pi/L)**2
Nx     = 100
xi     = 0.0
xf     = L
dx     = (xf-xi)/Nx
x      = np.zeros(Nx+1)
TT0      = np.zeros(Nx+1)


T0     = 1.0
k      = math.pi/L

for it in range(0,10):
 t=it*1.0   
 for ix in range(0,Nx+1):
  x[ix]  = xi + ix*dx
  TT0[ix]  = T0*math.sin(k*x[ix])*math.exp(-alfa*t)
 plt.xlabel("x")
 plt.ylabel("T(x)")
 plt.title('Decaimiento de temperatura')
 plt.grid()
 plt.plot(x,TT0,label='tempe')
 plt.ylim(0,1)   
 plt.legend()
 if it<  10                  : plt.savefig("Temp0{}.png".format(it))
 plt.close()