In [3]:

    

import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline


    

In [4]:

    

S =  25.8e-2 * 43.7e-2  # m3
m = 3.2 # kg

# Masse surfacique :
rhoS = m/S
print( rhoS )


    

    




28.38238163659908

In [5]:

    

k = 0.0262 # W/m/K, conductivité thermique
nu = 1.57e-5 #  m2·s−1 , viscosité cinématique air,
alpha = 2.22e-5 # m2·s−1, diffusivité thermique
Pr = 0.708 # Prandl


    

In [6]:

    

L = 4 # m, dimension caractéristique
U = 20e3/60/60 # m/s, vitesse caractéristique
print( U )


    

    




5.555555555555555

In [7]:

    

Re = U*L/nu # Reynolds,   turbulent si >3.10^5
print( Re )


    

    




1415428.1670205237

In [8]:

    

Reynolds = lambda u: u*L/nu


    

In [9]:

    

# Limite turbulence

v_lim = 3e5/L*nu
print( 'vitesse limite turbulence: %f m/s '% v_lim )


    

    




vitesse limite turbulence: 1.177500 m/s 

In [10]:

    

# Forcée, turbulent, Pr < 50  (cf. page 15)
h_FT = lambda u : k/L * 0.036 *  Reynolds(u)**(4/5) * Pr**(1/3) 

# Forcée laminaire
h_FL = lambda u : k/L * 0.664 * Reynolds(u)**(1/2) * Pr**(1/3)


    

In [11]:

    

u_span_T = np.linspace( 1.0, 15, 20 ) # m/sh_FT_span = h_FT( u_span )
u_span_L = np.linspace( 0, 1.7, 20 )


    

In [12]:

    

plt.figure( figsize=(10, 6) )
plt.plot( u_span_T, h_FT( u_span_T ), label='Forcée, turbulent' )
plt.plot( u_span_L, h_FL( u_span_L ), label='Forcée, laminaire' )
plt.plot( [0, 1.7], [5, 5], label='Naturelle, laminaire&turb.' )

# plt.plot( u_span_T, 6.5*u_span_T, label='Forcée, laMétéo-dec' )

plt.xlabel( 'vitesse vent m/s' )
plt.ylabel( 'h  W/m2/K' );
plt.legend();


    

In [13]:

    

theta = 37*np.pi/180


    

In [14]:

    

deltaT = 30
L = 4 # m


    

In [15]:

    

g = 9.81 #* np.cos(theta) #m/s-2
beta = 3e-3 # air, 20°C


    

In [16]:

    

Gr = g*beta*deltaT*L**3/nu**2
print('Grashof: %e'% Gr )
print('Rayleight: %e'% (Gr*Pr) )


    

    




Grashof: 2.292409e+11
Rayleight: 1.623026e+11

In [17]:

    

# Plaque horizontale chauffant vers le haut
h_NTh = k/L * 0.14*(Gr*Pr)**(1/3)
print( h_NTh )


# Vertical, turbulent (Mac Adams)
h_NTv = k/L * 0.13 * (Gr*Pr)**(1/3)

print( h_NTv )


    

    




5.002009169886503
4.6447228006088945

In [18]:

    

L = 20e-2 # m


    

In [19]:

    

Gr = g*beta*deltaT*L**3/nu**2
print('Grashof: %e'% Gr )
print('Rayleight: %e'% (Gr*Pr) )


    

    




Grashof: 2.865512e+07
Rayleight: 2.028782e+07

In [20]:

    

# limite de turbulence ...
# vertical :
h_NLv = k/L * 0.677* (Pr)**(1/2)/(0.95+Pr)**(1/4)*Gr**(1/4)

print( h_NLv )


# horizontale :
h_NLh = k/L * 0.54* (Pr*Gr)**(1/4)

print( h_NLh )


    

    




4.811505774877057
4.74759779703654

In [21]:

    

ep = 20e-2 # m
k = 0.035 # W/m/K

S_plafond = 2*4.59*7.94  # m2 , surface toit


    

In [22]:

    

print( 'U_toit = %.3f W/K'%(ep*k*S_plafond) )


    

    




U_toit = 0.510 W/K

In [23]:

    

h_vitre = 2.8 # W/ (m2.K)


    

In [24]:

    

h_vitre = 2.8 # W/ (m2.K)

S_vitre = 0.6*0.8*2 + 1.2*0.8 + 0.3*0.72*4 + 0.25**2 # m2 
print('surface vitrée: %.2f m^2' % S_vitre )

print( '> U_vitre : %.3f W/K'%( h_vitre*S_vitre ) )


longueur_cadres = (0.6+0.8)*4 + (1.2+0.8)*2 + 2*(0.3+0.72)*4 + 4*0.25
print( 'longueur cadres: %.1f m' % longueur_cadres )

psi = 0.016
k_bois = 0.15 + psi #  
U_cadres = k_bois*longueur_cadres # W/K
print( '> U_cadres : %.3f W/K'%( U_cadres ) )

print(' ')
print( '> U_tot : %.3f W/K'%( U_cadres +  h_vitre*S_vitre ) )


    

    




surface vitrée: 2.85 m^2
> U_vitre : 7.970 W/K
longueur cadres: 18.8 m
> U_cadres : 3.114 W/K
 
> U_tot : 11.084 W/K

In [25]:

    

# pour du béton :
rhoCp = 1400e3 # J/m3/K
k = 1.75 # W/m/K


    

In [26]:

    

# Distance de pénetration dans les murs :
temps_carac = 60*60*12 # 12h

D = k/rhoCp # diffusivité
distance = np.sqrt( D*temps_carac  )

print( 'Longeur carac. diff. mur: %f cm' % (distance*100) )


    

    




Longeur carac. diff. mur: 23.237900 cm

In [27]:

    

surface_murs = 58 + 2*22.7

ep_utile = 0.08  # 8cm

M_mur = surface_murs*ep_utile*rhoCp


    

In [28]:

    

print( 'masse thermique murs: %.2e J/K'% M_mur )


    

    




masse thermique murs: 1.16e+07 J/K

In [31]:

    

h = 10
print( M_mur/h/60/60/24 )


    

    




13.403703703703703

In [32]:

    

Volume_appart = 22.7 * 7.94  # m3


    

In [33]:

    

# http://www.engineeringtoolbox.com/air-properties-d_156.html
rho_air = 1.2051 # kg/m3, 20°C
Cp_air = 0.005 * 1e3 # J/(kg K), 20°C

rhoCp_air = Cp_air*rho_air


    

In [34]:

    

print( 'masse air appart: %f kg'% (Volume_appart*rho_air) )


    

    




masse air appart: 217.204814 kg

In [35]:

    

M_air = Volume_appart*rho_air*Cp_air
print( 'masse thermique air appart: %f J/K'% M_air )


    

    




masse thermique air appart: 1086.024069 J/K

In [ ]:

    

A = 1.2*0.3  # m2
v = 0.5 # m/s


    

In [ ]:

    

taux = ( A*v ) /  Volume_appart

print( taux*60*60 )


    

In [ ]:

    

q_min = 34 # m3/min  +- 10%

q_min = q_min - 0.1*q_min


    

In [ ]:

    

taux = (q_min*60)/  Volume_appart


    

In [ ]:

    

print( taux )


    

In [ ]:

    

taux = 10 # Volume / heure
U_aeration = q_min *60*60 * rhoCp_air

print( 'U_ventilateur: %f W/K' % U_aeration  )


    

In [ ]:

    

# http://www.ecro.fr/fr/principes-solutions/principes/taux-de-brassage-renouvellement.html

taux = 2 # V/h


    

In [ ]:

    

Volume_appart = 22.7 * 7.94  # m3
U_aeration = taux *Volume_appart  /60/60 * rhoCp_air


    

In [ ]:

    

print( 'U aération nat: %f W/K' % U_aeration  )


    

In [ ]:

    




    

In [ ]:

    

12/2.3


    

In [ ]:

    

3.5*5


    

In [ ]: