In [1]:

```
#Variable declaration:
Gr = 100.0 #Grashof number
Re = 50.0 #Reynolds number
#Calculation:
LT = Gr/Re**2 #Measure of influence of convection effect
#Result:
if (LT<1.0):
print "The free convection effects can be neglected."
elif (LT>1.0):
print "The free convection effects can not be neglected."
```

In [2]:

```
#Variable declaration:
Ts = 110.0+273.0 #Surface temperature of plate (K)
Too = 30.0+273.0 #Ambient air temperature (K)
L = 3.5 #Height of plate (m)
g = 9.807 #Gravitational acceleration (m^2/s)
#Calculation:
Tf = (Ts+Too)/2 #Film temperature (K)
DT = Ts - Too #Temperature difference between surface and air (K)
#From appendix:
v = 2.0*10**-5 #Kinematic viscosity for air (m^2/s)
k = 0.029 #Thermal conductivity for air (W/m.K)
Pr = 0.7 #Prandtl number
B = 1.0/Tf #Coefficient of expansion (K^-1)
Gr = g*B*DT*L**3/v**2 #Grashof number
Ra = Gr*Pr #Rayleigh number
#Result:
print "The Grashof number is :",round(Gr/10**11,2)," x 10^11 ."
print "The Rayleigh number is :",round(Ra/10**11,2)," x 10^11 ."
```

In [3]:

```
#Variable declaration:
#From example 10.2:
Ra = 1.71*10**11 #Rayleigh number
#Result:
if (Ra>10**9):
print "The convection flow category is turbulent."
elif(Ra<10**9):
print "The convection flow category is laminar."
```

In [4]:

```
#Variable declaration:
#From Table 10.1:
c = 0.1 #Constant c
m = 1.0/3.0 #Constant for turbulent free conection
#From example 10.2:
Ra = 1.71*10**11 #Rayleigh number
k = 0.029 #Thermal conductivity (W/m.K)
L = 3.5 #Thickness of plate (m)
#Calculation:
Nu = c*Ra**m #Average Nusselt number
h = Nu*k/L #Average heat transfer coefficient (W/m^2.K)
#Result:
print "The average heat transfer coefficient is :",round(h,1)," W/m^2.K ."
```

In [6]:

```
from math import log,e
#Variable declaration:
Ts = 200.0+460.0 #Surface temperature of pipe (°R)
Too = 70.0+460.0 #Air temperature (°R)
D = 0.5 #Diameter of pipe (ft)
R = 0.73 #Universal gas constant (ft^3.atm.R^−1.lb.mol^−1)
P = 1.0 #Atmospheric pressure (Pa)
MW = 29.0 #Molecular weight of fluid (mol)
#From Appendix:
mu = 1.28*10**-5 #Absolute viscosity (lb/ft.s)
k = 0.016/3600.0 #Thermal conductivity (Btu/s.ft.°F)
g = 32.174 #Gravitational acceleration (ft/s^2)
#Calculation:
Tav = (Ts+Too)/2 #Average temperature (°R)
v = R*Tav/P #kinematic viscosity (ft^3/lbmol)
p = MW/v #Air density (lb/ft^3)
B = 1.0/Tav #Coefficient of expansion (°R^-1)
DT = Ts-Too #Temperature difference (°R)
Gr = D**3*p**2*g*B*DT/mu**2 #Grashof number
#From equation 10.5:
Cp = 0.25 #Air heat capacity (Btu/lb.°F)
Pr = Cp*mu/k #Prandtl number
GrPr = 10**8.24 #Rayleigh number
#From Holman^(3):
Nu = 10**(1.5) #Nusselt number
h = Nu*(k/D)*3600.0 #Air heat transfer film coefficient (Btu/h.ft.°F)
#Result:
print "The required air heat transfer film coefficient is :",round(h,2)," Btu/h.ft.°F ."
```

In [7]:

```
#Variable declaration:
Ts = 120.0+460 #Surface temperature of plate (°R)
Too = 60.0+460 #Ambient temperature of nitrogen (°R)
L = 6 #Height of plate (ft)
#From Appendix:
p = 0.0713 #Air density (lb/ft^3)
k = 0.01514 #Thermal conductivity (Btu/h.ft.°F)
v = 16.82*10**-5 #Kinematic viscosity (ft^2/s)
Pr = 0.713 #Prandtl number
g = 32.2 #Gravitational acceleration (ft/s^2)
#Calculation:
Tf = (Ts+Too)/2 #Mean film temperature (°R)
B = 1.0/Tf #Coefficient of expansion (°R^-1)
Gr = g*B*(Ts-Too)*L**3/v**2 #Grashof number
Ra = Gr*Pr #Rayleigh number
#From equation 10.13(Table 10.2) and costants from Table 10.1:
h = 0.10*(k/L)*Ra**(1.0/3.0) #Free convection heat transfer coefficient (Btu/h.ft^2.°F)
#Result:
print "The free convection heat transfer coefficient is :",round(h,3)," Btu/h.ft^2.°F ."
print "There is a calculation mistake in the book for calculating 'Gr', so, value of 'h' alters from that given."
```

In [8]:

```
#Variable declaration:
#From example:
h = 0.675 #Free convection heat transfer coefficient (Btu/h.ft^2.°F)
A = 6.0*8.0 #Area of plate (ft^2)
Ts = 120.0 #Surface temperature of plate (°F)
Too = 60.0 #Ambient temperature of nitrogen (°F)
#Calculation:
Q = h*A*(Ts-Too) #Heat loss (Btu/h)
#Result:
print "The heat loss is :",round(Q,-1)," Btu/h ."
print " The 'h' obtained in the previous example differs, therefore, 'Q' obtained here also fiffers from that given in book."
```

In [9]:

```
#Variable declaration:
Ts = 113.0+273.0 #Surface temperature of bulb (K)
Too = 31.0+273.0 #Ambient air temperature (K)
D = 0.06 #Diameter of sphere (m)
g = 9.8 #Gravitational acceleration (m/s^2)
#Calculation:
Tf = (Ts+Too)/2 #Mean temperature (K)
#From Appendix:
v = (22.38*10**-5)*0.0929 #Kinematic viscosity (m^2/s)
Pr = 0.70 #Prandtl number
k = 0.01735*1.729 #Thermal conductivity (W/m.K)
B = 1.0/(Tf) #Coefficient of expansion (K^-1)
Gr = g*B*(Ts-Too)*D**3/v**2 #Grashof number
Ra = Gr*Pr #Rayleigh number
#From equation 10.13:
h = (k/D)*0.6*Ra**(1.0/4.0) #Heat transferred from bulb (W/m^2.K)
#Result:
print "The heat transferred from bulb to air is :",round(h,2)," W/m^2.K ."
```

In [10]:

```
from math import pi
#Variable declaration:
#From example 10.9:
h = 9.01 #Heat transferred from bulb (W/m^2.K)
D = 0.06 #Diameter of sphere (m)
Ts = 113.0+273.0 #Surface temperature of bulb (K)
Too = 31.0+273.0 #Ambient air temperature (K)
#Calculation:
A = pi*D**2 #Surface area of bulb (m^2)
Q = h*A*(Ts-Too) #Heat transfer lost by free convection from light bulb (W)
#Result:
print "The heat transfer lost by free convection from light bulb is :",round(Q,2)," W ."
```

In [11]:

```
#Variable declaration:
#From example 10.9-10.10:
Q = 8.36 #Heat transfer lost by free convection from light bulb (W)
#Calculation:
E = Q/100.0*(100.0) #Percent energy lost by free convection (%)
#Result:
print "The percentage of the energy lost by free convection is :",round(E,2)," % ."
print "The energy lost fraction is :",round(E/100.0,4)," ."
```

In [13]:

```
#Variable declaration:
F = 50.0 #Buoyancy flux of gas (m^4/s^3)
u = 4.0 #wind speed (m/s)
#Calculation:
xc = 14*F**(5.0/8.0) #Downward distance (m)
xf = 3.5*xc #distance of transition from first stage of rise to the second stage of rise (m)
Dh = 1.6*F**(1.0/3.0)*u**-1*xf**(2.0/3.0) #Plume rise (m)
#Result:
print "The plume rise is :",round(Dh)," m ."
```