Chapter 9: Forced Convection

ILLUSTRATIVE EXAMPLE 9.1, Page number: 135

In [9]:
#Variable declaration:
D = 1.0                     #Diamete of vessel (ft)
L = 1.5                     #Length of vessel (ft)
T1 = 390.0                  #Surface temperature of vessel (°F)
T2 = 50.0                   #Surrounding temperature of vessel (°F)
h = 4.0                     #Convective heat transfer coefficient (Btu/h.ft.°F)

#Calculation:
A = pi*D*L+2*pi*(D/2)**2    #Total heat transfer area (ft^2)
Q = h*A*(T1-T2)             #Rate of heat transfer (Btu/h)
R = 1/(h*A)                 #Thermal resistance (°F.h/Btu)

#Result:
print "The thermal resistance of vessel wal is :",round(R,4)," °F.h/Btu ."
The thermal resistance of vessel wal is : 0.0398  °F.h/Btu .

ILLUSTRATIVE EXAMPLE 9.2, Page number: 135

In [2]:
'''Referring to the previous example, convert the resistance to K/W and °C/W.
'''

#Variable declaration:
#From example 9.1:
R = 0.0398                      #Theral resistance (°F.h/Btu)
Btu = 3.412                     #Btu/h in a watt
C = 1.8                         #Change in degree fahrenheit for a degree change in celsius
K = 1                           #Change in degree celsius for a unit change in Kelvin

#Calculation:
Rc = R*Btu/C                    #Thermal resistance in degree cesius per watt (°C/W)
Rk = Rc/K                       #Thermal resistance in Kelvin per watt (K/W)

#Result:
print "The thermal resistance in °C/W is :",round(Rc,3)," °C/W."
print "The thermal resistance in K/W is :",round(Rk,3)," K/W."
The thermal resistance in °C/W is : 0.075  °C/W.
The thermal resistance in K/W is : 0.075  K/W.

ILLUSTRATIVE EXAMPLE 9.3, Page number: 136

In [3]:
#Variable declaration:
h = 48.0                    #Convective heat transfer coefficient (Btu/h.ft.°F)
A = 2*1.5                   #Total heat transfer area (ft^2)
Ts = 530.0                  #Surface temperature of plate (°F)
Tm = 105.0                  #Maintained temperature of opposite side of plate (°F)
kW = 3.4123*10**3           #Units kW in a Btu/h

#Calculation:
Q = h*A*(Ts-Tm)             #Heat transfer rate in Btu/h (Btu/h)
Q1 = Q/kW                   #Heat transfer rate in kW (kW)

#Result:
print "The heat transfer rate in Btu/h is :",round(Q)," Btu/h."
print "The heat transfer rate in kW is :",round(Q1,2)," kW."
The heat transfer rate in Btu/h is : 61200.0  Btu/h.
The heat transfer rate in kW is : 17.94  kW.

ILLUSTRATIVE EXAMPLE 9.4, Page number: 136

In [22]:
#Variable declaration:
TS = 10+273                     #Outer surface temperature of wall (K)
Q = 3000.0                      #Heat transfer rate (W)
h = 100.0                       #Convection coefficient of air (W/m^2)
A = 3.0                         #Area of glass window (m^2)

#Calculation:
TM = TS-Q/(h*A)                 #Bulk temperature of fluid (K)

#Result:
print "The bulk temperature of fluid is :",round(TM)," K."
print "The bulk temperature of fluid is :",round(TM-273)," °C."
The bulk temperature of fluid is : 273.0  K.
The bulk temperature of fluid is : 0.0  °C.

ILLUSTRATIVE EXAMPLE 9.5, Page number: 137

In [23]:
#Variable declaration:
h = 24.0                    #Plant operating hour per day (h/day)
d = 350.0                   #Plant operating day per year (day/yr)

#Calculation:
N = h*d                     #Operating hours per year (h/yr)
#From example 9.1:
Q = 8545.0                  #Rate of energy loss (Btu/h)
Qy = Q*N                    #Steady-state energy loss yearly (Btu/yr)

#Result:
print "The yearly steady-state energy loss is :",round(Qy/10**7,2)," x 10^7 Btu/yr."
The yearly steady-state energy loss is : 7.18  x 10^7 Btu/yr.

ILLUSTRATIVE EXAMPLE 9.7, Page number: 148

In [25]:
from sympy import symbols, integrate

#Variable declaration:
x = 0.3                         #Length from the leading age of the plate (m)
L = 1.2                         #Length of plate (m)
TS = 58.0                       #Surface temperature of plate (°C)
Ta = 21.0                       #Temperature of flowing air (°C)

#Calculation:
hx = 25/x**0.4                  #Local heat transfer coefficient at 0.3m (W/m^2.K) (Part 1)
y = symbols('y')                #Length
hy = 25/y**0.4                  #hx at the end of the plate (W/m^2.K)
h = integrate(hy, (y,0,L))/L    #Average heat transfer coefficient (W/m^2.K)
Q = hx*(TS-Ta)                  #Heat flux at 0.3m from leading edge of plate (W/m^2)
hL = 25/L**0.4                  #Local heat transfer coefficient at plate end (W/m^2.K) (Part 2) 
r = h/hL                        #Ratio h/hL at the end of the plate

#Result:
print "1. The heat flux at 0.3 m from the leading edge of the plate is :",round(Q)," W/m^2."
print "2. The local heat transfer coefficient at the end of the plate is :",round(hL,1)," W/m^2.K."
print "3. The ratio h/hL at the end of plate is :",round(r,3)," ."
1. The heat flux at 0.3 m from the leading edge of the plate is : 1497.0  W/m^2.
2. The local heat transfer coefficient at the end of the plate is : 23.2  W/m^2.K.
3. The ratio h/hL at the end of plate is : 1.667  .

ILLUSTRATIVE EXAMPLE 9.8, Page number: 150

In [26]:
#Variable declaration:
#From example 9.7:
b = 1.0                     #Width of plate (m)
L = 1.2                     #Length of plate (m)
TS = 58.0                   #Surface temperture of plate (°C)
Ta = 21.0                   #Air flow temperature (°C)
h = 38.7                    #Average heat transfer coefficient (W/m^2.K)

#Calculation:
A = b*L                     #Area for heat transfer for the entire plate (m^2)
Q = h*A*(TS-Ta)             #Rate of heat transfer over the whole length of the plate (W)

#Result:
print "The rate of heat transfer over the whole length of the plate is :",round(Q,-1)," W."
The rate of heat transfer over the whole length of the plate is : 1720.0  W.

ILLUSTRATIVE EXAMPLE 9.9, Page number: 150

In [27]:
from math import pi
#Variable declaration:
m = 0.075                           #Mass rate of air flow (kg/s)
D = 0.225                           #Diameter of tube (m)
mu = 208*10**-7                     #Dynamic viscosity of fluid (N)
Pr = 0.71                           #Prandtl number
k = 0.030                           #Thermal conductivity of air (W/m.K)

#Calculation:
Re = 4*m/(pi*D*mu)                  #Reynolds number
#From equation 9.26:
Nu = 0.023*(Re**0.8)*(Pr**0.3)      #Nusselt number
h = (k/D)*Nu                        #Heat transfer coefficient of air (W/m^2.K)

#Result:
print "The Heat transfer coefficient of air is :",round(h,2)," W/m^2.K."
The Heat transfer coefficient of air is : 7.76  W/m^2.K.

ILLUSTRATIVE EXAMPLE 9.10, Page number: 150

In [4]:
#Variable declaration:
D = 0.902/12.0                  #Inside diameter of tube (ft)
T_in = 60.0                     #Temperature water entering the tube (°F)
T_out = 70.0                    #Temperature water leaving the tube (°F)
V = 7.0                         #Average wave velocity water (ft/s)
p = 62.3                        #Density of water (lb/ft^3)
mu = 2.51/3600.0                #Dynamic viscosity of water (lb/ft.s)
Cp = 1.0                        #Viscosity of centipoise (Btu/lb.°F)
k = 0.34                        #Thermal conductivity of water (Btu/h.ft.°F)

#Calculation:
Re = D*V*p/mu                   #Reynolds Number
Pr = Cp*mu/k*3600               #Prandtl number
#From equation 9.26:
Nu = 0.023*(Re**0.8)*(Pr**0.4)  #Nusselt number
h = (k/D)*Nu                    #Average film heat transfer coefficient (Btu/h.ft^2.°F)

#Result:
print "The required average film heat transfer coefficient is :",round(h)," Btu/h.ft^2.°F."
The required average film heat transfer coefficient is : 1265.0  Btu/h.ft^2.°F.

ILLUSTRATIVE EXAMPLE 9.11, Page number: 151

In [10]:
#Variable declaration:
P = 1.0132 * 10**5              #Air pressure (Pa)
T = 300.0+273.0                 #Air temperature (K)
V = 5.0                         #Air flow velocity (m/s)
D = 2.54/100.0                  #Diameter of tube (m)
R = 287.0                       #Gas constant (m^2/s^2.K)
#From Appendix:
Pr = 0.713                      #Prandtl number of nitrogen
mu = 1.784*10**(-5)             #Dynamic viscosity of nitrogen (kg/m.s)
k = 0.0262                      #Thermal conductivity of nitrogen (W/m.K)
Cp = 1.041                      #Heat capacity of nitrogen (kJ/kg.K)

#Calculation:
p = P/(R*T)                     #Density of air
Re = D*V*p/mu                   #Reynolds number
#From table 9.5:
Nu = 0.023*(Re**0.8)*(Pr**0.3)  #Nusselt number
h = (k/D)*Nu                    #Heat transfer coefficient (W/m^2.K)

#Result:
print "The required Heat transfer coefficient is :",round(h,2)," W/m^2.K."
The required Heat transfer coefficient is : 17.57  W/m^2.K.

ILLUSTRATIVE EXAMPLE 9.12, Page number: 152

In [11]:
#Variable declaration:
T1 = 15.0                   #Water entering temperature (°C)
T2 = 60.0                   #Water leaving temperature (°C)
D = 0.022                   #Inside diameter of tube (m)
V = 0.355                   #Average water flow velocity (m/s)
TC = 150.0                  #Outside wall temperature (°C)
#From Appendix:
p = 993.0                   #Density of water (kg/m^3)
mu = 0.000683               #Dynamic viscosity of water (kg/m.s)
Cp = 4.17*10**3             #Heat capacity of water (J/kg.K)
k = 0.63                    #Thermal conductivity of water (W/m.K)

#Calculation:
Tav1 = (T1+T2)/2.0          #Average bulk temperature of water (°C)
Re = D*V*p/mu               #Reynolds number
Pr = Cp*mu/k                #Prandtl number
Tav2 = (Tav1+TC)/2.0        #Fluid's average wall temperature (°C)
#From Appendix:
mu_w = 0.000306             #Dynamic viscosity of fluid at wall (kg/m.s)
#From Table 9.5:
h = (k/D)*0.027*Re**0.8*Pr**0.33*(mu/mu_w)**0.14    #Heat transfer coefficient for water (W/m^2.K)

#Result:
print "The heat transfer coefficient for water is :",round(h,1)," W/m^2.K."
The heat transfer coefficient for water is : 2497.3  W/m^2.K.

ILLUSTRATIVE EXAMPLE 9.13, Page number: 153

In [12]:
#Variable declaration:
#From example 9.7:
h = 38.7                    #Average heat transfer coefficient (W/m^2.K)
L = 1.2                     #Length of plate (m)
k = 0.025                   #Thermal conductivity of air (W/m)

#Calculation:
Bi = h*L/k                  #Average Biot number

#Result:
print "The average Biot number is :",round(Bi)," ."
The average Biot number is : 1858.0  .

ILLUSTRATIVE EXAMPLE 9.14, Page number: 154

In [14]:
from math import pi
#Variable declaration:
k = 60.0                    #Thermal conductivity of rod (W/m.K)
p = 7850.0                  #Density of rod (kg/m^3)
Cp = 434.0                  #Heat capacity of rod (J/kg.K)
h = 140.0                   #Convection heat transfer coefficient (W/m^2.K)
D = 0.01                    #Diameter of rod (m)
kf = 0.6                    #Thermal conductivity of fluid (W/m.K)
L = 2.5                     #Length of rod (m)
Ts = 250.0                  #Surface temperature of rod (°C)
Tf = 25.0                   #Fluid temperature (°C)

#Calculation:
#Case 1:
a = k/(p*Cp)                #Thermal diffusivity of bare rod (m^2/s)
#Case 2:
Nu = h*D/kf                 #Nusselt number
#Case 3:
Bi = h*D/k                  #Biot number of bare rod
#Case 4:
Q = h*(pi*D*L)*(Ts-Tf)      #Heat transferred from rod to fluid (W)

#Result:
print "1. The thermal diffusivity of the bare rod is :",round(a/10**-5,2)," x 10^-5 m^2/s."
print "2. The nusselt number is :",round(Nu,2)," ."
print "3. The Biot number is :",round(Bi,4)," ."
print "4. The heat transferred from the rod to the fluid is :",round(Q)," W."
1. The thermal diffusivity of the bare rod is : 1.76  x 10^-5 m^2/s.
2. The nusselt number is : 2.33  .
3. The Biot number is : 0.0233  .
4. The heat transferred from the rod to the fluid is : 2474.0  W.