# Chapter 7 : Heat transfer by free convection¶

## Example 7.1 page : 129¶

In :
# Variables
tp = 200.;                                   # Temperature of heated plate in degF
ta = 60.;                                    # Temperature of air in degF
tf = (tp+ta)/2;                             # Temperature of film in degF
delt = tp-ta;                               # Temperature difference in degF
Z = 950000.;                                 # As referred from the chart for corresponding temperature
L = 18/12.;                                  # Height of vertical plate in ft

# Calculations
X = L**3*(delt)*Z;
# This value shows that it is laminar range so formula is as follows
h = 0.29*(delt/L)**.25;                      # Heat transfer coeeficient in Btu/hr-ft**2-degF

# Results
print "The film coefficient for free convetion for the heated plate is %.1f Btu/hr-ft**2/degF"%(h)

The film coefficient for free convetion for the heated plate is 0.9 Btu/hr-ft**2/degF


## Example 7.2 page : 131¶

In :
# Variables
tp = 300.;                                    # Temperature of heated plate in degF
ta = 80.;                                     # Temperature of air in degF
tf = (tp+ta)/2;                              # Temperature of film in degF
delt = tp-ta;                                # Temperature difference in degF
Z = 610000.;                                  # As referred from the chart for corresponding temperature
L = 7./12;                                    # Height of vertical plate in ft

# Calculations
A = L*L;                                     # Area of square plate in ft**2
X = L**3*(delt)*Z;

# This value shows that it is turbulent range , so formula for heat transfer coefficient is as follow
h = 0.22*delt**(1./3);                         # Temperature coeeficient in Btu/hr-ft**2-degF
q = h*A*delt;                                # Heat loss in Btu/hr

# Results
print "The film coefficient for free convetion for the heated plate is %.2f Btu/hr-ft**2-degF"%(h);
print " The heat loss by natural convection from the square plate is %.2f Btu/hr"%(q);


The film coefficient for free convetion for the heated plate is 1.33 Btu/hr-ft**2-degF
The heat loss by natural convection from the square plate is 99.42 Btu/hr


## Example 7.3 page : 132¶

In :
import math

# Variables
D = 0.375;                                   # Outer diameter in ft
T1 = 200.;                                    # Pipe surface temperature in degF
T2 = 70.;                                     # Air temperature in degF
Tf = (T1+T2)/2;                              # Film temperature at whih physical properties is to be measured
delT = T1-T2;
rho = 0.0667/32.2;                           # Density in slug/ft**3
u = 0.0482/32.2;                             # Vismath.cosity in slug/ft-hr
b = 1./(460+T2 );
Cp = 0.241*32.2;                             # Heat capacity in Btu/slug-ft

# Calculations
# The value of specific heat is related to 1 lb mass so it must be multiplied to 32.2 to convert it into slugs
k = 0.0164;                                  # Thermal conductivity in Btu/hr-ft-degF
g = 32.2*3600;
# Unit of time used is hour so it must be converted to sec. Hence 3600 is multiplied
Ngr = D**3*rho**2*b*g*delT/(u**3);              # Grasshops number
Npr = u*Cp/k;                                # Prandtls number
A = math.log(Ngr*Npr);

# Tha value of A is 6.866
# Now seeing the value of nusselt number from the table
Nnu = 25.2;                                  # Nusselt number
h = Nnu*k/D;                                 # Heat transfer coefficient
q = h*delT;                                  # Heat loss per unit area in Btu/hr

# Results
print "Heat loss per unit square foot is %d Btu/hr-ft**2"%(q);

Heat loss per unit square foot is 143 Btu/hr-ft**2


## Example 7.4 page : 134¶

In :
# Variables
tp = 200.;                                    # Temperature of heated plate in degF
ta = 70.;                                     # Temperature of air in degF
tf = (tp+ta)/2;                              # Temperature of film in degF
delt = tp-ta;                                # Temperature difference in degF
Z = 910000.;                                  # As referred from the chart for corresponding temperature
D = 4.5/12;                                  # Diameter of pipe in ft

# Calculations
X = D**3*(delt)*Z;
# This value lies between X = 1000 to X = 10**9 , so formula for heat transfer coefficient is as follow

h = 0.27*(delt/D)**(1./4);                      # Temperature coeeficient in Btu/hr-ft**2-degF
q = h*delt;                                   # Heat loss in Btu/hr

# Results
print "The film coefficient for free convetion for the heated plate is %.2f Btu/hr-ft**2-degF"%(h);
print " The heat loss by natural convection from the square plateis %d Btu/hr"%(q);

The film coefficient for free convetion for the heated plate is 1.17 Btu/hr-ft**2-degF
The heat loss by natural convection from the square plateis 151 Btu/hr