# Chapter 5 : Steady-state heat conduction in bodies with heat sources¶

## Example 5.1 page : 108¶

In [2]:
# Variables
Di =  10./12;                                      # inside diameter of the coil in ft
x = 7./48;                                         # thickness of coil in ft
ts = 70.5;                                        # Initial temp. of coil in degF
Rm = 12.1;                                        # resistance of coil
e = 0.0024;                                       # Temperature coefficient of coil in degF
i = 0.009;                                        # Initial current in amp
V = 0.1;                                          # Initial Voltage in volts

# Calculations
Rs = V/i;                                         # Initial resistance in ohms
Thm = (Rm/Rs-1)/e;                                # Mean temperature in degF
Th0 = 1.5*Thm;                                    # Increase in temperature in degF
to = ts+Th0;                                      # Maximum temperature in degF

# Results
print "The maximum temperature of the coil was %.1f degF"%(to);

# note : rounding off error

The maximum temperature of the coil was 126.1 degF


## Example 5.2 page : 109¶

In [4]:
import math
# Variables
r = 1./4;                                     # radius in inches
to = 300.;                                    # outer surface temperature of cylinder in degF
q0 = 10.;                                     # i2r heat loss in Btu-in**2/hr
k = 10.;                                      # thermal conductivity of the material in Btu/hr-ft-degF

# Calculations and Results
tc = to+(q0*r*r)*12 /(4*k);                  # temperature at center
delt = tc-to;
print "The temperature diference between center and outer surface is %.2f degF"%(delt);

# Total energy within the cylinder must be transferred to as heat to outer surface

v = math.pi*r**2;                                 # Volume of heatinf element in in**3
q1 = q0*v;                                   # heat flow to outer surface in Btu/sec
tr = -q1*r/(2*k);                            # derivative of temperature wrt radius
q = q1*12;                           # Heat flow at the outer surfae in Btu/hr-ft
print " Heat transfer per unit length at the outer surface is %.1f Btu/hr"%(q);

The temperature diference between center and outer surface is 0.19 degF
Heat transfer per unit length at the outer surface is 23.6 Btu/hr