# Chapter 8: Unsteady-State Heat Conduction¶

### ILLUSTRATIVE EXAMPLE 8.4, Page number: 122¶

In [4]:
from math import pi,sin,e

#Variable declaration:
k = 9.1                 #Thermal coductivity of steel rod (Btu/h.ft.°F)
p = 0.29*1728           #Density of steel rod (lb/ft^3)
Cp = 0.12               #Heat capacity of steel rod (Btu/lb.°F)
P = 15+14.7             #Absolute pressure (psia)
Ta = 71.0               #Initial temperature (°F)
L = 20.0/12.0           #Length of rod (ft)
t = 30.0/60.0           #Time taken (h)
x = 0.875/12.0          #Length from one of end (ft)
#From assumption:
n = 1.0                 #First term
#From tables in Appendix:
Ts = 249.7              #Saturated steam temperature (°F)

#Calculation:
a = k/(p*Cp)            #Thermal diffusivity  (ft^2/s)
T = Ts+(Ta-Ts)*(((n+1)*(-1)**2 + 1 )/pi)*e**((-a*((n*pi)/L)**2)*t)*sin((n*pi*x)/L) #Temperature 0.875 inches from one of the ends after 30 minutes (°F)

#Result:
print "The temperature 0.875 inches from one of the ends after 30 minutes is :",round(T)," °F."

The temperature 0.875 inches from one of the ends after 30 minutes is : 232.0  °F.