In [1]:

```
from __future__ import division
import math
#Variables
k=35; #Thermal Conductivity, [W/m*K]
T1=110 # Temperature of front[C]
T2=50; # Temperature of back,[C]
A=0.4 #area of slab,[m**2]
x=0.03; #Thickness of slab,[m]
#Calculations
q=-k*(T2-T1)/(1000*x); #formula for heat flux[KW/m^2]
Q=q*A; #formula for heat transfer rate[KW]
#Results
print "Heat flux is:",q,"KW/m^2\n"
print "Heat transfer rate is:",Q,"KW \n"
```

In [2]:

```
from __future__ import division
import math
from sympy import solve,symbols
#Variables
x=symbols('x');
k1=372; # Thermal Conductivity of slab,W/m*K
x1=0.003; # Thickness of slab,m
x2=0.002 # Thickness of steel,m
k2=17; # Thermal Conductivity of steel,W/m*K
T1=400; # Temperature on one side,C
T2=100 #Temperature on other side,C
#Calculations
Tcu=solve(x+2*x*(k1/x1)*(x2/k2)-(T1-T2),x);
#q=k1*(Tcu/x1)=k2*(Tss/x2);
Tss = Tcu[0]*(k1/x1)*(x2/k2); # formula for temperature gradient in steel side
Tcul=T1-Tss;
Tcur=T2+Tss;
q=k2*Tss/(1000*x2); # formula for heat conducted, kW\m^2
#Results
print "Temperature on left copper side is :",round(Tcul,3),"C\n"
print "Temperature on right copper side is :",round(Tcur,3),"C\n"
print "Heat conducted through the wall is :",round(q,3),"kW\m^2\n"
print "Our initial approximation was accurate within a few percent."
```

In [3]:

```
from __future__ import division
import math
#Variables
q1=6000; #Heat flux, W*m**-2
T1=120; #Heater Temperature, C
T2=70; #final Temperature of Heater, C
q2=2000; #final heat flux, W*m**-2
#Calculations
h=q1/(T1-T2) #formula for average heat transfer cofficient
Tnew=T2+q2/h; #formula for new Heater temperature, C
#Results
print "Average Heat transfer coefficient is:",h,"W/(m^2*K)\n"
print "New Heater Temperature is:",round(Tnew,3),"C\n"
```

In [4]:

```
from __future__ import division
import math
from numpy import array
from numpy import linspace
import matplotlib.pyplot as plt
from pylab import *
%matplotlib inline
#Variables
h=250; #Heat Transfer Coefficient, W/(m**2*K)
k=45; #Thermal Conductivity, W/(m*K)
c=180; #Heat Capacity, J/(kg*K)
a=9300; #density, kg/m**3
T1=200; #temperature, C
D=0.001; #diameter of bead, m
t1=linspace(0,5,50); #defining time interval of 0.1 seconds
T=linspace(0,5,50);
i=0;
#Calculations
while i<50:
T[i]=T1-c*math.exp(-t1[i]/((a*c*D)/(6*h))); #Calculating temperature at each time in degree C
i=i+1;
plt.plot(t1,T);
plt.xlabel("Time(in sec)");
plt.ylabel("Temperature(in degree C)");
plt.title("Thermocouple response to a hot gas flow");
plt.show();
Bi = h*(D/2)/k; #biot no.
#Results
print "The value of Biot no for this thermocouple is",round(Bi,5);
print "Bi is <0.1 and hence the thermocouple could be considered as a lumped heat capacity system and the assumption taken is valid.\n"
```

In [1]:

```
from __future__ import division
import math
from sympy import solve,symbols
#Variables
x=symbols('x');
T1=293; #Temperature of air around thermocouple, K
T2=373; #Wall temperature, K
h=75; #Average Heat Transfer Coefficient, W/(m**2*K)
s=5.67*10**-8; #stefan Boltzman constant, W/(m**2*K**4)
#Calculations
x=solve((h*(x-T1)+s*(x**4-T2**4)),x); #Calculating Thermocouple Temperature, K
y=x[1]-273; #Thermocouple Temperature, C
#Results
print "Thermocouple Temperature is :",round(y,3),"C\n"
```

In [3]:

```
from __future__ import division
import math
from sympy import solve,symbols
#Variables
x=symbols('x');
e=0.4; #emissivity
T1=293; #Temperature of air around Thermocouple, K
T2=273; #wall Temperature, K
h=75; #Average Heat Transfer Coefficient, W/(m**2*K)
s=5.6704*10**-8; #stefan Boltzman constant, W/(m**2*K**4)
#Calculations
z=solve(((s*e*((373)**4 - (x)**4)) - h*(x-293)),x); #Calculating Thermocouple Temperature, K
y=z[0]-273; #Thermocouple Temperature, C
'''NOTE: Equation written is absolutely correct and solving this equation
should give real result as: 296.112 i.e. 23.112 C, but somehow python is giving wrong result.'''
#Results
print "Thermocouple Temperature is :",round(y,1),"C \n"
```