# Chapter 9 : Thermal radiation basic relations¶

## Example 9.1 Page No : 378¶

In [1]:
import math

# Variables
T = 5527;			#Temperature of black body in degree C
D = (1.39*10**6);			#Diameter of the sun in km
L = (1.5*10**8);			#Distance between the earth and sun in km

# Calculations
q = (5.67*10**-8*(T+273)**4*D**2)/(4*L**2);			#Rate of solar radiation in W/m**2

# Results
print 'Rate of solar radiation on a plane normal to sun rays is %3.0f W/m**2'%(q)

Rate of solar radiation on a plane normal to sun rays is 1377 W/m**2


## Example 9.2 Page No : 383¶

In [2]:
# Variables
T = (727+273);			#Temperature of black body in K
l1 = 1;			#Wavelength in micro meter
l2 = 5;			#Wavelength in micro meter
F1 = 0.0003;			#From Table 9.2 on page no. 385
F2 = 0.6337;			#From Table 9.2 on page no. 385

# Calculations
a = (5.67*10**-8*T**4)/1000;			#Heat transfer in kW/m**2
F = (F2-F1)*a;			#Fraction of thermal radiation emitted by the surface in kW/m**2

# Results
print 'Fraction of thermal radiation emitted by the surface is %3.1f kW/m**2'%(F)

Fraction of thermal radiation emitted by the surface is 35.9 kW/m**2


## Example 9.3 Page No : 384¶

In [3]:
# Variables
t = 0.8;			#Transmittivity of glass in the region except in the wave length region [0.4,3]
T = 5555;			#Temperature of black body in K

# Calculations
ao = 0;			#a0 in micro K
a1 = (0.4*T);			#a1 for the wavelength 0.4 micro meter in micro K
a2 = (3*T);			#a1 for the wavelength 3 micro meter in micro K
F0 = 0;			#From Table 9.2 on page no.385
F1 = 0.10503;			#From Table 9.2 on page no.385
F2 = 0.97644;			#From Table 9.2 on page no.385
t1 = t*(F2-F1);			#Average hemispherical transmittivity of glass

# Results
print 'Average hemispherical transmittivity of glass is %3.2f'%(t1)

Average hemispherical transmittivity of glass is 0.70


## Example 9.4 Page No : 386¶

In [1]:
# Variables
l = 0.5;			#Wavelength at maximum intensity of radiation in micro meter
C3 = 0.289*10**-2   #mK

# Calculations
T = C3/(l*10**-6);			#Temperature according to Wien's print lacement law in degree C
E = (5.67*10**-8*T**4)/10**6;			#Emissive power umath.sing Stefan-Boltzmann law in MW/m**2

# Results
print 'Surface temperature is %3.0f K Emissive power is %3.1f MW/m**2'%(T,E)

Surface temperature is 5780 K Emissive power is 63.3 MW/m**2


## Example 9.5 Page No : 389¶

In [6]:
# Variables
Ts = (827+273);			#Surface temperature in degree C
E = (1.37*10**10);			#Emmisive power in W/m**3

# Calculations
Eblmax = (1.307*10**-5*Ts**5);			#Maximum emissive power in W/m**3
e = (E/Eblmax);			#Emissivity of the body
lmax = ((0.289*10**-2)/Ts)/10**-6;			#Wavelength correspoing to the maximum spectral intensity of radiation in micro meter

# Results
print 'Wavelength corresponding to the maximum spectral intensity of radiation is %3.2f micro meter'%(lmax)

Wavelength corresponding to the maximum spectral intensity of radiation is 2.63 micro meter


## Example 9.6 Page No : 389¶

In [7]:
import math
# Variables
T = (1400+273);			#Temperature of the body in K
l = 0.65;			#Wavelength in micro meter
e = 0.6;			#Emissivity

# Calculations
T = (1./((1./T)-((l*10**-6*math.log(1./e))/(1.439*10**-2))));			#Temperature of the body in K
Tb = (T-273);			#Temperature of the body in degree C

# Results
print 'Temperature of the body is %3.0f degree C'%(Tb)

Temperature of the body is 1467 degree C


## Example 9.7 Page No : 391¶

In [2]:
# Variables
Ts = (37+273);			#Temperature of metallic bar in K
T = 1100;			#Interior temperature in K
a = 0.52;			#Absorptivity at 1100 K
e = 0.8;			#Emissivity at 310 K

# Calculations
Q = (a*5.67*10**-8*T**4)/1000;			#Rate of absorption in kW/m**2
E = (e*5.67*10**-8*Ts**4)/1000;			#Rate of emission in kW/m**2

# Results
print 'Rate of absorption is %3.2f kW/m**2 \n \
Rate of emission is %3.2f kW/m**2'%(Q,E)

Rate of absorption is 43.17 kW/m**2
Rate of emission is 0.42 kW/m**2


## Example 9.8 Page No : 391¶

In [9]:
# Variables
e1 = 0.3			#Emissivity of glass upto 3 micro meter
e2 = 0.9;			#Emissivity of glass above 3 micro meter
t = 0.8;			#Transmittivity of glass in the region except in the wave length region [0.4,3]

# Calculations
E = (5.67*10**-8*5780**4)/10**6;			#Emissive power in MW/m**2
F1 = 0.10503;			#From Table 9.2 on page no.385
F2 = 0.97644;			#From Table 9.2 on page no.385
I = (E*10**6*(F2-F1))/10**6;			#Total incident radiation in MW/m**2
T = (t*I);			#Total radiation transmitted in MW/m**2
t1 = (e1*I);			#Absorbed radiation in MW/m**2 in wavelength  [0.4,3] micro meter
t2 = (e1*E*F1);			#Absorbed radiation in MW/m**2 in wavelength not in the range [0.4,3] micro meter
t3 = (e2*(1-F2)*E);			#Absorbed radiation in MW/m**2 in wavelength greater than 3 micro meter
R = (t1+t2+t3);			#Total radiation absorbed in MW/m**2

# Results
print 'Total radiation transmitted is %3.2f MW/m**2 \n \
Total radiation absorbed is %3.2f MW/m**2'%(T,R)

Total radiation transmitted is 44.12 MW/m**2
Total radiation absorbed is 19.88 MW/m**2