Short Notes: Radiation Network Analysis | Short Notes for Mechanical Engineering PDF Download

 Page 1


Radiation Network Analysis  
The analysis of radiation exchange between surfaces is complicated because of 
reflection. This can be simplified when surfaces are assumed to be black surfaces 
Planck's Law: Planck suggested following formula, monochromatic emissive power 
of a black body.
Where, c = Velocity of light in vacuum = 2.998 x 1 o8 m/s 
h = Planck’s constant = 6.625 x 10"3 4 J-s 
A = Wavelength, 
k = 1.3805 x 10'2 3 J/K 
T = absolute temperature.
(E/b) = monochromatic emissive power of a black body.
Electrical Network Approach for Radiation Heat Exchange
Consider the radiant heat exchange between two non-black surfaces. An electric
network representing space and surface resistance to radiation are following
£bi J2 ....... ^&2
•—A V A W —•—AW vW —•—ANAAAV—•
A kT
Total missive power
1
At £ 1 A, Ft _ 2 A2s .2
An electrical netw ork betw een tw o non black surfaces
At e -t A2 £ 2
Page 2


Radiation Network Analysis  
The analysis of radiation exchange between surfaces is complicated because of 
reflection. This can be simplified when surfaces are assumed to be black surfaces 
Planck's Law: Planck suggested following formula, monochromatic emissive power 
of a black body.
Where, c = Velocity of light in vacuum = 2.998 x 1 o8 m/s 
h = Planck’s constant = 6.625 x 10"3 4 J-s 
A = Wavelength, 
k = 1.3805 x 10'2 3 J/K 
T = absolute temperature.
(E/b) = monochromatic emissive power of a black body.
Electrical Network Approach for Radiation Heat Exchange
Consider the radiant heat exchange between two non-black surfaces. An electric
network representing space and surface resistance to radiation are following
£bi J2 ....... ^&2
•—A V A W —•—AW vW —•—ANAAAV—•
A kT
Total missive power
1
At £ 1 A, Ft _ 2 A2s .2
An electrical netw ork betw een tw o non black surfaces
At e -t A2 £ 2
((?;-; )*t
Et - Et
1 - £, 1 1 - £,
-----*¦+--------- 1 - -----*-
A: s, A1 Fx _, A: s2
or (Q-:)*r = (Ft V z A ^ ( T*~ T1 ) 
Here, New Gray Body Factor
Al sx Fu A: s2
Where, E -| = Emissivity for body 1 
£2 = Emissivity for body 2 
Cases
• In case of black surfaces, £ 1 = £2 = 1, (Fg ) i2 = F-|.2
• In case of parallel planes, A-\=A2 and F1 .2 = 1
• In case of concentric cylinder or sphere, F-|.2 = 1
(F ) = ________ 1 ________
1 1- g . , h 1 + * A
si si ^2
Where,
A= 1
A: r2
(for concentric cylinder)
A = A
A2 K
(for concentric sphere)
• When a small body lies inside a large enclosure
F. , =1. a « A. =~ A = 0 
' A:
— A + l
Radiation Shield: Radiation shields reduce the radiation heat transfer by effectively 
increasing the surface resistance without actually removing of heat from overall 
system.
Page 3


Radiation Network Analysis  
The analysis of radiation exchange between surfaces is complicated because of 
reflection. This can be simplified when surfaces are assumed to be black surfaces 
Planck's Law: Planck suggested following formula, monochromatic emissive power 
of a black body.
Where, c = Velocity of light in vacuum = 2.998 x 1 o8 m/s 
h = Planck’s constant = 6.625 x 10"3 4 J-s 
A = Wavelength, 
k = 1.3805 x 10'2 3 J/K 
T = absolute temperature.
(E/b) = monochromatic emissive power of a black body.
Electrical Network Approach for Radiation Heat Exchange
Consider the radiant heat exchange between two non-black surfaces. An electric
network representing space and surface resistance to radiation are following
£bi J2 ....... ^&2
•—A V A W —•—AW vW —•—ANAAAV—•
A kT
Total missive power
1
At £ 1 A, Ft _ 2 A2s .2
An electrical netw ork betw een tw o non black surfaces
At e -t A2 £ 2
((?;-; )*t
Et - Et
1 - £, 1 1 - £,
-----*¦+--------- 1 - -----*-
A: s, A1 Fx _, A: s2
or (Q-:)*r = (Ft V z A ^ ( T*~ T1 ) 
Here, New Gray Body Factor
Al sx Fu A: s2
Where, E -| = Emissivity for body 1 
£2 = Emissivity for body 2 
Cases
• In case of black surfaces, £ 1 = £2 = 1, (Fg ) i2 = F-|.2
• In case of parallel planes, A-\=A2 and F1 .2 = 1
• In case of concentric cylinder or sphere, F-|.2 = 1
(F ) = ________ 1 ________
1 1- g . , h 1 + * A
si si ^2
Where,
A= 1
A: r2
(for concentric cylinder)
A = A
A2 K
(for concentric sphere)
• When a small body lies inside a large enclosure
F. , =1. a « A. =~ A = 0 
' A:
— A + l
Radiation Shield: Radiation shields reduce the radiation heat transfer by effectively 
increasing the surface resistance without actually removing of heat from overall 
system.
Radiation shield
A
I
| E l £ 3
f
| U
1 3 2
Radiation shield diagram
f
^ /> 1 . . . « ^ 1 J3 £ & -> ^3 ^2 ^tr
*— vVNM/W— 1• — 1AWVW—1 •
1 - £ i 1 1 - e 1 1 - £ 1 1 1 - e 2
At Ct At Ft-3 At £3 A3 £ 3 ^3 F3-2 A$ e 2
Radiation network for 2 parallel infinite places separated by one shield
(QuX,= (Q -^X, (4 = 4 = 4 )
a < 7 (t;4 - t *) a a cr 3 4 - r / )
1 1
£. i- — 1
1
(61- 2)* =
1+ 1 - 1
Aa(T*-T*)
1 1 1 1 1 1 -r
,£1 £3 . -3 f:
K Q i-:)^] " lth shield
[(Q i-:)« tl " ith o u t s h ie ld
1 + 1 - 1
1 + 1 - 1
If £1 = £2 = £3 
Then,
1 + 1 - 1
(&3)»,= (£-:)»,=
and
t * = l r t4- 7;4)