Download Lecture 9 Chap.4 Thermal Radiation Introduction

2CH204 Heat Transfer Op. Handouts
Chemical Engineering Department, IT
Lecture 9
Chap.4 Thermal Radiation
Introduction:
The exact nature of radiation is still not fully understood. Two theories have been
proposed to explain the phenomenon of radiation:
Wave theory, proposed by Maxwell.
Quantum theory, proposed by Max Planck.
Thermal radiations exhibit characteristics similar to those of visible light, and follow
optical laws. These can reflected, refracted and are subject to scattering and absorption
when they pass through a media. They get polarized and weakened in strength with
inverse square of radial distance from the radiating surface.
Surface Emission Properties
( I ) Total emissive power (E):
( II ) Monochromatic (spectral ) emissive power ( E ):
(III) Emission from real surface – emissivity:
Emissivity ( ) :
Normal Total Emissivity, n,
Absorptivity, Reflectivity and Transmissivity:
By the conservation of energy principle,
Ga + G r + G t = G
Dividing both sides by G, we get
Ga/G + Gr/G + Gt/G = G/G
++=1
----- ( I )
Black body:
Opaque body:
A transparent body
White body:
Reflections are of two types:
Regular reflection
diffused reflection,
Gray body:
Colored body
Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta
Handouts Prepared by Nimish Shah
-1-
Chap.5 Radiation
2CH204 Heat Transfer Op. Handouts
Chemical Engineering Department, IT
Lecture 10
Black body:
A black body has the following properties:
( I ) It absorbs all the incident radiation falling on it and does not transmit or reflect
regardless of wavelength and direction.
( II ) It emits maximum amount of thermal radiations at all wavelengths at any specified
temperature.
(III) It is a diffuse emitter ( i.e., the radiation emitted by a black body is independent of
direction).
The Stefan- Boltzmann Law:
i.e.
Eb = σ T4
------
(I )
Equation (I ) can be written as
Eb = 5.67 ( T/100)4
Kirchhoff’s Law:
The law states that at any temperature the ratio of total emissive power E to the total
absorptivity α is a constant for all substances, which are in thermal equilibrium with their
environment.
A1 E1 = α1 A 1 Eb
ε=α
(α is always smaller than 1. Therefore, the emissive power E is always smaller than the
emissive power of a black body at equal temperature).
Thus, kirchhoff’s law also states that the emissivity of a body is equal to its absorptivity
when the body remains in thermal equilibrium with its surroundings.
Plank’s Law:
In 1990 Max Plank showed by quantum arguments that the spectrum distribution of the
radiation intensity of a black body is given by
2c 2 h 5
---- (Planck’s law)
( E  )b 
 ch 
exp
 1
 kT 
A plot of (Eλ)b as a function of temperature and wavelength is given in fig.
It should be carefully noted that Plank’s distribution law holds for a hypothetical black body.
Real surfaces show marked deviation from Plank’s law.
Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta
Handouts Prepared by Nimish Shah
-2-
Chap.5 Radiation
2CH204 Heat Transfer Op. Handouts
Chemical Engineering Department, IT
Lecture 11
Wien’s Displacement Law:
In 1893 Wien established a relationship between the temperature of a black body and the
wavelength at which the maximum value of monochromatic emissive power occurs. A peak
monochromatic emissive power occurs at a particular wavelength. Wien’s displacement law
state that the product of λmax and T is constant i.e
λmax T = Constant
i.e.
λmax T = 2898 µ m K = 0.0029 m k
This law holds true for more substances; there is however some daviation in the case of a
metallic conductor where the product λmax T is found to be vary with absolute temperature.
It is used in predicting very high temperature through measurement of wavelength.
A combination of Planck’s law and Wien’s displacement law yields the condition for the
maximum monochromatic emissive power for black body.
5
 2.898 * 10  3 


0
.
374
*
10
T
C 1 (  max )  5


( E b ) max 

2
 C2 
 1.4388 * 10 
 1
 1
exp
exp
3 

 2.898 * 10 
  max T 
or (Eλb )max = 1.285 * 0.10-5 T5
W/m2 per meter wavelength
15
Key points :
1. To find Emissive power or Total Emissive power, use Stefan Boltzmann Law
2. To find Monochromatic Emissive power, use Planck’s Law
3. To find wavelength or Temperature at which radiation is maximum, use Wien’s law.
4. To find maximum Monochromatic Emissive power of body, use combination of
Planck’s Law & Wien’s law.
Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta
Handouts Prepared by Nimish Shah
-3-
Chap.5 Radiation
2CH204 Heat Transfer Op. Handouts
Chemical Engineering Department, IT
Lecture 12
Radiation Shields:
In certain situations it is required to reduce the overall heat transfer between two radiating
surfaces. This is done by either using materials which are highly reflective or by using
radiation shields between the heat exchanging surfaces.
The radiation shields reduce the radiation heat transfer by effectively increasing
the surface resistances without actually removing any heat from the overall system. This
sheets of plastic coated with highly reflecting metallic films on both sides serve as very
effective radiation shields. These are used for the insulation of cryogenic storage tanks. A
familiar application of radiation shields is in the measurement of the temperature of a fluid
by a thermometer or a thermocouple which is shielded to reduce the effects of radiation.
The bulb of a thermometer or a thermocouple junction, used for measurement of
fluid temperature, should be shielded in order to reduce radiation effects to minimum.
Otherwise the temperature indicated may involve some error.
Refer blow fig. Let us consider two parallel planes, 1 and 2, each of area A ( A1 = A 2
= A) at temperatures T1 & T2 respectively with a radiation shield placed between them as
shown in below fig.
1
1

1
[(Q12 ) net ] with shield
1  2
- (VII)

[(Q12 ) net ] without shield  1
  1

1
1
 
 1    
 1 




3
2
 1
  2

(Q12 ) net 
A (T14  T24 )
 1 
1
1

 2   2
1  2
3 
Reference: Engineering Heat Transfer By R.Prakash & C.D.Gupta
Handouts Prepared by Nimish Shah
-4-
Chap.5 Radiation