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MMU FET EME 4016 HEAT TRANSFER

RADIATION 1

Thermal radiation is the mode of heat transfer by electromagnetic (EM) wavesthat are in the range of

wavelengths = 0.1 to 100 , and includes ultraviolet, visible light (0.380.76 ), and infraredregions. All bodies above 0 K emit radiation. The characteristics are

(1)

A medium is not necessary for radiation heat transfer.

(2)

The radiation effect gets more important as the temperature difference increases.

(3)

It is more difficult to analyse than conduction and convection because of the wavelength effect

and the integral effect. However, we will mainly only study the radiative heat transfer between

surfaces, and not the temperature field.

Physical Mechanism

Radiation obeys the law = , where is the speed of light (3 10/), is the wavelength and is the frequency.

Radiation also obeys the quantum energy law = , where is the quantum of energy, isPlanksconstant(not convection coefficient), and is again the frequency.h=6.625 10-34 J.s

Radiation from a black bodyhas a distribution in energy that depends on wavelength as well as on the

temperature of the body, and is governed by Plancks law(1901), derived from quantum-statistical

thermodynamics:

(, ) =

In the above equation, is the radiation flux per unit wavelengthfor a black body [W/m2per m],cisthe speed of light, T is the absolute temperature [K], and kis Boltzmanns constant(not thermal

conductivity now). k= 1.3806610-23 J/moleculeK

When Plancks law is integrated over all wavelengths, the total radiation emitted is called the emissive

power of the black body , in [W/m2], given by

=

=5.669104

where the constant is in [W/m2K4] and known as Stefan-Boltzmanns constant().The result is Stefan-

Boltzmanns law.


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Radiation functions

In theory, the radiation from a black body within any band of wavelengths can be calculated by

evaluating the integration of radiation flux per unit wavelength over that range of wavelengths. In

practice, we use a pre-calculated radiation functionstable instead of doing the integration.

The radiation function F is aratioof the radiation from wavelengths 0 to , to the total radiation (from 0

to ).

F =

= ,, =,

However, because there is another variable temperature T involved, it would be more useful to use

radiation functions based on the product Tinstead of just .It turns out F is indeed a function of T, so

we can write

F =

, =

,

where the term , represents the radiation emitted from T=0 to the current T.

Hence the radiation emitted from to is represented by , =( ,- ,)

Re-writing shows the method to calculate , as

, = 4 [,

,

]

The ratios in the parenthesis (the Fs) are obtained from the table.

Example

A black surface is at 800. Calculate the fraction of the total energy emitted between 3 and 4 .


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Wiens displacement law

This law states that in the variation of radiation flux per unit wavelength for a black body with respect to

the wavelength, there is a peak, corresponding to the wavelength . As the temperature of the bodyincreases, the peak shifts to a lower wavelength in accordance with the rectangular hyperbola

= 2897.6

Radiation properties

Although any body above 0 K gives out radiation following the S-B law, when an external radiation is

incident to a body, three additional effects may occur. The incident radiation may be reflected, absorbed

or transmitted. The fraction of radiation reflected is called reflectivity(), the fraction absorbed is calledabsorptivity(), and the fraction transmitted is called transmissivity (). Obviously, for conservation ofenergy, + + = 1.

In general, there are two types of reflection, specular reflection, where the radiation is reflected like by

a mirror, and diffuse reflectionwhere the radiation is reflected to all direction. Real surfacesmay have

both characteristics.

Gray body

For a non-black or gray body or surface, its emissive power is less than that of a black body , for thesame temperature. Thus < , and we may define a ratio called emissivity .

=

Obviously, for a black body, its emissivity is 1. For a gray body, =

Kirchhorffs law

Kirchhorffs law states that for a gray body in thermal equilibrium, emissivity is equal to absorptivity. In

equation form, = . For a black body, = = 1, meaning all radiation incident are absorbed, andradiation of all wavelengths are emitted.


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Emissivity of real surfaces

The gray body is an idealized real body, or its emissivity is an averaged value of a real surface.

RADIATION EXCHANGE BETWEEN BLACK BODIES

(a) Special case of infinite parallel plates

For two infinite parallel plates 1 and 2, or two finite parallel plates close to each other, there is a

net heat transfer by radiation from 1 to 2, if > , given by

= 4 4 = (4 4)Or = (4 4), where = =

(b) General case where geometry is important.

When not all the radiation from one surface reaches the other surface, then the geometry is

important. For two general surfaces with areas and named

and

, and at temperatures

and

, respectively, the net heat transfer between them may be viewed from two references.

From the point of view of, the net heat transfer by radiation is = (4 4),where represents the fraction of net radiation fromthat reaches.

The is known as a view factor, or shape factor, or configuration factor, or geometric factor,or simply F factor.

However, from the point of view of, the net heat transfer by radiation is = (4 4),

where represents the fraction of net radiation fromthat reaches.


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Clearly, both net heat transfers are the same (there is only one net heat transfer to speak of), we

must have = Or (4 4) = (4 4)

This gives the relation = This is known as the reciprocity relation, a useful relation in view factor manipulation.

In general, in a multiple surfaces situation, the reciprocity relation can always be written for any

pairs of surfaces.

(c) Network representation

We can re-write the heat rate equation = (4 4) as

= (4 4)=( )= ( )

In this way, we can see that the (

) can be regarded as a thermal resistance driven by the

potential of .


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(d)

View factors manipulation

View factor derivations have been widely studied, using purely geometry considerations. In this

course, we will obtain basic view factors from charts (or tables or given equations), and we will

learn manipulations to derive other view factors based on the known basic or given view factors.

In addition to the reciprocity relation, the conservation of energy relationis useful in view factor

manipulations. For instance, if there are 3 surfaces in an enclosure as shown, we can write straight

away the following:

+ + 3 = 1 + + 3 = 13 + 3 + 33 = 1

Example 1

Two parallel black plates 0.5 by 1.0 m are spaced 0.5 m apart. One plate is maintained at 1000 and the other at 500 . What is the net radiant heat exchange between the two plates?

Example 2

Two parallel rectangular plates are each divided into two equal areas as shown. The four surfaces

are denoted by equal areas,,3and4. Describe a way to calculate the view factor 4.


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View factors between parallel coaxial disks


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