Chapter14

Radiation Heat Transfer

Radiation

Definition: It may be considered to be energy streaming through space at the speed of light, may originate in various ways.

Some types of materials will emit radiation when they are treated by external agencies.

All substances at temperatures above absolute zero emit radiation that is independent of external agencies.

Radiation that is the result of temperature only is called

thermal radiation.

Fundamental facts concerning radiation

Radiation moves through space in straight lines, or beams, and only substances in sight of a radiating body can intercept radiation from that body.

Radiation as such is not heat, and when transformed into heat on absorption, it is no longer radiation.

• Some definitions: • The fraction that is absorbed is

called absorptivity α.

The fraction that is transmitted is called transmissivity τ.

The fraction of the radiation falling on a body that is reflected is called reflectivity ρ.

•The sum of these fractions must be unity, or

ρ+ α + τ =1 (14-1)

The maximum possible absorptivity is unity. A body which absorbs all incident radiation is called a black body.

The maximum possible reflectivity is unity. A body which reflects all

incident radiation is called a white body.

Emission of radiation

The radiation emitted by any given mass of substance is independent of other material in sight of , or in contact with the mass.

The net energy gained or lost by a body is the difference between the energy emitted by the body and that absorbed by it from the radiation reaching it from other bodies.

When bodies at different temperatures are placed in sight of one another inside an enclosure, the hotter bodies loss energy by emission of radiation faster than they receive energy by absorption of radiation from the cooler bodies, and temperatures of hotter bodies decrease.

Wavelength of radiation

Known electromagnetic radiations cover an enormous range of wavelengths, from the short cosmic rays to long wave broadcasting wave.

Although radiation of any wavelength is, in principle, convertible into heat on absorption by matter, the portion of the electromagnetic spectrum that is of importance in heat flow lies in the wavelength range between 0.5 and 50µm.

Visible light covers a wavelength range of about 0.38 to 0.78 µm

At temperature above about 5000ºC heat radiation in the visible spectrum become significant.

The higher the temperature of the

radiating body, the shorter the predominant wavelength of the thermal radiation emitted by it.

Emissive power

The monochromatic energy emitted by a radiating surface depends on the temperature of the surface and on the wavelength of the radiation.

At constant surface temperature, a curve can be plotted showing the rate of energy emission as a function of the wavelength.

The monochromatic radiation emitted in this manner from unit area in unit time, divided by the wavelength, is called the monochromatic radiating power Wλ.

For the entire spectrum of the radiation from a surface, the total radiating power W is the sum of all the monochromatic radiations from the surface, or , mathematically,

(14-2)0

W W d

Blackbody radiation

A blackbody has the maximum attainable emissive power at any given temperature. The ratio of the total emissive power W of a body to that of a blackbody Wb is by definition the emissivity ε of the body, thus

b

W

W

Emissivities of solids

Emissivity usually increases with temperature.

Emissivities of polished metals are low, in the range 0.03 to 0.08. Emissivities of most oxidized metals range from 0.6 to 0.85, those of nonmetals from 0.65 to 0.95.

Practical source of blackbody radiation

No actual substance is a blackbody, although some materials, such as certain grades of carbon black, do approach blackness.

Laws of blackbody radiation

A basic relationship for blackbody radiation is the Stefan-Boltzmann law, which states that the total emissive power of a blackbody is proportional to the fourth power of the absolute temperature, or

Wb=σT4 (14-3)

Where σ is a universal constant

The distribution of energy in the spectrum of a blackbody is known accurately. It is given by Planck’s law

(14-7)Where C1 and C2 are constant.

1/2

51

,

TCb e

CW

Planck’s law can be shown to be consistent with the Stefan-Boltzmann law by substituting Wb,λ from Eq(14-7) into Eq(14-2) and integrating.

Absorption of radiation by opaque solids

Kirchhoff’s law

at temperature equilibrium, the ratio of the total radiating power of any body to the absorptivity of that body depends only upon the temperature of the body.

Thus, consider any two bodies in temperature equilibrium with common surroundings. Kirchhoff’s law states that

1 2

1 2

W W

If the first body is blackbody, α1=1,

and

Thus

21

2b

WW W

22

b

W

W

By definition, the emissivity of the second body ε2 is

22 2

b

W

W

• Thus, when any body is at temperature equilibrium with its surroundings, its emissivity and absorptivity are equal. Kirchholff’ law applies whether or not the two surfaces are at same temperature.

Radiation between surfaces The total radiation from a unit

area of an opaque body of area A1, emissivity ε1, and absolute temperature T1 is

(14-14)

41 1

1

qT

A

• Qualitatively, the interception of radiation from an area element of a surface by another surface of finite size can be visualized in terms of the angle of vision.

The equation for two bodies radiating each other can be written in the form

(14-25)

The factor F is called the view factor or angle factor; it depends upon the geometry of the two surface

4 412 1 2q AF T T

If surface A1 is chosen for A, Eq(14-25) can be written

(14-26)

If surface A2 is chosen

(14-27)

4 412 1 12 1 2q A F T T

4 412 2 21 1 2q A F T T

In general, for gray surfaces, Eq(14-26) and Eq(14-27) can be written

F12 and F21 are the overall interchange factor and are functions of ε1 and ε2.

4 4 4 412 1 12 1 2 2 21 1 2q A F T T A F T T

• Two large parallel planes

(14-39)12

1 2

11 1

1F

One gray surface completely surrounded by another

(14-40)12

1

1 2 2

11 1

( 1)F

AA

Combined heat transfer by conduction- convection and radiation

• The total heat transfer from hot bodies to its

• surroundings is as follows

Or

)()(/ 44 TTTThA

q

A

qAq wwwc

rcT

))((/ TThhAq wrcT

• Where hr is a radiation heat transfer coefficient,

• Defined by

)( TTA

qh

w

rr