RadiationFundamental Concepts

EGR 4345

Heat Transfer

Thermal Radiation

Occurs in solids, liquids, and gases Occurs at the speed of light Has no attenuation in a vacuum Can occur between two bodies with a colder

medium in between

Fundamental Concepts

Ts > Tsur

q rad,net

Types of Radiation

Two categories– Volumetric phenomenon – gases, transparent solids– Surface phenomenon – most solids and liquids

Thermal radiation – emitted by all substances above absolute zero

Includes visible & infrared radiation & some UV radiation.

Fundamental Concepts

Background

Electromagnetic radiation – energy emitted due to changes in electronic configurations of atoms or molecules

where =wavelength (usually in m), =frequency In a vacuum c=co=2.998x108 m/s

Other media: c= co /n where n=index of refraction

c

Background, cont.

Radiation – photons or waves? Max Planck (1900): each photon has an

energy of

h=Planck’s constant=6.625 x 10-34 Js Shorter wavelengths have higher energy

hche

Radiation Spectrum

Radiation Properties

Magnitude of radiation varies with wavelength – it’s spectral.

Radiation is made up of a continuous, nonuniform distribution of monochromatic (single-wavelength) components.

Magnitude & spectral distribution vary with temp & type of emitting surface.

Emission Variation with Wavelength

Radiation Properties

Directional distribution – a surface doesn’t emit the same in all directions.

Nomenclature

Nomenclature

Nomenclature

Spectral Intensity

Spectral Intensity of the Emitted Radiation, I,e

– Rate at which radiant energy is emitted at the wavelength, , in the (, ) direction, per unit solid angle about this direction, and per unit wavelength interval d about

Spectral Intensity

Spectral Intensity

Heat Flux

Emissive Power

Spectral, hemispherical emissive power – E

– Rate at which radiation of wavelength is emitted in all directions from a surface per unit wavelength d about and per unit surface area

– Flux based on actual surface area (not projected)– Hemispherical often not used as emission is in all

directions from surface

Total emissive power, E

Emissive Power

Emissive Power

Diffuse emitter – intensity of the emitted radiation independent of direction

ee II ,, ,,

Spectral Irradiation

Spectral Irradiation, G – Rate at which radiation of wavelength is incident

on a surface per unit area of the surface and per unit wavelength d about

Total Irradiation, G

Spectral Irradiation

Spectral Radiosity

Spectral Radiosity, J – Rate at which radiation of wavelength is leaves a

unit area of surface, per unit wavelength interval d about

Total Radiosity, J

Spectral Radiosity

Blackbody Radiation

Blackbody – a perfect emitter & absorber of radiation Emits radiation uniformly in all directions – no

directional distribution – it’s diffuse Joseph Stefan (1879)– total radiation emission per

unit time & area over all wavelengths and in all directions:

=Stefan-Boltzmann constant =5.67 x10-8 W/m2K4

24 mW TEb

Planck’s Distribution Law

Sometimes we’re interested in radiation at a certain wavelength

Spectral blackbody emissive power (Eb) = “amount of radiation energy emitted by a blackbody at an absolute temperature T per unit time, per unit surface area, and per unit wavelength about the wavelength .”

Planck’s Distribution Law

Emitted radiation varies continuously with At any the magnitude of the emitted radiation

increases with increasing temperature The spectral region in which the radiation is

concentrated depends on temperature, with comparatively more radiation appearing at the shorter as the temperature increases

Sun – approximated as a blackbody at 5800 K, radiation is mostly in the visible region

Planck’s Distribution Law

For a surface in a vacuum or gas

Other media: replace C1 with C1/n2

Integrating this function over all gives us the equation for Eb.

constant sBoltzmann'J/K 1038051

Kμm 104391

mμmW 1074232

where

μmmW 1

23

42

24821

2

25

1

-

o

o

b

x.k

x.khcC

x.hcC

TCexp

CTE

Radiation Distribution

Radiation is a continuous function of wavelength

Radiation increases with temp.

At higher temps, more radiation is at shorter wavelengths.

Solar radiation peak is in the visible range.

Wien’s Displacement Law

Peak can be found for different temps using Wien’s Displacement Law:

Note that color is a function of absorption & reflection, not emission

Km 52897 .T powermax

Blackbody Radiation Function

We often are interested in radiation energy emitted over a certain wavelength.

This is a tough integral to do!

Blackbody Radiation Function

Use blackbody radiation function, F

If we want radiation between 1 & 2,

40

T

dTE

TF

b

TFTFTF1221