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Lecture-1. Governing Laws for Thermal Radiation

Contents of the lecture

1.1 Heat Transfer Mechanisms

1.2 Electromagnetic Radiation

1.6 Geometrical Considerations

1.7 Governing Laws for Thermal Radiation

1.8 Blackbody Radiation in a Wavelength Interval

1.10 Historical Note – Origin of Quantum Mechanics

1.11 Blackbody Emission into a Medium Other than Vacuum

1.12 Summary

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Heat transfer (or heat) is energy in transit due to

a temperature difference

HEAT TRANSFER MODES

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

in J

Heat transfer rate

in W (J/s)

Heat flux

in W/m2

The convention (in this lecture series) is

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Radiation which is given off by a body

because of its temperature is called

thermal radiation

A body of a temperature larger than 0 K

emits thermal radiation

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

A scene from “Silence of the lambs”

A photograph of a car

The number plate has been wiped out

taken with

an

ordinary

camera

taken with

an

infrared

camera

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

RELEVANCE OF THERMAL RADIATION

Whenno medium is present radiation is the only

mode of heat transfer

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

ELECTROMAGNETIC WAVES

Classical theory

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

SPEED, FREQUENCY and WAVELENGTH

For any wave:

Determined by

the source

Determined

by the medium

For electromagnetic waves:

c=3·108 m/s ( in vacuum)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

SPEED, FREQUENCY and WAVELENGTH

For a medium other than vacuum:

The frequency stays the same so,

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

1 micrometer = 10-6 m

1 nanometer = 10-9 m

1 angstrom = 10-10 m

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Photon energy in J

Energy in

electron volts

Number of photons in a joule of energy

Short radio waves

ν=107

4.1·10-8

1.5·1026

4.1

1.5·1018

6.63·10-27

X-rays

ν=1018

6.63·10-16

4.1·103

1.5·1015

Visible light waves

ν=1015

6.63·10-19

Gamma rays

ν=1020

6.63·10-14

4.1·105

1.5·1013

Example 1.1 (Calculate energy of photons)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

1.6 Geometrical Considerations

1.6.1 Normal to a Surface Element

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

in radiance

Example 1.2

Derive formula for calculating the length of an arc and

the circumference of a circle.

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

in steradians

Derive formula for calculating the area of a sphere

How to calculate the solid angle?

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

How to calculate the solid angle?

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

How to calculate the solid angle?

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Now we can complete the integration since we know

how to calculate the solid angle:

Solid angle for a hemisphere is

Solid angle for a sphere is

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

1.6.4 Radiation Intensity and Irradiation

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

for isotropic incoming radiation

Irradiation

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

An important integral in radiation

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

absorptivity

transmissivity

1.7 Governing Laws for Thermal Radiation

1.7.1 Black Body Radiation

Real surfaces (bodies)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Definition of a black body

A black body is defined as an ideal body that all

incident radiationpass into it and internally absorbs

all the incident radiation.

This is true for radiation of all wavelengths and for all angles

of incidence

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Properties:

Black body is a perfect emitter

In a black body enclosure radiation is isotropic

Black body is a perfect emitter in each direction

Black body is a perfect emitter at any wavelength

Total radiation of a black body into vacuum is a

function of temperature only

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

The angular distribution of radiation intensity

emitted by a black body

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

See Example 1.4 of the lecture notes to understand

the meaning of:

Frequency distribution

Cumulative frequency distribution

Relative cumulative frequency distribution

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Histogram and frequency polygon of heights of 130 students

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Cumulative distribution

(less than the upper class boundary)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Students smaller than 174 cm

The relative cumulative distribution

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Cumulative distribution

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

We are looking for a wavelength that maximizes

the Planck’s function for a given temperature

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Stefan-Boltzmann

constant

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

1.8 Blackbody Radiation in a Wavelength Interval

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

1.9 Blackbody Emission into a Medium Other than Vacuum

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Planck’s function in vacuum

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Wien’s Displacement Law

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

1.10 Historical Note – Origin of Quantum Mechanics

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

deriving a and b constants

from the first principle

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Quantification of energy (Max Planck – 1990)

m=1,2,3,... – quantum number

Ten years later Planck wrote:

“My futile attempts to fit the elementary quantum of

action (h) somehow into the classical theory continued for

a number of years, and they cost me a great deal of efforts”

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

In 1905 Albert Einstein made an assumption

the energy of a light was concentrated into

localized bundles – later called photons

Planck, the originator of the h constant, did not accept

at once Einstein’s photons. In 1913 Planck wrote about

Einstein “that he sometimes have missed the target in his

speculations, as for example in his theory of light quanta,

cannot really be held against him”

In 1918 – Planck received a Nobel prize “for his discovery

of energy quanta”

In 1921 – Einstein received his Nobel prize “for his service to

theoretical physics and specially for discovery of the law of photoelectric effect”

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

Students should understand:

The concepts of radiation intensity and emissive power

The radiation laws for black-body radiation

Planck’s law

Wien’s law

Stefan-Boltzmann law

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)

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