Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Lecture-1. Governing Laws for Thermal Radiation Contents of the lecture 1.1 Heat Transfer Mechanisms 1.6 Geometrical Considerations 1.7 Governing Laws for Thermal Radiation 1.8 Blackbody Radiation in a Wavelength Interval 1.11 Blackbody Emission into a Medium Other than Vacuum 1.10 Historical Note – Origin of Quantum Mechanics 1.12 Summary 1.2 Electromagnetic Radiation

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) What is heat transfer? 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/ Lecture 1 (Governing Laws) The convention (in this lecture series) is Heat transfer ratein W (J/s) Amount of heat (energy) in J Heat fluxin W/m 2

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ 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/ Lecture 1 (Governing Laws) A scene from “Silence of the lambs” taken with an ordinary camera taken with an infrared camera A photograph of a car The number plate has been wiped out

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) RELEVANCE OF THERMAL RADIATION When no medium is present radiation is the only mode of heat transfer

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) ELECTROMAGNETIC WAVES Classical theory Quantum theory

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

SPEED, FREQUENCY and WAVELENGTH For any wave: Determined by the medium Determined by the source For electromagnetic waves: c=3·10 8 m/s ( in vacuum)

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ 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/ Lecture 1 (Governing Laws) COMMON UNITS FOR WAVELENGTH 1 micrometer = m 1 nanometer = m 1 angstrom = m

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Example 1.1 (Calculate energy of photons) Frequency (Hz) Photon energy in J Energy in electron volts Number of photons in a joule of energy Short radio waves ν= · · ·10 26 Visible light waves ν= · ·10 18 X-rays ν= · · ·10 15 Gamma rays ν= · · ·10 13

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

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) 1.6 Geometrical Considerations Normal to a Surface Element

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

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Example 1.2 Derive formula for calculating the length of an arc and the circumference of a circle. Plane angle in radiance

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Derive formula for calculating the area of a sphere The solid angle in steradians How to calculate the solid angle?

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) How to calculate the solid angle?

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) How to calculate the solid angle?

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

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Radiation Intensity and Irradiation indicates direction

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Irradiation for isotropic incoming radiation

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) For isotropic radiation An important integral in radiation

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Black Body Radiation Real surfaces (bodies) reflectivity absorptivity transmissivity 1.7 Governing Laws for Thermal Radiation

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) BLACK BODY RADIATION Definition of a black body A black body is defined as an ideal body that all incident radiation pass 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/ Lecture 1 (Governing Laws) BLACK BODY RADIATION 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/ 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/ Lecture 1 (Governing Laws) Planck’s Radiation Law

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Planck’s Radiation Law

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Planck’s Radiation Law

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ 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/ Lecture 1 (Governing Laws) Height per class (cm) Number of students -Frequency Class mark (cm) TOTAL Example 1.4

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Histogram and frequency polygon of heights of 130 students Example 1.4

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Example 1.4

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Height (cm)Number of students Less than 153 cm Less than 160 cm Less than 167 cm Less than 174 cm Less than 181 cm Less than 188 cm Less than 195 cm Less than 201 cm Less than 208 cm Cumulative distribution (less than the upper class boundary) Example 1.4

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Students smaller than 174 cm The relative cumulative distribution Example 1.4

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Cumulative distribution Example 1.4

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Wien’s Displacement Law 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/ Lecture 1 (Governing Laws)

Wien’s Law

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Stefan-Boltzmann Law Stefan-Boltzmann constant

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) 1.8 Blackbody Radiation in a Wavelength Interval

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

1.9 Blackbody Emission into a Medium Other than Vacuum

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) n- refractive index Planck’s function in vacuum

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) Stefan-Boltzmann Law Wien’s Displacement Law

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) 1.10 Historical Note – Origin of Quantum Mechanics

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ Lecture 1 (Governing Laws) The challenge was in deriving a and b constants from the first principle

Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/ 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/ 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/ Lecture 1 (Governing Laws) 1.12 Summary 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