Advanced Heat Transfer Lecture1 by HC120520153636

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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)
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 2005/2006 - Lecture 1 (Governing Laws)
The convention (in this lecture series) is


  Amount of heat (energy) Q in J

                                  
               Heat transfer rate Q                               in W (J/s)


                                 Heat flux               
                                                         q        in W/m2




  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
taken with                                                                                   taken with
    an                                                                                          an
 ordinary                                                                                     infrared
 camera                                                                                       camera


                    The number plate has been wiped out
      Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
 RELEVANCE OF THERMAL RADIATION

                     
                     Qconduction  T1  T2
                     
                     Q            T T
                         convection                  1           2
                     
                     Qradiation  T1  T2
                                    4    4


 When no 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




                            Quantum theory
      E photon  h  v                     h  6.63 10             34
                                                                              J s
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:

                               w   
       Determined                                            Determined by
       by the medium                                         the source


For electromagnetic waves:

                                 c   
                    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:

                                                        c
                          c medium 
                                                  n medium
The frequency stays the same so,

                                                         
                           medium 
                                                   nmedium


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



                        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)
          Example 1.1 (Calculate energy of photons)
                               Energy in       Number of
Frequency        Photon
                                electron      photons in a
    (Hz)      energy in J                    joule of energy
                                  volts
Short radio
   waves       6.63·10-27       4.1·10-8       1.5·1026
   ν=107
Visible light
   waves       6.63·10-19          4.1         1.5·1018
   ν=1015
  X-rays
   ν=1018      6.63·10-16        4.1·103       1.5·1015

  Gamma
   rays                   6.63·10-14                  4.1·105                   1.5·1013
  ν=1020
 Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
THERMAL RADIATION




   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)
1.6.2 Solid Angle




Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
     Example 1.2
  Derive formula for calculating the length of an arc and
  the circumference of a circle.


                ds  R  d                                               Plane angle
                                                                          in radiance
                2
  s  R   d  R   2  1 
                1

Length of an arc  Radius  Plane angle in radians

 Circumfere of the circle  R  2
          nce
    Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
 Derive formula for calculating the area of a sphere


               dA  R  d         2
                                                                  The solid angle
                                                                  in steradians
            2
A  R   d  R  2  1 
       2                       2

            1



Area of a part of the sphere 
 Radius   Solid angle in steradians
                         2


      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?

                                   dAs
                               d  2
                                   R

dAs  R  d   R  sin   d   R 2  sin   d  d


                       d  sin   d  d



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:
                               2                    2 2
                 A  R 2   d  R 2    sin  d  d 
                                1                  1 1


 R   2  1    cos   
    2                                          2
                                                1


                                  R   2  1   (cos 1  cos 2 )
                                          2



Area (hemispher e)  R  2  (1  0)  2  R      2                                              2



   Solid angle for a hemisphere is                                          2
   Solid angle for a sphere is                                             4
    Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
            1.6.3 Area and Projected Area




                                             dAP  dA  cos



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

                               indicates direction

                                            W
i  is the spectral intensity in 2
'

                                 m (Projected Area )  sr  m


                                       W
 i  is the total intensity in 2
    '

                              m (Projected Area )  sr
                                             
                                    i   i  d
                                      '           '

                                             0
        Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
                                 Irradiation

                                      g                  i ( , ,  )  cos  d
                                                             '
                                      
                                                all directions

                                               2  / 2
                                      g          i ( , ,  )  cos  sin   d  d 
                                                       '
                                      
                                              0 0


                                      for isotropic incoming radiation
                                                                /2
                                             1
                                              i   sin(2 )  d (2 ) 
                                        g            '

                                             2           0



                                           i   cos(2 ) 0    i
                                        1       '                 /2     '

                                        2
Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
        For isotropic radiation

                                    g     i
                                                             '



                                     g   i
                                                                 '


    An important integral in radiation
                                           2  / 2

    
hemisphere
             cos  d 
                                          
                                             cos  sin   d  d  
                                             0      0



         Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
 1.7 Governing Laws for Thermal Radiation
               1.7.1 Black Body Radiation
Real surfaces (bodies)
                                             g    g    g   g
                                                                 


                                               reflectivity
                                                                     absorptivity




                                                                                  transmissivity

 Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - 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 2005/2006 - 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 2005/2006 - Lecture 1 (Governing Laws)
The angular distribution of radiation intensity
emitted by a black body




eb            ib  cos  d  ib                        cos  d    ib
                  '                 '                                            '

          hemisphere                                    hemisphere
  Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
                     1.7.2 Planck’s Radiation Law


                                                                C1                    1
eb ( , T )    ib ( , T ) 
                                    '
                                                                             C 2 / T
                                                                 e 5
                                                                                            1
                                                       16
            C1  3.7418 10                                       W m            2


                                                             2
           C2  1.438769 10                                            mK


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




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




Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
                                             eb ( , T )
                                                             C1            1
                                                                      C / T
                                                 T 5
                                                              T  e 2  1
                                                                    5




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)
Example 1.4
                     Height per               Number of                    Class mark
                     class (cm)                 students                      (cm)
                                              -Frequency
                       153-159                      4                             156
                       160-166                     12                             163
                       167-173                     18                             170
                       174-180                     25                             177
                       181-187                     33                             184
                       188-194                     22                             191
                       195-201                     11                             198
                       202-208                      5                             205
                                              TOTAL 130
      Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
Example 1.4

     Histogram and frequency polygon of heights of 130 students

                                    35

                                    30
    Number of students per height




                                                                                         f(x)

                                    25

                                    20

                                    15
                                               P
                                    10                                                                    Q

                                     5

                                     0
                                         149       156   163   170   177    184    191      198    205        212
                                                                     Height (cm)
               Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
Example 1.4



        Q

Area   f ( x)  dx    (4  12  18  25  33  22  11  5)   130
         P



             Δ  7cmis the width of the class

        Area  the total number of students (130)




     Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
Example 1.4
                     Cumulative distribution
                (less than the upper class boundary)
              Height (cm)         Number of students
              Less than 153 cm               0
              Less than 160 cm               4
              Less than 167 cm              16
              Less than 174 cm              34
              Less than 181 cm              59
              Less than 188 cm              92
              Less than 195 cm             114
              Less than 201 cm             125
              Less than 208 cm             130
      Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
Example 1.4


    Students smaller than 174 cm

                                                                                          174
                                 1                     1
F(less than174cm)  4  12  18     (4  12  18)  
                                                                                          f ( x)  dx
                                                                                            0




    The relative cumulative distribution
                                                                        174


                              4  12  18                                f ( x)  dx
       F (less than 174 cm)                                           0
                                                                         
                                 130      
                                                                          f ( x)  dx
                                                                         0


     Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
Example 1.4
                                                                      Cumulative distribution
                                                                                                                                                     1.0
   F(x) Cumulative Frequency (No. of Students)



                                                 120




                                                                                                                                                           F(x) Relative Cumulative Frequency
                                                                                                                                                     0.8
                                                 100


                                                  80                                                                                                 0.6

                                                  60
                                                                                                                                                     0.4
                                                  40

                                                                                                                                                     0.2
                                                  20


                                                   0                                                                                                 0.0
                                                          150           160          170          180          190           200          210
                                                                                            Height (cm)
                                                  Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
                  1.7.3 Wien’s Displacement Law
 We are looking for a wavelength that maximizes
 the Planck’s function for a given temperature

eb ( , T ) 

                       C1
                        e5
                                        C 2 / T
                                                 1
                                                         1
                                                               C1    e       5
                                                                                         C2 / T
                                                                                                    1  1



  
deb
 d
             C1 C2 / T
      (5)  6  e
             
                          
                          1
                        1                          
      
          C1
            5
                  (1)  e          C 2 / T
                                                 1        e
                                                         2       C 2 / T
                                                                             C2
                                                                               (1)    0
                                                                              T
                                                                                         2




                   T    C2 / T
                           C2     1
                           5 1 e
   Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
                     C2     1
        f (  T )         C2 /  T
                                          T 
                     5 1 e
                   0.010




                   0.005
                                         max·T = 0.0028977756 m·K
                                                (C3-Wien's constant)
   f(·T) in m·K




                   0.000




                   -0.005




                   -0.010
                        0.000   0.002      0.004          0.006           0.008          0.010
                                               ·T in m·K
Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
                                Wien’s Law


          max T  C3  2,898 μm  K




Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
                    1.7.4 Stefan-Boltzmann Law
                                     
                          eb   eb ( , T )  d  ?
                                
                                     0
    
                 C1                        T 4  C1    3 0
                                                                                            C2
eb                                 d               d                          
     0  5   eC 2   /  T
                                1          C2  e  1
                                                4
                                                                                            T
                                     0
                                         3               
                                      e 1  d  15
                                     

                                   C1 
                               eb  4   T 4    T 4
                               
                                   C2 15

                                                                           Stefan-Boltzmann
  5.67 10 W/(m  K )         8                2           4
                                                                              constant
     Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
1.8 Blackbody Radiation in a Wavelength Interval




                              2

                               e ( , T )  d
                                
                                                           1
                                                                     2

                                                             4  
                              
           F1T _ 2T         1
                                                               e ( , T )  d
                                                                
                              
                                                          T 1
                               e ( , T )  d
                                
 Advanced Heat Transfer - Prof.0Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
                               2
                 1
                    4  b
F1T _ 2T           e ( , T )  d 
                        
                 T 1
                 1    2               1
                                                            
                   4   b
                    e ( , T )  d   eb ( , T )  d   F0 _ 2T  F0 _ 1T
                                          
                T  0
                                       0                   
                                                            




       Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
                  T                        1T
              1  2 eb ( , T )                eb ( , T )           
F1T _ 2T                    d (T )                  d (T )   F0 _ 2T  F0 _ 1T
               0
                       T 5
                                             0
                                                    T 5
                                                                       
                                                                       




         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
                                             C1                   1
              eb ( , T ) 
                                                         C2 / T
                                              e5
                                                                        1
                        c                                                
                   cm                                        m 
                        n                                               n
                                                                         h  cm
  C1m  2  h  cm  C1 / n 2
                  2
                                                              C2 m              C2 / n
                                                                           k


     emb (m , T )  n  eb ( , T )
                                                       3


     Advanced Heat Transfer - Prof. Dr.-Ing. R. Weber - Winter 2005/2006 - Lecture 1 (Governing Laws)
ebm (m , T )  n  eb ( , T )
                                                     3



 n- refractive index



                                      Planck’s function in vacuum




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

                    ebm  n    T
                                         2                    4



 Wien’s Displacement Law

                                       C3
                          max,n  T 
                                       n


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)
                     a            1                   The challenge was in
eb ( , T ) 
                            b / T
                     e
                      5
                                       1             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)

                            E  m h  v
                            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

                                     E  h 
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)
   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




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

								
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