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Heat Transfer  
Conduction   Convection


Joseph F. Alward, PhD    
Department of  Physics
University of the Pacific

Ludwig Boltzmann








There are three mechanisms by which
thermal energy is transported.

Terdapat tiga makanisma caramana haba di pindahkan.

 1.  Convection (Olakan)      2.  Conduction (Konduksi )     3.   Radiation (Pancaran)  






   Convection / Olakkan                                              
      Latin:  com (together) + vehere (to carry); the bulk movement of thermal energy in fluids

Hot water rises, cools,
and falls.
Air panas naik, menyejuk dan jatuh

Heated air rises, cools, then
falls.  Air near heater is
replaced by cooler air, and
the cycle repeats.
Udara panas naik, menyejuk kemudian jatuh
udara berhampiran pemanas
diganti oleh udara sejuk

What if coils were at
the bottom?
Bagaimana jika gelung diletakkan di bawah?





   Natural Convection

Air above warmer ground

Inversion layer.  Air near
ground is more dense than
air higher up; no convection
currents to lift pollutants.

Very hot, low-density
air is buoyed upward,
carrying thermal
energy with it.



  Conceptual Questions and Topics
(1)  Wind chill factor.    (2)  Drapes hung close to a cold window.  (3) Clothing.
(4)  To keep warm on a cold day, should you wear a fur coat with the hair inside,
or out?  (5)  Should you lower the blinds and draw the curtains on a hot day?








Moderate Temperatures Near Large Bodies of Water

Warm land is cooled during the day, while cooler land is warmed at night.






  Forced Convection  

Hot piston cylinders in automobile
engine are cooled by water forced
around them.

 Hot room air is forced outside, while
 cooler air replaces it.






   Heat Conduction          
          H = kA (T2 - T1)/L  

   T2                                              T1       
     k = thermal conductivity   [J/s-m-C]  







    Heat Conduction

Steel:  k = 14  J/s-m-C

How much energy is
conducted in 40 seconds?
H= kA (T2 - T1)/L
H= 14 (2)(475)/10
    = 1330 J/s

Q= Ht = 1330 (40)
   = 5.32 x 104 J




Suppose a human could live for two hours (120 minutes) unclothed
in air at 45 F.  How long could he live in water at 45 F?

How do the thermal conductivities of water and air compare?







    Table of Thermal Conductivities
Substance Thermal Conductivity
 k [J/(s-m-C)]
Substance Thermal Conductivity
 k [J/(s-m-C)]
Syrofoam      0.010 Glass      0.80
Air      0.026 Concrete      1.1
Wool      0.040 Iron      79
Wood      0.15 Aluminum      240
Body fat      0.20 Silver      420
Water      0.60 Diamond     2450

   Water has 23 times the thermal conductivity that air has.  The human in
    the question above would live for only 120/23 = 5.2 minutes. 






  Floating Water Drops
 Water at the bottom of the drops is
 evaporated and provides insulation
 against further evaporation.
 Pan must be very hot.










   A Thermal Conductivity Problem
H= kA DT /L

How many joules of thermal energy
flow through the wall per second?


Heat is like a fluid:  whatever flows
through the insulation must also
flow through the wood.

(Solution is given below.)







  Thermal Conductivity Problem Solution
H= kA DT /L

k (insulation) = 0.20 J/(s-m-C)
k (wood)      = 0.80 J/(s-m-C)

Across insulation:
Hins = (0.20)(40)(25 - T)/0.076                 (1)
     = 2631.6 -105.3 T                                 (2)
Across wood
Hwood = (0.80)(40)(T - 4)/0.019
      = 1684.2 T - 6736.8
Heat is like a fluid:  whatever flows through the
insulation must also flow through the wood:

Hwood  =  Hins  
1684.2 T - 6736.8 = 2631.6 -105.3 T        (3)
1789.5 T = 9368.4                                       (4)
            T = 5.235 C                                      (5)
H= Hwood = Hins                                            (6)
H= 1684.2 (5.235) - 6736.8 = 2080 J/s     (7)
H= 2631.6 - 105.3 (5.235)   = 2080 J/s     (8)  





   Ice is a Thermal Insulator

Ice upon freezing gives up heat to
plants.  Ice also has a low thermal

 Ice on  cooling coils will
 slow the removal of thermal
 energy from the air.







Conceptual Questions

1.  When one steps from a shower on a cold morning, why does
the tile floor seem so much colder than the air?

2.  Place a wooden spoon and a metal spoon in the freezer.  Which
will cool faster?  After several hours, what would they feel like?

3.  Why do people become "flushed" when overheated?




  Stefan-Boltzmann Law of Radiation
Energy radiated per second: 

       H = esAT4

e = emissivity (0-1)
s = Stefan-Boltzmann constant
    = 5.67 x 10-8 J/(s-m2-K4)
A = surface area of object
T = Kelvin temperature

Ludwig Boltzmann
(1844-1906) committed
suicide because he
thought his life's
work was in vain.


 How much energy is radiated by this
 object in ten minutes?

 t = 10 x 60 seconds = 600 s

 Q = radiant energy = H t

 H =  esA T4

 Q = (0.8)(5.67x10-8)(5)(500)4 x (600)
     = 8.5 x 106 J

      H = esAT4 








   Absorption and Emission of  Radiation

 Energy out = Energy in
 Emitted energy/Incident energy = Emissivity = e.  






Example:  How much does the human body radiate?
Body temperature = 37 C = 37 +273 = 310 K,
Estimate surface area A = 1.5 m2        e = 0.70

H = esA T4
        = (0.70)(5.67 x 10-8)(1.5 m2)(310)4
        = 550 watts (5 light bulbs)
The sun provides about 1000 watts per square
meter at the Earth's surface.  30 % is reflected by
human skin.  700 watts is absorbed per square






   Calculating the Sun's Temperature
What is the Sun's temperature?  (Assume the Sun's emissivity is 1.)
Distance from Sun to Earth:  R = 1.5 x 1011 m    
Area of sphere of radius R = 4pR2      H = 1000 x 4pR2 = 2.83 x 1026 J/s
Radius of the Sun = r = 6.9 x 108 m
Surface area of the Sun = A = 4pr2 = 5.98 x 1018 m2
esAT4 = H       s = 5.67 x 10-8 SI units       T = [H/(esA)]1/4 = 5375 K









If object at temperature T is surrounded by an
environment at temperature T0, the net heat flow is:

   Hnet = esA [T4 - T04]

:  Standing outdoors on hot August day:

Body temperature: 37 C = 37 +273 = 310 K,
Air temperature:     37 C = 310 K

   Hnet = esA [T4 - T04]  =  esA [3104 - 3104]
          = 0

Example:  Standing outdoors on a cold February

Body temperature = 37 C = 37 +273 = 310 K,
Air temperature = 0 C = 273 K

A = 1.5 m2     e = 0.70

Hnet = esA [T4 - T04]  
        = (0.70)(5.67 x 10-8)(1.5 m2)(3104 - 2734)
        = 219 watts 



In the example above, the net heat loss is 219 Joules per second. 
How many food Calories of energy will be lost in one hour?
1 Calorie = 1000 cal                                             4186 J = 1 Cal

One hour = 3600 seconds            Q = 219 x 3600 = 7.88 x 105 J

Number of Calories burned to replace that energy:  

7.88 x 105 J / (4186 J/Cal) = 188 Cal










  Black Bodies
 Summer clothing:  white reflects
 radiant energy better than black.

 Until equilibrium is reached, white
 stripes on roads are at a lower
 temperature than unpainted asphalt.

 Wrap an ice-cube in black cloth
 and another in aluminum foil and
 place both in the sunshine.  What
 will happen?






Why is the pupil of the  
eye black? 




  Pipes in Solar Panels are Painted Black






Highly reflecting metal foil keeps
inside temperature low.

                    Solar cooker





  The Physics of Fur Coloring
Lemur at left is nocturnal,
so the dark fur poses no
disadvantage in absorbing
excessive sunlight.

Lemur at the right is active
during the day; it points
its belly toward the sun on
cold mornings.






 1.  The sun goes down, snow falls on cement playground and on an asphalt road.
      Why does the snow on the road melt sooner than on the cement?

2.  Two different materials at the same temperature have different emissivities.
     Which one glows the brightest?

3.  Why are fireplace pokers made of iron and not copper?

4.  Some animals have hair which is composed of solid tubular strands, while
     others have hollow, air-filled tubes.  Where would one more likely find
     the latter animal:  In cold climates, or warm?







5.  Steel reinforcement bars add stability to concrete walls.  Do they also
     enhance the insulating value of concrete?  

6.  Two identical cups of cocoa are sitting on a table.  One has a metal spoon
     in it and one does not.  After five minutes, which cup is cooler?

7.  In Alaska, a lack of snow allowed the ground to freeze down to a depth
     of about one meter, causing buried water pipes to freeze and burst.  Why
     did a lack of snow lead to this situation?

8.  Several days after the end of a snowstorm, the roof of a house is completely
     covered with snow, another house's roof has no snow.  Which house is
     probably better insulated?






9.  To keep your hands as warm as possible during skiing, should you wear
     mittens, or gloves? (Mittens, except for the thumb, do not have individual
     finger compartments.)

10.  Could one keep warmer in winter wearing a fur coat inside-out, with the
       fur next to the skin?