Heat Transfer   Conduction   Convection Radiation ---------------------------------- Joseph F. Alward, PhD     Department of  Physics University of the Pacific

Ludwig Boltzmann        (1844-1906)

There are three mechanisms by which thermal energy is transported.  1.  Convection      2.  Conduction      3.   Radiation

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

Hot water rises, cools, and falls.

Heated air rises, cools, then falls.  Air near heater is replaced by cooler air, and the cycle repeats.

What if coils were at the bottom?

   Natural Convection

Air above warmer ground rises.

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                   (joules/second)    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 conductivity.

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.

  Example

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 meter.

   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] Example:  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 morning: 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?