1. Phy 202: General Physics II
Ch 13: Heat Transfer

2. Jean Baptiste Fourier (1768-1830)
French mathematician
Originally wanted to become a priest but drawn to mathematics
Contemporary of Laplace, Lagrange, Biot & Poisson
Served as Precept under Napoleon
Worked on:
mathematics
heat conduction
Yesterday was my 21st birthday, at that age Newton and Pascal had already acquired many claims to immortality.

3. Types Heat Transfer Convection Conduction Radiation
Heat energy that is carried from place to place by the bulk movement of a fluid
Conduction
Heat energy that is transferred directly through a material
Radiation
Heat energy that is transferred by means of electromagnetic waves (radiant energy or light)

4. Conduction
Heat flow due to collisions between neighboring atoms (a sort of “domino effect”)
The rate of conductive heat flow (Q/Dt) is:
proportional to temperature difference between 2 regions in a conducting pathway material (DT)
proportional to cross sectional area of material (A)
proportional to ability of material to conduct heat (k) {called thermal conductivity}
inversely proportional to length of conducting pathway (L)
Combining all of these elements forms Fourier’s Heat Equation (1609):
Q/Dt = k (A.DT) / L (Rate of Heat Flow in W) Or
Q = [k (A .DT) / L] .Dt (Heat Flow in J)

5. Conductive Heat Flow
Conduction depends on temperature difference between 2 regions & how far apart those regions are separated
Increasing the cross-sectional area increases amount of heat that will flow in a given time
Consider conduction through 2 layers of different materials
Of course, the relative ability to conduct heat is an intrinsic property of different materials !!

6. Convection When a fluid is warmed:
Volume expands (thermal volume expansion)
Density decreases
Buoyant forces exerted by cooler (denser) fluids causes warmer fluids to rise
Remember Archimedes’ Principle ???
As warmer fluids rise they cool and descend warmer fluids beneath push them out of the way
The net result is a natural mixing that occurs, called convection
Convection is a very efficient form of thermal transfer
Heat energy gets rapidly dispersed throughout the bulk of a fluid
When mixing is induced artificially (i.e. with a fan) convection occurs more rapidly & efficiently, this is called forced convection

7. Examples of Convection
Convection currents in a saucepan
Convection Currents in heating & cooling appliances

8. Q/Dt = e (s A.T4) (Rate of Radiant Heat Flow in W)
Radiation
All objects emit(or radiate) energy in the form of electromagnetic waves
The rate of radiant energy emitted is related:
Surface area (A)
The 4th power of the surface temperature (T4) {in kelvin!!}
The ability of an object absorb/emit radiant energy, called emissivity (e)
e is 0 for a perfect reflector
e is 1 for a absorber/emitter
e is between 0 & 1 for normal substances and varies with wavelength
Combined together we have Stefan-Boltzmann’s Law of Radiation:
Q/Dt = e (s A.T4) (Rate of Radiant Heat Flow in W)
where s = 5.67 x 10-8 J/s.m2.K4 (the Stefan-Boltzmann Constant)
Consider both emission & radiation: determine net power generated by a wood stove
surface area = A = 3.5 m2
e = 0.90
Tstove = 471 K in a room at Troom=303K

9. Effect of Emissivity on Absorption of Radiant Energy
All bodies emit as well as absorb radiant energy
When a body is in thermal equilibrium:
Qabsorbed = Qemitted
Dark objects will reach higher equilibrium T than lighter objects (e.g. consider pavement and concrete on a hot day!)
Good emitters are also good absorbers of radiant energy (e ~ 1)
Poor emitters are also good poor of radiant energy (e ~ 0)
Compare Rate of energy emitted for a light (e=0.1, T=310K) and dark (e=0.9, T=315K) colored object on a hot day!
Q/Dt = e light (s A.T4)light = (0.1)(310K)4 = 0.10 or 10%
Q/Dt = e dark (s A.T4)dark = (0.9)(315K)4 Or
lightT4light = e darkT4dark which means T4light/T4dark= e dark/e light
Tlight = Tdark(e dark/e light)1/4

10. The Greenhouse Effect
The presence of our atmosphere helps the Earth maintain a moderate & livable temperature range, due to a process called the Greenhouse Effect:
Radiant energy (short wavelength) from the sun is absorbed by the surface of earth
The earth’s surface radiates energy (long wavelength)
Some of the long wavelength radiation is reflected by the earth’s atmosphere by so called “Greenhouse Gases”
The reflected long wavelength radiation is reabsorbed by the earth’s surface
This positive feedback process heats the surface of the earth and keeps the surface warmer at night
Do not confuse Greenhouse Effect (Good!) with Global Warming (Bad!)
Global warming is believed to be due to an increased production of greenhouse gases which may increased the amount of long wavelength radiation reflected back to the Earth