Phy 202: General Physics II

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Phy 202 General Physics II

• Ch 13 Heat Transfer

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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.

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Types Heat Transfer

• Convection
• 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)

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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 Fouriers
  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)

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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

• Of course, the relative ability to conduct heat
  is an intrinsic property of different materials !!

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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

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Examples of Convection

• Convection currents in a saucepan

• Convection Currents in heating cooling
  appliances

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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-Boltzmanns 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)

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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)

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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 earths surface radiates energy (long
  wavelength)
• Some of the long wavelength radiation is
  reflected by the earths atmosphere by so called
  Greenhouse Gases
• The reflected long wavelength radiation is
  reabsorbed by the earths 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