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

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Phy 202: General Physics II

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Phy 202 general physics ii

Phy 202: General Physics II

Ch 13: Heat Transfer

Jean baptiste fourier 1768 1830

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.

Types heat transfer

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)



  • 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)


    Q = [k (A .DT) / L] .Dt (Heat Flow in J)

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

Conductive Heat Flow

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



  • 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

Examples of convection

Convection Currents in heating & cooling appliances

Convection currents in a saucepan

Examples of Convection



  • 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)

Effect of emissivity on absorption of radiant energy

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)

The greenhouse effect

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

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