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# Phy 202: General Physics II PowerPoint PPT Presentation

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

Phy 202: General Physics II

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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

• heat conduction

• Yesterday was my 21st birthday, at that age Newton and Pascal had already acquired many claims to immortality.

### 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

• Heat energy that is transferred by means of electromagnetic waves (radiant energy or light)

### 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)

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 !!

### 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

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

• 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 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