Heat Transfer

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Heat Transfer

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Thermal Expansion and Heat Transfer
Thermal Expansion
A rod of length L will expand by L when its temperature
increases by T. It is found L is proportional to T,
L = LT,
where  is the one dimensional thermal expansion coefficient.
These coefficients appear in tables and vary depending on the
material. Thermal expansion is important in engineering
applications--- even electrical engineers have to be aware of this
phenomenon in the design of microcircuits.
Heat Transfer
Heat transfer falls under the category of redundant phrases. But
it is part of the language, so we continue to use it.
There are three modes of heat transfer.
 Conduction
In this case, the energy transfer takes place between two points
of an object (e.g. a solid) that are held at different temperatures.

More specifically, say we have a solid cylinder of length L and
cross-sectional area, A. If one end of the rod (x=0) is held at a
high temperature, TH, and the other end of the rod (x=L) is held
at a low temperature, TC, then energy will flow from x=0 toward
x=L. The power transmitted in Watts we write as,
H  dQ/dt (thermal power or thermal current)
The law of heat conduction states,
H = -kA dT/dx ,
where k is called the thermal conductivity of the material, dT/dx
is called the temperature gradient. The minus sign is present to
assure energy flows from hot to cold.
The above takes on a simpler form for the case of our cylinder,
H = -kA {TC – TH}/L .
A table of k values is in your textbook—metals generally have
large k values, while styrofoam a low value.
 Convection
Convection is energy transfer by the movement of a hot fluid. It
is difficult (but not impossible) to model convection with a
simple expression, so just be aware of what it is. Convection is
very important in the weather where massive thermal currents
develop.

 Radiation
Radiation transfers energy because electromagnetic radiation
waves are made of energy, for example, sunlight.
Ultimately radiation arises from the acceleration of electric
charge, now you know how to create light. The law of radiation
states,
H = e  A T4
[Stefan-Boltzmann Law]
e = emissivity (dimensionless fraction)
 = Stefan-Boltzmann universal constant
A = surface area of emitting body
T = absolute temperature of emitting body.

EXAMPLES [in class]

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