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Heat Transport: Conduction, Convection, Radiation
Michael Fowler
Conduction
If different parts of an isolated solid are at different temperatures, heat will flow from the hot
places to the cold ones until eventually all is at the same temperature.
By “isolated” here we
mean that the solid is not able to exchange heat with
the outside world.
Experimentally, it is found that for most substances the rate of heat flow at any point is
proportional to the temperature gradient—how fast the temperature is changing with position. To
give an example, consider heat flowing down a thin rod, heated at one end, and assume the rod is
wrapped in insulation so all the heat flows
down
the rod, none escapes from the surface. The
natural unit of heat flow down the rod is how many joules per second pass a fixed point in the
rod.
It is found that:
dQ
dT
dt
dx
∝
where
Q
is in joules,
T
in degrees Kelvin,
x
is meters down the rod. The heat flow rate is then in
joules per second, or watts.
It is evident from this equation that if heat is supplied at a steady rate
to one end of the rod, and drains from the other end, the temperature distribution will ultimately
settle down to
= constant, a linear drop along the rod from one end to the other.
/
dT dx
It is also found experimentally that a rod of double the crosssection carries twice the heat
current at the same temperature difference.
(This is also true for electric current, but remember it
is not true for water in a pipe—the “caloric” fluid evidently doesn’t act like a viscous liquid.)
This makes it possible to define a
coefficient of
thermal conductivity
κ
for a particular material
by
dQ
A
dt
=
for heat flow across an area
A
(in square meters) for a given temperature gradient
.
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 Fall '07
 MichaelFowler
 Convection, Heat, Radiation, Heat Transfer, Heat Flow, heat transport, Michael Fowler

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