Heat
is energy or more precisely transfer of thermal energy.
As energy, heat is measured in watts (W) whilst
temperature is measured in degrees Celsius (°C) or
Kelvin (K). The
words “hot” and “cold” only make sense on a relative
basis. Thermal energy travels from hot material to cold
material. Hot material heats up cold material, and cold
material cools down hot material. It is really that
simple. When you feel
heat, what
you are sensing is a transfer of thermal energy from
something that's hot to something that is cold.
The discipline of heat transfer is
concerned with only two things: temperature, and the
flow of heat. Temperature represents the amount of
thermal energy available, whereas heat flow represents
the movement of thermal energy from place to place.
On a microscopic scale, thermal energy is related to the
kinetic energy of molecules. The greater a material’s
temperature, the greater the thermal agitation of its
constituent molecules (manifested both in linear motion
and vibrational modes).
Conduction
The most
efficient method of heat transfer is conduction.
This mode of heat transfer occurs when there is a
temperature gradient across a body. In this case,
the energy is transferred from a high temperature region
to low temperature region due to random molecular motion
(diffusion). Conduction occurs similarly in liquids and
gases. Regions with greater molecular kinetic energy
will pass their thermal energy to regions with less
molecular energy through direct molecular collisions. In
metals, a significant portion of the transported thermal
energy is also carried by conductionband electrons.
Different materials have varying abilities to conduct
heat. Materials that conduct heat poorly (wood,
styrofoam) are often called insulators. However,
materials that conduct heat well (metals, glass, some
plastics) have no special name.
The
simplest conduction heat transfer can be described as
“onedimensional heat flow” as shown in the following
figure.
The rate of heat flow from one side of an object to the
other, or between objects that touch, depends on the
crosssectional area of flow, the conductivity of the
material and the temperature difference between the two
surfaces or objects.
Mathematically, it can be expressed as
where q
is the heat transfer rate in watts (W), k is the
thermal conductivity of the material (W/m.K), A
is the cross sectional area of heat path, and
is
the temperature gradient in the direction of the flow
(K/m).
The above equation
is known as Fourier’s law of heat conduction. Therefore,
the heat transfer rate by conduction through the object
in the above figure can be expressed as
Where L
is the conductor thickness (or length),
DT
is the temperature difference between one side and the
other (for example,
DT
= T_{1} – T_{2} is the
temperature difference between side 1 and side 2).
The quantity (DT/L)
in Equation (16.5) is called the temperature gradient:
it tells how many 0C or K the temperature changes per
unit of distance moved along the path of heat flow. The
quantity L/kA is called the thermal resistance
Thermal
resistance has SI units of kelvins per watt (K/W).
Notice from Equation (16.6) that the thermal resistance
depends on the nature of the material (thermal
conductivity k and geometry of the body d/A).
We realize from the above equations, we realize the heat
transfer rate as a flow, and the combination of thermal
conductivity, thickness of material and area as a
resistance to this flow.
Considering
the temperature as a potential function of the heat
flow, the Fourier law can be written as
If we define
the resistance as the ratio of potential to the
corresponding transfer rate, the thermal resistance for
conduction can be expressed as
It is clear
from the above equation that decreasing the thickness or
increasing the crosssectional area or thermal
conductivity of an object will decrease its thermal
resistance and increase its heat transfer rate.
Convection
A
slower method of heat transfer is convection, which
involves fluid currents that carry heat from one place
to another. In conduction, energy flows through a
material but the material itself does not move. In
convection, the material itself moves from one place to
another. The convection heat transfer is comprised of
two mechanisms: random molecular motion (diffusion) and
energy transferred by bulk or macroscopic motion of the
fluid. Heat transfer from a solid to a fluid (liquid or
gaseous) is more complex than solidsolid transfer as
heat differentials within the fluid generally cause
internal movement known as convection currents. As
volume increases with temperature, warmer areas of a
fluid have less mass than colder areas. Air is poor
conductor of heat, but it can easily flow and carry heat
by convection. The use of sealed, doublepaned windows
replaces the larger air gap between a storm window and
regular window with a much smaller gap. The smaller air
gap minimizes circulating convection currents between
the two panes.
The magnitude of convective heat flow
within the fluid depends upon the area of contact with
the solid, its viscosity, velocity past the solid, flow
characteristics and the overall temperature difference
between the two. The term convection has also been used
historically to describe the transport of heat from one
solid to another separated by a fluid medium.
Newton’s law of
cooling expresses the overall effect of convection:
Where h
is the convection heat transfer coefficient (W/m^{2}K),
A is the surface area,
DT
= T_{s} – T_{f} is the
temperature difference between the surface temperature
T_{s}, and the fluid temperature T_{f}
. As in the case of conduction, thermal resistance is
also associated with the convection heat transfer and
can be expressed as
The convection heat transfer may be
classified according to the nature of fluid flow.
Forced
convection occurs when the flow is caused by external
means, such as a fan, a pump, etc.
Radiation
The
least efficient method of heat transfer is radiation.
Radiant heat is simply heat
energy in transit as electromagnetic radiation. All
materials radiate thermal energy in amounts determined
by their temperature, where the energy is carried by
photons of light in the infrared and visible portions of
the electromagnetic spectrum.
In this case, heat moves through space as an
electromagnetic radiation without the assistance of a
physical substance. All objects that contain heat
emit some level of radiant energy. The amount of
radiation is inversely proportional to its wavelength
(the shorter the wavelength the greater the energy
content) which is, in turn, inversely proportional to
its temperature (in °K).
The Sun’s heat
is an example of thermal radiation that reaches the
Earth. Radiative heat is transferred directly into the
surface of any solid object it hits (unless it is highly
reflective), but passes readily through transparent
materials such as air and glass.
An ideal thermal radiator or a blackbody, will emit
energy at a rate proportional to the forth power of its
absolute temperature and its surface area.
Mathematically, that is
where
s
is a proportionality constant (StefanBoltzmann constant
= 5.669
´
10^{8} W/m^{2}.K^{4}). The
above equation is called the StefanBoltzmann law of thermal
radiation and it applies only to the blackbodies. The
fourthpower temperature dependence implies that the
power emitted is very sensitive to temperature changes.
If the absolute temperature of a body doubles, the
energy emitted increases by a factor of 2^{4} =
16.
For bodies not
behaving as a blackbody a factor known as emissivity
e, which relates the radiation of a surface to that
of an ideal black surface is introduced. The equation becomes
The emissivity ranges from 0 to 1; e
= 1 for a perfect radiator and absorber ( a blackbody)
and e = 0 for a perfect radiator. Human skin, for
example, no matter what the pigmentation, has an
emissivity of about 0.97 in the infrared part of the
spectrum. While a polished aluminum has an emissivity of
about 0.05.
Thermal
radiation from a body is used as a diagnostic tool in
medicine. A thermogram shows whether one area is
radiating more heat than it should, indicating a higher
temperature due to abnormal cellular activity.
Thermography or thermovision in medicine is based on the
natural thermal radiation of the skin. Most advantage is
the radiance free of the measuring principle.
Certain
body regions have different temperature levels. If one
exposes the body e.g. to a cooling attraction, then the
body zones of the skin react, in order to repair the
heat balance of the body. Thereby the thermal regulation
of diseased body regions and organs is different to
healthy one. The socalled "regulation thermography" is
based on this principle.
Summary
Picture: University of Wisconsin
