Information

C. Surface Loading Capacity
Generation of heat has great
importance in electrical engineering,
no matter whether it should be
controlled as far as possible or
whether it is intended to be used.
The main questions to be answered
in this connection is what
temperature a current-carrying wire,
ribbon, sheet etc. will reach during
operation.
Answering this question is
somewhat difficult, since the
determining factors, like type of
insulation and shape of the resistive
conductor, cooling conditions,
surface deterioration during
operation and other properties of the
material, which for their part again
depend on the temperature, can
often only be a matter for
conjecture.
Current-Carrying Capacity of Wires
In order to make things easier to
control, simple models, suitable to
be converted into practical
solutions, are chosen for tests and
measurements. Such a model is
formed e.g. by a straight bare wire,
stretched in still air of 20°C,
whereby the natural movement of
the air is in no way impeded, and
which is loaded by current. This
model has the advantage that the
temperature of the wire can be
determined on the basis of its
thermal expansion in addition to
other methods.
If a current i flows through a
conductor with the length l and the
resistance R, then the electrical
power P, converted into heat, is
calculated as follows:
P = i
2
· R
Inserting
page 5
q
l
R ⋅=
ρ
the following results:
2
2
4
d
li
P
⋅
⋅⋅⋅
=
π
ρ
The amount of heat created per cm²
of wire surface is called the surface
load n of the wire; it is expressed in
watts (W) per square centimeter
(cm
-2
).
Using the above formula, then after
inserting the determining values for
the surface in the following results:
3
2
04053.0
d
i
n
t
⋅⋅
=
ρ
i = Current in Amps
=
t
ρ
Resistivity in Ω x mm” x m
-1
at temperature t (°C)
d = Wire diameter in mm
The surface load is a measure of
the temperature the wire will
achieve under given environmental
conditions. It is not a material-
dependent quality, but must be
chosen in accordance with the
respective conductor material and
application.
The upper limit should, of course,
be determined on the basis of the
maximum working temperature of
the conductor in order to ensure
adequate scale and corrosion
resistance etc.
Fig.1 shows the relationships
between surface load and wire
operating temperature for wires of
different materials with 0.5mm
diam.
In general, a current-carrying wire
very quickly achieves, after
switching-on the current, a
stationary state, in which the
amount of heat produced within a
unit of time equals the amount of
heat dissipated. When using the
model mentioned above: “Streched
wire in still air of 20°C”, then the
heat is dissipated by convection –
removal through air flow – and
radiation. Under the conditions
quoted the heat is removed mainly
by convection, while heat removal
by radiation is worth mentioning
only at temperatures >400 – 600°C.
The share of heat radition,
however, increases with
temperature by a factor of T
4
.
The diameter of the conductor, too,
affects the kind of heat dissipation.
Fig. 2 shows the interaction of
convection and radiation in
dependence on the wire diameter.
In the area of the hatched border
line heat removal by convection
equals that by radiation. At lower
temperatures and smaller wire
diameters heat removal by
convection prevails; at higher
temperatures and larger wire
diameters heat removal by radiation
is in excess.
Fig. 2 shows also that the share of
convection in heat dissipation
grows with decreasing wire
diameter. This is due to the fact that
for thinner wires the heat transfer
from wire to air improves
considerably. In practice this means
that, for the same operating
temperature, thin wires can be
loaded more heavily than thick
wires.
By suppressing convection, e.g. by
lowering the atmospheric pressure,
the curve is shifted to the left; this
means that the share of radiation
increases. On the other hand the
curve can be shifted to the right e.g.
by using a fan. Provided the
electrical power is kept constant, in
the latter case the wire temperature
would be substantially lower.
The diagrams mentioned above –
Figs. 1 and 2 – apply to horizontally
arranged straight wires in still air. In
practice this arrangement is very
rarely chosen, especially for thin
wires. Wires wound on cores or
Fig. 1: Overtemperature of Wire against Air in
Dependence on the Surface Load in Watt/cm² and on
Different Materials.