
Heat Transfer
The key to understanding ampacity is to learn about heat transfer. The
definition of ampacity is given in the National Electrical Code (NEC) as "the
current in amperes a conductor can carry continuously under the conditions of
use without exceeding its temperature rating." To better understand
ampacity we need to examine how heat is transferred and thermal circuits in
respect to a current carrying conductor.
When current is carried by a conductor it must pass through the
electrical resistance of the conductor. When this happens heat is generated.
One unit of heat, watts, can be calculated by I squared times R, where R equals
the electrical resistance of the conductor in ohms and I equals the current in
amperes. The heat generated in the conductor passes through several thermal
barriers by convection, conduction, and radiation and dissipates into the air.
Possible thermal barriers are the conductor insulation, the air inside a duct,
the duct wall, the soil surrounding an underground duct, and any additional
thermal insulation applied such as polyurethane.
The transfer of heat follows a fundamental law in physics, and heat
always flows from the warmer object to the colder object, much like heat flowing
from the inside of a house through the walls to the outside on a cold day. The
rate of heat transfer is dependent on several variables and can be described by
a thermal equation that closely resembles ohms law (E=IxR), substituting heat
for current and thermal resistance for electrical resistance. In a heat
transfer equation the rate of heat transfer is directly dependent on the
difference in temperature between the conductor called TC and the ambient
temperature called TA. In a heat transfer equation TCTA = (IxIxR) x RCA, where
I is current in amperes, R is electrical resistance in ohms, and RCA is thermal
resistance in degrees Centigradecm/watt usually called thermalohmfeet. TC is
the maximum permissible operating temperature in degrees Centigrade of the
conductor. TA is the ambient temperature of the air or soil for underground
installations. Solving for I:
Letting heat, IxIxR in this case, be represented by W and thermal
resistance, RCA, by R with a line over it, we can draw a thermal circuit that
is similar to an electrical circuit.
NeherMcGrath equation
Founded by a man named Fourier in the 1850's, Equation No. 1 is
sometimes called the Fourier heat transfer equation. The equation in section
31015(b) of the NEC, called the NeherMcGrath equation, is a more complex
version of the Fourier heat transfer equation. The NeherMcGrath equation was
discovered by two cable engineers in 1957. In the NeherMcGrath (NM) equation,
Delta TD, is a term added to the ambient temperature, TA, to compensate for
heat generated in the jacket and insulation for higher voltages. Delta TD is
called the dielectric loss temperature rise and is insignificant for voltages
below 2000. Another term in the NM equation, (1+YC), is a multiplier used to
convert direct current resistance (RDC) to alternating current resistance or
impedance. For wire sizes smaller than No. 2 this term becomes insignificant.
Of course, we must remember that the NM equation was developed using the
standard power frequency of 60 hertz and sinusoidal wave forms for current and
voltage.
There are many equations used to calculate the various thermal
resistances for the conductor insulation, the air space between a conductor and
the inside of a conduit, the conduit or duct wall, and the thermal resistance
outside the conduit. Like electrical resistors, thermal resistances in series
are added and the total equals RCA.
Ambient temperature, TA, varies but usually 30 or 40 degrees Centigrade
is used for above ground installations. For underground installations TA is
universally 20 degrees Centigrade. Civil engineers working for the State of
Alaska Department of Transportation state that the actual measured temperature
30 inches beneath the surface is 19.3 degrees Centigrade near Fairbanks, Alaska.
This of course, is during the summer months. The conductor temperature, TC,
for most 600 volt building wire is 60, 75, or 90 degrees Centigrade. The
maximum insulation temperature for conductors is determined by conducting aging
and enlongation tests in environmental chambers.
In the NM calculation there are many variables in the 30 to 40 equations
used to account for the number of conductors, number and size of adjacent
conduits, number and size of adjacent duct banks, coefficient of surface
emissivity, number of cables, axial spacing between cables, extraneous heat
sources, and wind velocity. All these factors and more effect the calculation
of ampacity. An analysis of the NM calculation reveals many details about
ampacity: for instance, the ampacity of conductors in a bright and shiny conduit
in free air is higher then the ampacity in a dull and dark conduit because of
the coefficient of surface emissivity and its effect on the radiation of heat.
Also, one of the most criticized faults of the NM calculation is revealed: The
calculation is based on one single linear foot of a conductor that may be
several hundred feet long where the conditions vary dramatically along the
entire length.
There are ampacity tables in the National Electrical Code that are
sufficient for most installations. However, the tables in the NEC are very
crude approximations and therefore include a substantial safety margin. There
are instances where the application of the ampacity tables including the safety
margins are insufficient requiring engineers, installers, and inspectors to
perform actual NM calculations using one of the several software packages
available. For instance, there are no requirements in the NEC to address the
problem of excessive thermal insulation around cables and conduits. What
happens if there are several inches of polyurethane foam around a conduit?
There are no derating tables in the NEC for this kind of situation. Yet, the
addition of excessive thermal insulation will effect the ampacity of a
conductor, especially polyurethane foam that has three times the insulation
value of fiberglass. To address this problem we must remember that the NM
equation is a radial heat transfer equation and that the NM calculation is
performed on one typical foot of an installation that may be several hundred
feet long. Radial heat transfer means that heat flows outward at ninety degrees
to the length of the conductor as opposed to axial heat transfer where heat
flows along the length of the conductor. In the real world there is axial and
radial heat transfer. But the NM equation and the NEC assume that a conductor
and surrounding thermal barriers are infinitely long and uniform where no axial
heat transfer takes place. There are, however, some allowances in the NEC for
axial heat transfer. For instance, there are no derating for over three
current carrying conductors in a nipple if the nipple is not over 24 inches
long. Also, bundled cables are not required to be derated if the bundles are
not longer than 24 inches. There is also the ten per cent rule given in section
31015(c). These are situations where there is enough axial heat transfer to
prevent the conductors from overheating. It would also be prudent to assume
that where there is excessive thermal insulation not over 24 inches long, the
ampacity of the applicable conductors would not be effected because of axial
heat transfer.
