1. ENGR 3150 Honors Option
Wagner
Joule Heating in Aluminum 6061-T6 Busbar
Robert Neal
Spring 2015
05/05/2015

2. Abstract:
In this project the joule heating of a current carrying busbar was analyzed. The busbar is
made of aluminum alloy 6061-T6 and was geometrically created in COMSOL. Air geometry was
added to this model to create a simulation involving stationary and dynamic fluid flow.
COMSOL was then used to evaluate a steady state solution for each parameter given. It was
found that with no air flow at all around the bus bar, temperatures in the system exceeded
3000K. With a 2 ft/s air flow applied perpendicular to the length of the busbar the maximum
temperature in the system was roughly 330K. When a 2 ft/s air flow was applied parallel to the
length the maximum temperature in the system was roughly 470K. The differences in
temperature and the results of each simulation were consistent with the predicted behavior of
heat transfer expected from each geometry. Cross flow was predicted to have higher rates of heat
transfer from the busbar, with parallel flow having less heat transfer from the busbar and no flow
having the least heat transfer.
Introduction:
Running an electric current through an aluminum busbar generates heat from the
resistance of the busbar. Additionally different flow rates of air across the geometry will result in
different rates of heat transfer. By using COMSOLto create an accurate model of a given busbar
simulations can be run from the busbar to determine the temperature the busbar and air
surrounding it will reach. COMSOL worked to solve a steady state solution for the initial
parameters given for each scenario being evaluated. The temperature the busbar and air coupling
reached was determined from COMSOLand subsequently analyzed from graphical data.
Procedure:
To begin the simulation the geometry of the busbar was first loaded into COMSOL. The
busbar’s is an aluminum tube with a 6.625 in outside diameter, a thickness of 0.28 inches and a
length of 10 feet. Physical properties of the 6061-T6 aluminum alloy were then applied to the
busbar through use of COMSOL’s material manager. Next, the geometry of the air was created.
The surrounding air geometry was chosen to completely encompass the entire busbar.
Additionally, a type of heat transfer symmetry was applied at the boundary edges of the air to
simulate the air continuing out beyond the border dimensions in order to create a more accurate
simulation. The physical properties of air were loaded from COMSOL’s built in properties of air.
Next the individual simulation experiments were created in COMSOL. First the joule heating
module for the simulation was created. A specified current of 3719 amps was desired in the
busbar and with a known resistance of 38.97 micro-ohms in the busbar (3.897 micro-ohms per
foot). The required voltage to generate said current was then determined using Ohm’s law
(0.14492943 Volts). This voltage was applied to one end of the busbar and a ground was applied
to the opposite end, resulting in a simulated drop of our calculated voltage across the busbar thus
producing the desired current. The joule heating module of COMSOL was then set to analyze

3. thermal fluctuations from the joule heating in the busbar and subsequent heat transfer to the air.
Next, a constant temperature was applied at one end of the air geometry to represent a constant
temperature inflow of air. At this point the fluid flow module was introduced into the model. A
normal inlet velocity was defined at the same end of the air geometry as the constant temperature
air flow. An outflow was specified at the opposite end of the geometry to represent air flowing
out. These inlet velocities and constant temperature boundary conditions varied for each
experiment and were modified depending on the conditions being evaluated. Now both
experimental modules were set up and ready to use. To run the simulation the flow module was
selected for the first experiment in each step. The joule heating module was then selected to run
after the flow had been calculated in each step. This coupling of the experiments allowed for
COMSOL to generate the temperature distributions throughout the busbar and air from the initial
conditions until a steady state condition existed. Each given condition was then analyzed and
solved with the temperature and velocity parameters changing for each set up that was evaluated.
A graph was generated to display the temperature throughout the system and to display the
highest and lowest temperature in Kelvin. Additionally a slice view of this same graph was
generated. The conditions that were analyzed were current flow through the busbar with stagnant
air surrounding it, air moving in cross flow at 2 ft/s across the busbar, and air moving in parallel
flow across the busbar at 2 ft/s.

4. Results:
Figure 1: Steady state analysis of current carrying busbar with stagnant 100°F air (Note that this
simulation required constant temperature boundary conditions and both ends of the surrounding
air geometry are kept at 100°F)

5. Figure 2: Steady state analysis of current carrying busbar with stagnant 100°F air (slice view)

6. Figure 3: Steady state analysis with cross flow cooling of current carrying busbar with 100°F air
flowing 2ft/s (flow is cross flow in the Y direction)

7. Figure 4: Steady state analysis with cross flow cooling of current carrying busbar with 100°F air
flowing 2ft/s (slice view)

8. Figure 5: Steady state analysis with parallel flow cooling of current carrying busbar with 100°F
air flowing 2ft/s (flow is parallel flow in the X direction)

9. Figure 6: Steady state analysis with parallel flow cooling of current carrying busbar with 100°F
air flowing 2ft/s (slice view)
Discussion:
Stagnant Air
The first simulation analyzed the busbar in contact with stagnant air at 100°F. In Figure
1 the temperature gradient of the system is shown for steady state solution. It is important to note
that this simulation is not accurate with respect to predicting actual temperatures the busbar
would reach in a real physical setting for a number of reasons. First, COMSOLhas not
calculated changes in density in the air from temperature increase, and therefore has not created
any upward fluid flow from buoyant forces. Without this natural convection, the air stays
perfectly stagnant and in contact with the busbar which increases the temperature the air reaches
dramatically. Secondly, the boundary conditions for this experiment are not realistic. In the
heating module that is used for this simulation a constant temperature boundary condition is

10. required. The ends of the air geometry furthest from the busbar were set to a fixed 100°F. This
generates an unrealistic boundary condition and causes the air to be dramatically cooler near the
edges of the busbar than it would be in reality. This experiment serves to demonstrate that
without any air flow and therefor any convection, the temperatures the busbar would reach are
extreme. Looking at Figure 2 it is seen that the busbar reached over 3000K in this simulation.
Although this simulation’s results are not accurate with respect to a real world scenario, it still
serves as a good base reference point for how much heat is being generated. It is important to
note that although this model seems simple, the amount of calculations required to solve this
steady state solution is immense. This simulation was run with the coarsest resolution COMSOL
offered and still took roughly 15 minutes to solve. The next highest resolution was unable to find
a solution after an hour and was abandoned for the sake of time.
Cross flow
In the second simulation the busbar was analyzed with air flowing perpendicular to the
length of the bar at a rate of 2 ft/s. This serves as a good representation of actual ambient airflow
in an outdoor setting. The inlet air temperature is set to 100°F. Figures 3 and 4 show the
temperature gradient for the system in crossflow. The busbar reached a maximum temperature of
roughly 330 Kelvin, or about 134 Fahrenheit. Again it is important to note that there is no air
flow from changes in density in this simulation. If this flow was taken in to account the busbar
would have reached a lower maximum temperature. This simulation’s results more closely
approximate what would be expected from the busbar in a real world setting. Note that the
busbar and air reach their greatest temperature around the midpoint of the busbar. Again this
simulation was run with the coarsest resolution COMSOL offered for the sake of time. It would
be expected that a symmetric temperature gradient would be generated about the center of the
busbar with the parameters and geometry of this simulation. Resistance heating is expected to
heat the bar uniformly, but the temperature at the ends of the busbar is expected to be lowered
due to increased exposure to the lower temperature air. It is possible that the low resolution of
this simulation affected the temperature gradient’s symmetry, although the results still appear to
be plausible and close what would be expected.
Parallel
In the third simulation the busbar was analyzed with air flowing parallel to the length of
the bar at a rate of 2 ft/s. This simulation is more realistic than the initial stagnant air scenario,
and could be possible in a real world setting. Figures 5 and 6 show the maximum temperature
reached in the busbar was roughly 470 Kelvin or about 386 Fahrenheit. This is much hotter than
what was reached during the cross flow simulation, which is to be expected. As the air passed
over the busbar in cross flow it only came in contact with the busbar and heated up for a short

11. period of time, allowing for a greater cooling as the busbar had more cold air passing over it. In
parallel flow the air that was heated stayed in contact with the bar for much longer, causing the
end of the busbar furthest from the cold air inlet to be much hotter than the end closest. The
temperature at the cool end of the busbar is comparable to the cross flow simulation, while the
temperature at the opposing end is drastically hotter. Again this simulation does not take into
account fluid flow from density changes and therefor would have lower temperatures if this air
flow was incorporated.
Future Work:
The next step in the desired analysis of the busbar is to generate a model with turbulent
air at 100°F flowing on the inside of the busbar and run simulations with same stagnant air
around the bar and the same cross flow flowing over the bar as the previous simulations. This
model would have cylindrical air geometry inside the busbar that ends at the edges of the busbar
and rectangular air geometry around the busbar that also ends at the edges instead of extending
out as shown in the previous simulations. During the creation of the model COMSOL was unable
to allow a second fluid flow to be created inside the busbar. The inlet velocity and exit velocity
could not be specified for the new air geometry resulting in the simulation only showing stagnant
air inside the bar. Once the model has been properly created the stagnant air steady state solution
would be evaluated as well as the cross flow steady state solution. Additionally the steady state
solution for the cross flow simulation is to be evaluated again with insulation on the ends of the
busbar. This should negate the heat transfer from the open ends of the bar to the air and result in
a more uniform temperature gradient across the busbar.
Conclusion:
The simulations showed that cross flow is much more effective than parallel flow for
cooling a long, thin busbar, which is what would be predicted. Additionally with no fluid flow
the busbar would become incredibly hot. This was demonstrated by the first simulation and the
results in Figures 1 and 2. Each of the simulations run represents a very specific set of initial
conditions that serve to demonstrate the heat transfer of the busbar and air system that was given.
In reality, it is unlikely that the busbar will have air flowing perfectly perpendicular or parallel to
it, instead it will most likely have a combination between the two that fluctuates with time.
Although buoyant forces were not taken into account, the flow from density change and buoyant
forces would likely be small in comparison to the 2 ft/s flows specified in the simulations. The
results of these simulations indicate that a busbar in a combination of cross and parallel flow
would have a temperature between about 130 and 380 Fahrenheit. The real world convection
currents generated by the busbar heating would cause the overall temperature of the system to be
lower than what the simulations predict. Additionally real world fluctuation in fluid flow, heat
transfer, and other physical aspects would make a steady state condition for this busbar unlikely.