Examination of Heating in Rooftop Wiring Conduit
Submitted to: Timothy A. Shedd
By: Justin Chaudoir
May 15, 2014
University of Wisconsin – Madison
Department of Mechanical Engineering
Table of Contents
Executive Summary
Introduction
Heating in Rooftop Conduit
Radiation Calculation
FEHT Model
EMT Conduit
PVC Conduit
Electrical Heating in Conductor
FEHT Model
EES Model
Summary
References
Appendix
EES Radiation Calculations
Cross-sectional FEHT Analysis Material Properties
Cross-Sectional FEHT Parameters Calculations
EMT Conduit FEHT Results
Roof Surface Temperature Variation
PVC Conduit FEHT Results
Roof Surface Temperature Variation
Electrical Heating in Conductor EES Calculations
Executive Summary
The 2011 National Electrical Code requires that, when conduits are installed on rooftops, a pre-determined “temperature adder” must be added to the outdoor ambient temperature to ensure that the conductor is not used in a manner that may cause excessive, unsafe temperatures. This adder is meant to take heating from solar radiation into consideration.
However, is was suggested that more research is necessary to assess the validity and safety of the adder values. Since 2008, multiple reports have been generated that have produced contradictory results. In some cases, experimental results showed that the conductor temperatures in certain conduits reached unsafe values while other results showed that the temperature adders were appropriate. To address these contradictions and gain insight into the energy balance characteristics of rooftop conduits, multiple computer simulations were completed.
Theses simulations were completed using the FEHT Finite Element Analysis software (version 7.309) and Engineering Equation Solver (EES) software (version 9.678). Input parameters were determined both from the data obtained in previous experiments and by calculations. In all cases, values were chosen that represented conservative but appropriate conditions. ¾ inch PVC and EMT conduits were examined. In all cases, the conductor simulated was a 12 AWG XHHW-2 type conductor.
The simulations produced several important results. It was observed that in typical situations the rooftop temperature contributes to conductor heating as much, if not more than, solar radiation. Therefore, reducing or eliminating rooftop contact very effectively reduces conductor temperatures. If contact is not avoidable, light roofing material is desirable, as it will not absorb as much solar radiation as dark roofing material. Additionally, simulation showed that convection within the conduit plays an important role in reducing conductor temperature. By introducing an airflow as small as ½ mile per hour through the conduit, conductor temperatures can be significantly reduced.
Introduction
Using rooftop conduits to contain electrical wiring is common practice in many industrial and commercial buildings. When rooftop conduits are used, it is not unusual for them to be exposed to relatively high levels of solar radiation, as well as being heated by the rooftop surface. Currently, when conduits are placed on a rooftop there are designated temperature adders that must be used to establish the rated ampacity of wiring systems. However, recent reports and experiments have shown contradicting results regarding the adequacy of these temperature adders. In a 2011 report by David Dini of Underwriters Laboratories Inc., several potential conduit-conductor combinations were tested and experienced significant temperature increases when exposed to ambient Las Vegas radiation. However, other reports have shown that temperature increases from rooftop exposure fall within the previously established temperature adder system.
In an attempt to expose the important variables in a rooftop conduit heating distribution, it is desirable to create heat transfer simulations that help to understand each parameter and its effects on conductor temperature. In this report, finite element analysis (FEA) software and equation solving software results are used to examine the characteristics of typical conduit-conductor combinations and establish methods for mitigating the risk of high temperatures in rooftop conductors.
Heating in Rooftop Conduit
First, a simple cross-sectional model was used to examine the theoretical heat distributions in a rooftop-mounted conduit. In this analysis, 12 AWG XHHW-2 wire was modeled first in a ¾ inch EMT conduit and then in a ¾ inch PVCconduit. Several system parameters were manipulated in an effort to determine which had the most significant impact on the conduit temperature. These included surface contact, roof color, and radiation exposure. Nominal input parameters were determined based upon previous reports and measurements. Table 1 summarizes important parameters.
Table 1: Summary of Key ParametersParemeter / Nominal Value
Ambient Temperature [F] / 105
EMT Diameter [mm] / 23.42
EMT Thickness [mm] / 1.24
PVC Diameter [mm] / 26.67
PVC Thickness [mm] / 3.18
XHHW-2 Diameter [mm] / 3.581
XHHW-2 Insultation Thickness [mm] / 0.762
Solar Radiation [W/m^2] / 1000
Wind Speed [mph] / 1
Radiation Calculation
To prepare for an FEA of the heat distribution in the conduits, it was first necessary to determine the heat flux in the conduit due to solar radiation. In Dini’s report, solar radiation was measured during midsummer days and found to reach peak radiation of approximately 1400 W/m^2. However, because of the relatively long time constant of the conduit system, it is more appropriate to assume a more continuous radiation value. For the purpose of this report, a radiation of 1000 W/m^2 was used. This value represents an approximate average of peak sunlight radiation values.
To determine how much of this radiation would be absorbed by the conduit it was necessary to perform surface interaction calculations. These calculations were simplified by solving for one half of the conduit at a time. Figures 1 and 2 below show diagrams of the radiation systems used.
Figure 1: Radiation Model for Lower Half of ConduitFigure 2: Radiation Model for Upper Half of Conduit
For this calculation, the conduit was labeled as surface 1, the rooftop as surface 2, and the surroundings as surface 3. The resistances with the subscript “s” represent surface resistances, and all other resistances represent space resistances. Emissivity values of 0.85 for a dark roof surface and 0.7 for a light roof were used. These reflect measurements recorded by Dini. Table 2 below summarizes the results. For complete calculations, see the Engineering Equation Solver (EES) code in the appendix.
Table 2: Summary of Radiation Calculation ResultsConduit Surface / Radiation [W/m^2]
Top Half / 394.2
Bottom Half (Dark Roof) / 183.4
Bottom Half (Light Roof) / 291.4
FEHT Model
FEHT FEA was used to examine three main system parameters; angle of contact with roof surface, rooftop temperature, and distance from roof. The basic input parameters were direct solar radiation, solar radiation reflected from the roof surface, convection from the conduit to the surroundings, and conduction from the roof surface (if the conduit is in contact with the roof). The radiation values were obtained using the calculations explained above. Convection was estimated assuming 1 mph wind velocity and a 26°C (47 °F) temperature difference between the conduit and ambient air. This estimate is conservative because wind speeds observed during previous experiments were almost always above 1 mph and convection is strongly dependent on wind speed. Using this method, the heat transfer coefficient for convection was found to be approximately 14.5 W/m2K. Ambient air temperature was assumed to be 105 °F, approximately the worst-case temperature measured in previous reports. Conduction from the roof surface was estimated assuming a contact resistance of 0.61 K/W. This led to a heat transfer coefficient of approximately 222 W/m2K. Details on material parameters can be found in the appendix.
EMT Conduit
The first model examined was that of the ¾” EMT Conduit with the 12 AWG XHHW-2 Conductor. Figure 3 below shows the model, meshing, and inputs used for the FEA. Symmetry was assumed to simplify the model. Also note that the model represents a horizontal view of the conduit, with rooftop on the right and solar radiation on the left.
Figure 3: Model of EMT Conduit with 12 AWG XHHW-2 ConductorThe first parameter varied was the roof surface temperature. Figures 4 and 5 below show the results of changing the roof surface from 350 K to 315 K (170 °F to 107 °F). Radiation was held constant using values calculated for a dark roof, and contact angle was held at 10 degrees. For complete results, see the appendix.
Figure 4: EMT Conduit with Roof Surface at 350 K (77 °C, 170 °F)Figure 5: EMT Conduit with Roof Surface at 315 K (42 °C, 107 °F)
The results above show that when the conduit is in contact with the roof surface the conductor temperature is highly dependent on the roof surface temperature. When the roof surface is 170 °F (77 °C), the conductor temperature rise above ambient is approximately 54°F (30 °C). When the roof surface is 107 °F (42 °C), the conductor temperature rise above ambient is approximately 13°F (7.2 °C). This means that when the conduit is in contact with the roof, it is important that the roof does not reach temperatures significantly above ambient temperature.
The next parameter varied was angle of contact between the roof surface and the conduit. This angle could change depending on the hardness of the roof and conduit materials and the pressure applied when mounting the conduit. For this simulation, a high roof surface temperature was chosen; 350 K (77°C, 170°F). Figures 6 and 7 below show the results of varying the angle of contact from 10 to 30 degrees.
Figure 6: EMT Conduit with Roof Surface at 350 K (77 °C, 170 °F), 10 Degree Contact AngleFigure 7: EMT Conduit with Roof Surface at 350 K (77 °C, 170 °F), 30 Degree Contact Angle
These results show that as the angle of contact between the roof and conduit increases, the conductor temperature approaches that of the roof surface. With a 10 degree angle of contact, the conductor is approximately 10 °F (5.6 °C) below roof temperature. With a 30 degree angle of contact, the conductor is only about 3 °F (1.7 °C) below roof temperature. This means that reducing the contact angle when the roof is hot will reduce the conductor temperature. Conversely, if the roof surface is cooler than the conduit, increasing contact angle will act to reduce conductor temperature. However, it is unlikely that the roof surface will ever be significantly cooler than the conduit.
Lastly, the simulation was adjusted to examine the effect of removing the conduit from the roof surface. To simplify the analysis, only the worst cases were considered. For the simulation with roof contact, the worst case is a dark, hot roof with a large contact angle. For the simulation without roof contact, the worst case is a cooler, light roof that reflects more solar radiation to the conduit. Figures 8 and 9 below illustrate the results of these simulations.
Figure 8: EMT Conduit with Roof Surface at 350 K (77 °C, 170 °F), 30 Degree Contact AngleFigure 9: EMT Conduit Raised off of Roof Surface
These results show that the temperature of the conductor is significantly reduced in a conduit that is raised off of the roof surface. When the conduit is in contact with the roof, the conductor temperature is approximately 62 °F (34.4 °C) above ambient temperature. When the conduit is not in contact with the roof, the conductor temperature is approximately 41 °F (22.8 °C ) above the ambient. This represents an overall 21 °F (11.7 °C) drop in conductor temperature. This drop would also increase with a dark roof because levels of reflected solar radiation would be lower.
PVC Conduit
The second model examined represented a ¾” PVC conduit with a 12 AWG XHHW-2 conductor. The model was constructed in a similar manner to that used for the EMT model. Figure 10 below shows the model, meshing, and inputs used for the FEA.
Figure 10: Model of PVC Conduit with 12 AWG XHHW-2 ConductorAs above, the first parameter varied was the roof surface temperature. Figures 11 and 12 below show the results of changing the roof surface from 350 K to 315 K (170 °F to 107 °F). Radiation was held constant using values calculated for a dark roof, and contact angle was held at 10 degrees. For complete results, see the appendix.
Figure 11: PVC Conduit with Roof Surface at 350 K (77 °C, 170 °F)Figure 12: PVC Conduit with Roof Surface at 315 K (42 °C, 107 °F)
As with the EMT conduit, these results show a strong relationship between roof temperature and conductor temperature. With the roof temperature at 170 °F (77 °C), the conductor temperature is approximately 53 °F (29.4 °C) above ambient temperature. With the roof temperature at 107 °F (42 °C), the conductor temperature is approximately 11 °F (6.1 °C) above ambient temperature. This supports the results of the EMT conduit, showing that maintaining a safe conductor temperature depends on a roof temperature that is not significantly higher than ambient temperature.
The next parameter varied was angle of contact between the roof surface and the conduit. This angle could change depending on the hardness of the roof and conduit materials and the pressure applied when mounting the conduit. For this simulation, a high roof surface temperature was chosen; 350 K (77 °C, 170 °F). Figures 13 and 14 below show the results of varying the angle of contact from 10 to 30 degrees.
Figure 13: PVC Conduit with Roof Surface at 350 K (77 °C, 170 °F) and 10 Degree Contact AngleFigure 14: PVC Conduit with Roof Surface at 350 K (77 °C, 170 °F) and 30 Degree Contact Angle
These results also support the EMT model, showing that as contact angle between the roof and conduit increases, the conductor temperature increases. With a contact angle of 10 degrees the conductor temperature is approximately 158 °F (70.0 °C), 12 °F (6.7 °C) below roof temperature. With a contact angle of 30 degrees the conductor temperature is approximately 166 °F (74.4 °C), 4 °F (2.2 °C) below roof temperature. Once again, this suggests that when the roof is hot it is important to minimize the amount of contact between the conduit and roof.
Lastly, the simulation was adjusted to examine the effect of removing the conduit from the roof surface. Once again, only the worst cases were considered. Figures 15 and 16 below illustrate the results of these simulations.
Figure 15: PVC Conduit with Roof Surface at 350 K (77 °C, 170 °F) and 30 Degree Contact AngleFigure 16: PVC Conduit Raised off of Roof Surface
As expected, these results also agree with those obtained with the EMT conduit. When the conduit is in contact with the hot, dark roof the conductor temperature is approximately 61 °F (33.9 °C) above ambient temperature. When the conduit is removed from the roof the conductor temperature is approximately 38 °F (21.1 °C) above ambient temperature. Once again, removing the conduit from the roof surface dramatically decreases the conductor temperature rise.
Electrical Heating in Conductor
The next analysis completed involved simulating the heat generated in a conductor that is carrying maximum rated current. For this analysis a 12 AWG XHHW-2 conductor was selected to represent a typical scenario. As stated in the 2011 National Electrical Code, this conductor is rated for a current of 20 amps at 75 °C. In practice, this current is always limited by the circuit breakers, so the actual current in the conductor was a maximum of 80 percent of the 75 °C rating, or 16 amps. To simplify the simulation, the conductor was modeled as a single wire with a diameter of 2.057 mm. Key parameters are summarized in table 3 below and complete calculations can be found in the appendix.
Table 3: Summary of Important Parameters for Electrical Heating SimulationParameter / Value
Diameter / 2.057[mm]
Conductivity / 394.6 [W/m*K]
Resistivity / 1.68e-8 [Ω-m]
75 °C Rating / 20 A
Actual Current / 16 A
Heat Generation / 389,433 [W/m^3]
FEHT Model
The next method used to examine heat generation in the XHHW-2 conductor was FEA of the wire alone. This was also carried out using the software program FEHT. In this model it was assumed that one end of the wire was contacting a heat sink held at 41 °C, or approximately 105 °F. This temperature was chosen to represent the ambient temperature conditions observed in previous experiments. Furthermore, symmetry was used to constrain the end of the conductor opposite the heat sink to experience zero heat flux. The total length of the conductor was modeled as 25 cm and the diameter as approximately 2.0 mm. This length was chosen due to software constraints, however the trends observed still indicate the characteristics of realistic systems. Figure 17 below shows the FEHT model used.
Figure 17: Model of XHHW-2 conductorFor the first simulation, all heat conduction was constrained to take place within the conductor, not through conduction or convection to the surroundings. As discussed above, the internal generation in the conductor was approximated as 389,433 W/m3. The model and results are pictured in figure 18below.
Figure 18: Temperature Contours in Conductor Without ConvectionThese results show a 30 °C (53 °F) temperature rise in the 25 cm wire. Next, convection was added to the simulation. A heat transfer coefficient was estimated assuming free convection of a cylinder in EES. The temperature at the surface of the conductor was estimated as 55 °C (131 °F) and the ambient temperature as 41 °C (105 °F). With these values, the heat transfer coefficient was calculated to be 17.5 W/m2K. With this added convection, the temperatures in the conductor were dramatically decreased, as shown if figure 19 below.
Figure 19: Temperature Contours in Conductor With convectionIn this case, the temperature rise was reduced to 16 °C (23 °F). These results demonstrate some very important characteristics of the conductor. The model shows that the temperature increase in the conductor is considerable in a strictly adiabatic scenario. However, the introduction of convective heat transfer from the conductor has a strong impact on the temperature increase in the wire, more than halving the temperature rise. Of course, several assumptions and approximations were made to produce these results. To further refine the calculations, a numerical model of the conductor heat transfer was simulated in EES. The results of this simulation are detailed in the following section.
EES Model
Using a numerical solution to simulate the electrical heating in a XHHW-2 conductor allows for a more accurate solution in several ways. First, it eliminates the inaccuracies introduced by the scale and modeling limitations in the FEHT software. Second, it allows for the use of more precise parameters and calculations. This means that the EES model provides a more realistic representation of the characteristics of the conductor.