NBS

PUBLICATIONS A11100 T10t,45

NAT'L INST. OF STAND & TECH R.I.C.

NBSIR 80-2129

M:S%i

Modeling for Determination of

Temperatures of Electrical Cables

ithin Thermally" Insulated Walls

David D. Evans

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

U S. Department of Commerce

Washington, D C. 20234

October 1980

iterim Report

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. < j MODELING FOR DETERMINATION OF

TEMPERATURES OF ELECTRICAL CABLES

WITHIN THERMALLY INSULATED WALLS

NOV 2 4 1980

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David D. Evans

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Washington, D.C. 20234

October 1980

Interim Report

Prepared for: Department of Energy

Washington, D.C. 20545

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation

NAitONAL BUREAU OF STANDARDS, Ernest Ambler, Director
w7 i - iO— 4 t-

<*. • <• » ’

*

- , *
PREFACE

This report is one of a group documenting National Bureau of

Standards research and analysis efforts in developing energy and cost

data in support of the Department of Energy (DoE) /National Bureau of

Standards (NBS) Building Energy Conservation Criteria Program. This

work was supported by DoE/NBS Task Order A008-BCS under Interagency

Agreement No. EA 77 A 01 6010.
TABLE OF CONTENTS

Page

PREFACE iii

LIST OF FIGURES v

LIST OF TABLES v

Abstract 1

1. INTRODUCTION 1

2. EXPERIMENTAL DATA 3

3. MODELS 4

3.1 350 Node Network - Wall Model 5 3.2 3 Node - Cylindrical Model 8

3.3 13 Node Model - Heat Sink Effects of Wood Studs .... 10

4. CONCLUSIONS 12

5. ACKNOWLEDGEMENTS 13

6. REFERENCES 13

iv
LIST OF FIGURES

Page

Figure 1. Typical wall section 14

Figure 2. Beausoliel's measurements for an AWG-12 2-G NM cable

insulated with glass fiber 15

Figure 3. Temperature distribution for an AWG-12 2-G NM cable

with 20 amperes current load in a 12 cm thick

insulation slab (one-half of slab thickness shown) . . 16

Figure 4. Temperature distribution for an AWG-12 2-G NM cable

with 20 amperes current load in an insulation slab

with wood facing (one-half of slab thickness shown) . 17

Figure 5. Temperature of AWG-12 electric cable in wall space

with constant current flow of 20 amperes (heat flow

perpendicular to the cable) 18

Figure 6. Thirteen node model of wall space 19

Figure 7. Predicted and measured temperature profiles - AWG-12

cable, 20 amperes 20

Figure 8. Predicted and measured temperature profiles - AWG-12

cable, 15 amperes 21

Figure 9. Predicted and measured temperature profiles - AWG-12

cable, 27 amperes 22

LIST OF TABLES

Page

Table 1. Material thermophysical properties used in the

calculations 23

v

MODELING FOR DETERMINATION OF TEMPERATURES OF ELECTRICAL

CABLES WITHIN THERMALLY INSULATED WALLS

David D. Evans

Abstract

Models have been developed to predict the

temperature rise caused by resistive heating of a current-carrying electric cable within an insulated

wall cavity, with emphasis on simplified models to

minimize computation time. Predictions are compared

to measurements performed on an AWG-12 2-G NM cable

installed in a laboratory wall space mock-up. Results

of the two-dimensional model are within 15 percent of

the measured temperatures. The heat sink effect of

the wood studs within the wall on the temperature

rise of the section of cable passing through them

is demonstrated both with experiment and calculation.

Key words: Electric wiring; resistive heating;

thermal insulation; thermal model; wiring system.

1 . INTRODUCTION

Existing electric cables strung through the wall cavity and attic

spaces in a building may be encapsulated by thermal insulation. Accompanying the present increased use of thermal insulation have been

questions about the potential harmful effects of increased operating

temperatures for thermally insulating the building electrical wiring

systems

.

Electric current limits for cables are established by considering

the temperature limits for the electrical insulation material used to cover the conductors in the cable. In establishing the operating temperatures of current-carrying electric cables, the heat generated by the

current flow in the conductors is considered to be dissipated through

1
the cable jacket directly into air at a temperature of 30°C [1]\ The

established principle for general wiring is that no conductor shall be

used under such conditions that its temperature, even when carrying

current, will exceed the specific maximum operating temperature for the

type of electrical insulator involved.

Thermal insulation surrounding electric cables inhibits the

dissipation of heat generated by the electric current in the conductors.

For thermally insulated cables the heat that normally would be dissipated from a current-carrying cable surface to the surrounding air must

conduct through the layer of the thermal insulation before dissipation

to the air. This additional insulation causes an increase in the temperature of the cable above that for a cable exposed directly to air

under an identical current load condition.

Mr. Robert Beausoliel in the Center for Building Technology at the

Notional Bureau of Standards (NBS) has conducted experiments in which

the surface temperatures of an AWG-12 2-G NM electric cable routed

horizontally through stud spaces within a laboratory wall mock-up were measured in strategic places [2]. Measurements were made of the transient temperature rise for the cable in response to 15 amperes, rated 20

amperes, and overload 27 amperes steady current.

Experimental investigations of the operating temperatures of

electric cables over a range of current loads, insulation types, and

installation conditions can be time consuming and costly. However,

mathematical models can be developed to predict the transient temperature

rise of the cable in response to a steady current load or to directly

calculate the steady operating temperatures. Mathematical models, once verified by comparison with existing test data such as those available

from Beausoliel’ s tests, may be used to extend the data to other conditions

of interest.

Numbers in brackets refer to the references listed in section 6.

2
Mathematical models vary in complexity. Detailed models that are capable of accounting for all the physical phenomena involved in transient heating problems require large and efficient computer systems to

execute. To achieve greatest accuracy, small space and time step intervals requiring large storage and execution times must be used to provide

solutions of interest. Approximate models that account for the salient

features of the configuration of the thermally insulated wire, but

simplify the calculation effort by lumping the effects of various

materials and geometries into a simple thermal network for analysis, are also available. The approximate models can provide solutions with

sufficient accuracy for engineering or design purposes from computer

codes that do not require burdensome storage or execution times.

This report discusses the features of several models of varying

complexity, all directed towards predicting the temperatures of electric

cables in an insulated wall space with geometry similar to the walls

tested by Beausoliel. In previous work by Evans [3] steady operating

temperatures for insulated wires were calculated based on a cylinder of

insulation surrounding the cable. Calculations are presented in this

report that demonstrate, for comparative purposes, the transient temperature rise of a cable surrounded by a cylinder of insulation as well as the same cable buried within a slab of insulation. Either calculation

may be used to model electric cables within wall spaces. A simple

thermal network is constructed as an approximate method of predicting

the cable temperature rise within the wall cavity, including the effects

of wood studs and the cable termination.

2 . EXPERIMENTAL DATA

Beausoliel [2] constructed three wall sections of the type shown in

figure 1. Each wall section was insulated with one of three types of

thermal insulation — blown glass fiber, blown cellulose, and ureaformaldehyde foam. Using thermocouples attached to the cable acket,

temperatures were measured at the locations shown in figure 1 on the

3
single cable in the upper half of the wall section, and a multi-cable

configuration (not shown) in the lower half of the wall section. Three

steady current loads were applied—15 amperes, rated 20 amperes, and

overload 27 amperes.

To limit the scope of the modeling work reported here, only the

data for the single cable in the glass fiber insulated wall tests of

Beausoliel [2] were studied. Figure 2 presents the measured temperature

of the cable jacket under the three current loads for the single cable

at locations 1, 4, 6 and 8 as indicated in figure 1. Thermocouple 8 in

the center of the wall cavity showed the greatest temperature rise at

all current loads. The temperature at location 4, in the adjacent end

stud space, was slightly lower than at location 8. The temperature at

location 6, where the cable passed through a hole in the wood stud was

lower than in either adjacent stud space. This indicates that some heat

conducted along the cable towards the wood stud from both adjoining

insulated spaces. This stud, as well as the others, acted as heat

sinks. The temperature at the exposed end stud, location 1, was the

lowest of those measured along the cable.

3 . MODELS

In the wall section mock-up, typical of home construction, shown in

figure 1, an electric cable is embedded in an insulation layer approximately 9 cm thick which is sandwiched between the wall facing materials

which also provide additional insulation. The total wall section

including facing materials varies in thickness from 12 to 14 cm. To

dissipate the resistive heat generated by current flow in the cable

conductors, the cable must operate sufficiently above ambient temperature to conduct the heat generated through the thermally insulated wall

space. In this section of the report various methods used for determining the temperature rise of the current-carrying electric cable will

be discussed.

4
3.1 350 Node Network - Wall Model

The simplest and most direct method of obtaining transient temperature

predictions for the cable within an insulated wall space is to code an explicit three-dimensional network that accounts for the geometry and

the different materials involved. The disadvantage with this approach

is that a prohibitive amount of computation time is usually needed to

obtain a full transient solution.

If attention is restricted to sections of the wall in which heat

flow is predominately perpendicular to the axis of the cable, a twodimensional model for heat conduction in the wall cross section may be

sufficient to provide accurate predictions of the cable operating temperatures. In the test walls constructed by Beausoliel, position 8,

which is far away from the heat sink effect of the studs, as indicated

in figure 1, best satisfies this condition.

For comparative purposes, the temperature distributions throughout

the cross sections of two different insulated wall space configurations

containing a current-carrying electric cable were calculated. If a cable is located in the center of the wall cross section, the entire

temperature distribution throughout the cross section may be determined

by only modeling one quadrant and making use of the symmetry. For a cable located in the center of a 12 cm x 98 cm wall cross section, one quadrant (6 cm x 49 cm) may be modeled using a 350 node grid with a uniform square array with 1 cm spacing. With this model, the node

located in one corner of the quadrant represents the cable. The

boundaries of the rectangular- shaped quadrant intersecting this corner must be lines of symmetry. The remaining two sides represent ambient

conditions and were modeled as the fixed constant temperature boundaries.

Using the 350 node system as described, transient temperature

conditions were calculated using an explicit forward differencing calculation initiated with all nodes at the ambient temperature of 25°C.

5
This calculation method is described by Rohsenow and Hartnett [4]

.

The

general recursive formula uses information available at time t to

calculate conditions at t + At:

T.

1

(t + At) = —cv.

l Du h

(t) Dj) ' T

*

(t) +

Ql

j ' j '

( 1 )

where T

.

1

t

At

is the temperature at the i-th node,

is time,

is time step.

cv. is the thermal mass associated with the i-th node.

l

k. . is the thermal conductance between the i-th and adjoining

j-th node.

is the heat generation rate at the i-th node.

Direct application of equation 1 to the one centimeter spacing grid

around the node representing the cable would not produce accurate predictions of the cable jacket temperature. Special calculations were

needed in this area of the grid because physically the location of the

cable jacket surface (radius 0.51) within the wall cross section being

modeled did not correspond to any grid points. Without changing the

grid size, the accuracy of the calculation may be improved by considering thermal conduction between the corner node representing the cable

jacket and the three adjacent nodes as special cases with modified

thermal conductances differing from the values that would be calculated

based on a straightforward analysis of the square grid. Effectively

this extends the representation of the cable jacket surface to the three

nodes adjacent to the corner. A straightforward calculation based on

the uniform grid proceeds from these three nodes.

The thermal conductances from the corner node representing the

cable jacket to the adjoining three nodes were calculated based on radial conduction of heat. Considering the symmetry boundaries at this

6
corner, the conductances to the two nodes on the boundaries are given

by:

K = TTk/ [8 £n(l/0.51) ] (2)

where k is the thermal conductivity of the glass fiber insulation

material. The conductance to the third node, diagonally across the 1 cm square grid space, is given by:

K = Trk/ [ 4 £n(/2"/0. 51) ] (3)

No direct conduction between the three nodes adjacent to the corner node

was assumed.

Discussions of the use of symmetry in thermal conduction problems

and methods to determine the thermal conductance between cylindrical

shells can be found in the textbook by Kreith [5].

For all calculations, the heat generated at the corner node

representing the cable was considered to be a function of both current

and the temperature of the node. For the AWG-12 cable, the resistive

heat generation per centimeter of cable length (Q) in units of W/cm was

given by:

Q

= 2 • I

2 • 4.8 (1+ 0.00427 T )

• 10" 5 (4)

w

where I is the current in amperes and T is the cable jacket temperature w

in degrees Celsius [3]. In the model only one quarter of the heat

generated is conducted into each quadrant.

Other thermal and physical properties of the material used in the

calculations are given in table 1.

Part of the total network and steady temperature distributions for

the two cases calculated are shown in figures 3 and 4. In figures 3 and

4, the cable is shown in the lower left-hand corner of the grid. The

7
temperatures shown in figure 3 are the steady conditions for an AWG-12

2-G NM cable carrying 20 amperes within a 12 cm thick slab of glass

fiber insulation material. The solution in figure 4 differs from figure

3 only by the substitution of a 1 cm thick wood facing material at the

ambient temperature edge in place of an equivalent thickness of insulation. Taking note of symmetry, figure 4 is the typical representation

of the two-dimensional conduction in a wall space with a 10 cm thick layer

of insulation faced on each side by a 1 cm thick layer of wood material.

As can be seen by comparison, the substitution of wood facing material

for 1 cm of insulation resulted in a 2.0°C decrease in steady operating

temperature of the cable jacket.

The steady operating temperatures shown in figures 3 and 4 were the

final steady-state result of a calculation of the transient temperature

conditions within the wall space.

3.2 3 Node - Cylindrical Model

The geometry of the wall space is complicated and the effective

overall thermal conductance for heat transfer from the embedded cable to

the exterior is difficult to calculate. If attention remains fixed on sections of wall space where heat flow is predominately perpendicular to

the axis of the cable, as discussed in the previous section, upper bound

estimates of the thermal conductance of the wall space may be calculated

based on a simple cylindrical geometry. The steady cable temperatures

calculated on the basis of insulation by a 12 cm diameter cylinder of

insulation will be equal to or lower than those calculated based on the

more complicated 12 cm thick slab of insulation simulating a wall

geometry discussed in the previous section.

To estimate the accuracy of the cylindrical shell approximation to

the wall geometry a comparative case to the 12 cm thick slab solution

(see figure 3) was calculated.

8
Using the same thermal properties, the transient temperature rise

for an AWG-12 2-G NM cable was calculated for a 12 cm diameter cylinder

of glass fiber insulation surrounding the cable. The symmetry of the

cylindrical geometry reduces the two-dimensional calculation for the

wall geometry to a one-dimensional calculation. In the cylindrical

approximation only three nodes are used. One node is used to represent

the cable, a second to represent the thermal insulation at the radius

dividing the insulation into two equal masses, and the third to represent ambient conditions at the outer surface of the insulation cylinder.

The explicit calculation scheme given by equation 1 applies to this

calculation where values of thermal conductance and thermal mass asso- ciated with each node are based on calculations assuming cylindrical

shells and the properties in table 1.

A comparison of the results between the temperature rise predicted

on the basis of the 350 node model for the 12 cm thick slab and that for

the 3 node 12 cm diameter cylindrical model is shown in figure 5 for a

20 ampere current load. The initial rates of temperature rise for both

models are nearly equal as would be expected, because the boundary

should have little influence at early times. At steady state, however,

the cable jacket temperature calculated by the approximate cylindrical

model (68.2°C) is 8 percent below the value calculated with the 350 node

network and wall geometry (74.0°C). To produce equal steady temperatures

the diameter of the cylinder would have to be increased 32 percent to

15.8 cm.

The steady-state temperature of an insulated cable is underestimated

by replacing the slab of insulation that simulates a wall space by a cylinder of insulation with diameter equal to the thickness of the slab.

However, the approximations are useful, primarily because the simplicity

greatly reduces the burden of the calculations. Execution times for the

350 node network are one thousand times that for the 3 node network.

9
The great reduction in calculation time enables more complicated threedimensional effects such as conduction along the wire to be modeled

using cylindrical approximations without producing large execution times

for the computer code.

3.3 13 Node Model - Heat Sink Effects of Wood Studs

Using the simplification of cylindrical shells to reduce the burden

of the calculation, a 13 node network was constructed that in the simplest way accounted for the effects of conduction both parallel and

perpendicular to the cable direction. The cylindrical symmetry reduced

the three-dimensional problem to a two-dimensional calculation. The

thirteen node network was constructed to represent the one and one-half

stud spaces instrumented in Beausoliel’s tests [2]. This network is

shown in figure 6, superimposed on a schematic of the wall space.

Basically, the three node method of representing conduction through

cylindrical shells perpendicular to the wire axis was used to represent

insulation, wood stud, and cable material. Heat flow paths were also

provided between these nodes to allow conduction parallel to the axis of

the cable.

Equation 1 was used with a fixed boundary condition of ambient

temperature at the outer boundary of the cylindrical shells and initial

ambient temperature everywhere. Thermal conductance values perpendicular

to the cable direction were calculated using

K =

2TTk (5)

S,n r /r T o I and parallel to the cable direction using

L

where r^ is the radial distance measured from the center of the cable to

a node.

10
is the radial distance measured from the center of the cable to

the adjacent node (r > r T ).

A is the cross-sectional area of the cylindrical shell Tr(r^ - r|)

.

L is the distance between nodes parallel to the cable direction.

k the thermal conductivity of the material.

As with previous calculations the outer diameter of the cylindrical

shell was set equal to 12 cm which was close to the thickness of

Beausoliel’s model test walls. Contact between various materials was

considered intimate; contact resistance was assumed to be equal to zero. Thermal properties for the electric cable, thermal insulation, and wood

stud materials used in the calculations are given in table 1. The wood

facing material was not modeled.

An explicit scheme, following equation 1, and using the 13 node

model of the wall space was coded and executed. The results can be

compared directly to measurements made by Beausoliel at the strategic

thermocouple locations 1, 4, 6, and 8 as illustrated in figure 1.

Figure 7 shows both predictions and experimental data at the strategic

points for 1/4, 1/2, 1 and 4 hours after a steady current of 20 amperes

was initiated in the AWG-12 cable.

As would be expected, considering the number of approximations

used, the calculated temperatures do not agree exactly with measurements,

but important characteristics are demonstrated. As discussed in section

3.2 the cylindrical model underestimates the steady temperature of the

cable in the wall space geometry, so that the predicted temperatures

after 4 hours current flow can be expected to be slightly lower than the

measured values. It is interesting to note that the steady (4 hour)

temperature predicted at position 8 is more than 5°C below the steady

temperature predictions from the cylindrical geometry solution discussed

in section 3.2 in which no heat flow was allowed parallel to the cable.

This decrease is predominately due to heat flow along the cable towards

11
the stud. Heat loss from the end stud at location 1 is overestimated by

the calculations, giving lower calculated temperatures. As indicated,

the agreement between the calculated and measured results is fair, but

it is obvious that the effective thermal mass of the wood studs and

cable are not modeled exactly. Although not performed, adjustments of

thermal properties for each of the materials can produce better agreement

between predictions and experiments.

For completeness, experimental results and calculated cable

temperatures are compared for the cases of 15 amperes and overload 27

amperes current load on the AWG-12 cable in figures 8 and 9. Changes in

the relative relationship between prediction and experimental data in

the 27 amperes load case (figure 9) , when compared to the 20 amperes

load (figure 7), have been judged to reflect the influence of an increase

in thermal conductance with increasing temperature for the insulation

material. Temperature dependent thermal properties for the thermal

insulation materials were not included in the model.

4. CONCLUSIONS

The predictions of the transient temperature rise of an electric

cable buried in an insulated wall space show the heat sink effects of

the wall studs through which the cable is routed. For the AWG-12 2-G

NM cable, carrying 20 amperes current load, calculations show that

conduction of heat along the wire to wood studs lowers the steady operating

temperature at least 5°C, compared to the operating temperature when no heat is dissipated parallel to the cable direction.

The present model can produce calculated results that are in fair

quantitative agreement with laboratory measurements by choosing representative values for the thermal and physical properties of materials.

Experimental data on the thermal properties of the insulation materials

used in the experimental work for a range of temperatures are needed

before further refinements in the model can be justified.

12
For heat conduction perpendicular to the cable direction, a simple

cylindrical shell approximation for the geometry of the wall space has

been shown to be a useful approximation to determine thermal response.

5 . ACKNOWLEDGEMENTS

The author is grateful for the assistance of Mr. Daniel Madrzykowski

in coding the programs for the models and helping to prepare the graphics

for this report.

6 . REFERENCES

[1] Allowable Ampacities of Insulated Conductors Rated 0-2000 Volts,

60°C to 90°C, Table 310-16, p. 132, National Electric Code, 1978,

National Fire Protection Assn., Boston, MA.

[2] Beausoliel, R. W., Temperatures produced by self-heating of wiring

when surrounded by thermal insulation within residential building

walls, Nat. Bur. Stand. (U.S.), NBSIR in process.

[3] Evans, D. D., Calculated operating temperatures of thermally

insulated electric cables, Nat. Bur. Stand. (U.S.), Tech. Note 1133

(1980)

.

[4] Rohsenow, W. M. and Hartnett, J. P., Handbook of Heat Transfer,

p. 4-47 (McGraw-Hill Book Co., New York, NY, 1973).

[5] Kreith, F., Principles of Heat Transfer (International Textbook Co.,

Scranton, PA, 1965)

.

13
FRONT VIEW SIDE VIEW

14
27

amperes

20

amperes

15

amperes

!

TIME

(hours)

Figure

2.

Beausoliel's

measurements

for

an

AWG-12

2-G

NM

cable

insulated

with

glass

fiber
SYMMETRY

BOUNDARY

Figure

29.4

T

Scale: K-lcm-H

i

74

Cable

jacket

SYMMETRY BOUNDARY

29.3

GLASS

28.8

FIBER INSULATION

28.1 27.2 26.1 25

30.5 30.1 29.0 27.8 26.4 25

32.3 31.5 30.2 28.6 26.8 25

34.5 33.4 31.6 29.6 27.3 25

37.5 35.8 33.4 30.7 27.9 25

41.6 38.9 35.6 32.0 28.5 25

47.1 42.6 37.8 33.4 29.1 25

54.3 46.5 39.9 34.4 29.6 25

62.3--49.1- 41.0—-34.9—-29.8——25

3. Temperature distribution for an AWG-12 2-G NM cable

with 20 amperes current load in a 12 cm thick

insulation slab (one-half of slab thickness shown)

16

FIXED

TEMPERATURE

BOUNDARY

All

temperatures

are

in

°C
SYMMETRY

BOUNDARY

GLASS FIBER INSULATION

T

Scale: h-lcm-H

Wood JCable SYMMETRY BOUNDARY

jacket

Figure 4. Temperature distribution for an AWG-12 2-G NM cable

with 20 amperes current load in an insulation slab

with wood facing (one-half of slab thickness shown)

17

FIXED

TEMPERATURE

BOUNDARY

All

temperatures

are

in

°C
«/>

(Go I aamvaadwai laxGvr aiavo

18

Figure

5.

Temperature

of

AWG-12

electric

cable

in

wall

space

with

constant

current

flow

of

20

amperes

(heat

flow

per;

endicular

to

the

cable)
\

\
70

65

60

55

50

45

40

35

30

25

iqui

©

Points - Beausoliel's data glass fiber insulation

©=!4 hr; ©='/2 hr; (T)=1 hr; (T)=4 hr

AMBIENT

J I I L 8 6 4 1 THERMOCOUPLE LOCATION

7. Predicted and measured temperature profiles - AWG-12 cable, 20 amperes

20
Figure 8. Predicted and measured temperature profiles - AWG-12 cable, 15 amperes

21
-1 I I L 8 6 4 1 THERMOCOUPLE LOCATION

F'igure 9. rredict id and measured temperaLui e pi of i i.t_ M'JG- 1 1 rable, 27 amperes

22
Table 1. Material thermophysical properties used

in the calculations

Material Thermal Conductivity

W/cm°C

Volometric Heat Capacity

(density x heat capacity)

J/cm3 °C

#12 electric cable 3.85* 2.86+

Glass fiber insulation 4.5 x 10"4 0.021

Wood facing 1.0 x 10" 3 0.94

* Copper wire only.

+2.34 J/cm°C (cable diameter = 1.02 cm)

23
NBS-1 1 4 A irev. a-78)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 80-21292.Gov't Accession No. 3. Recipient's Accession No.

4. TITLE AND SUBTITLE

MODELING FOR DETERMINATION OF TEMPERATURES OF ELECTRICAL

CABLES WITHIN THERMALLY INSULATED WALLS

5. Publication Date October 1980

6. Performing Organization Code

7. AUTHOR(S)

David D. Evans

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

10. Project/Task/Work Unit No. 7425106

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State, ZIP)

Department of Energy

Washington, D.C. 20545

13. Type of Report & Period Covered Interim

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

16. ABSTRACT (A 200-word or less factual summary of most si ghi ficant information. If document includes a signi ficant bibliography nr literature survey, mention it here.) Models have been developed to predict the temperature rise caused by resistive

heating of a current-carrying electric cable within an insulated wall cavity, with

emphasis on simplified models to minimize computation time. Predictions are compared

to measurements performed on an AWG-12 2-G NM cable installed in a laboratory wall

space mock-up. Results of the two-dimensional model are within 15 percent of the measu

temperatures. The heat sink effect of the wood studs within the wall on the

temperature rise of the section of cable passing through them is demonstrated both

with experiment and calculation.

17. KEY WORDS (six to twelve entries ; alphabetical order; capi tali ze only the first letter of the first key word unless a proper name;

separated by semicolons)

Electric wiring; resistive heating; thermal insulation; thermal model; wiring system.

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