NBS

REFERENCE publications

NBSIR 86-330

A 11 ID 2 L314L7

OF STANDARDS & TECH R.I.C.

n All 102631467

STOVE: A Predictive Model for

Heat Transfer From Solid-Fuel

Appliances

Richard D. Peacock

Richard A. Dipert

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

February 1987

U.S. DEPARTMENT OF COMMERCE

BUREAU OF STANDARDS

-QC

100

. U56

86-3300

1987

MBS

RESEARCH

INFORMATION CENTER

NBSIR 86-3300 h('/b

STOVE: A PREDICTIVE MODEL FOR

HEAT TRANSFER FROM SOLID-FUEL

APPLIANCES

Richard D. Peacock

Richard A. Dipert

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

February 1987

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

1

TABLE OF CONTENTS

LIST OF TABLES iii

LIST OF FIGURES iii

NOMENCLATURE iv

Abstract 1

1. INTRODUCTION 1

2. REVIEW OF PREVIOUS WORK 4

2 . 1 Fire Incidents Involving Wood Burning Appliances 4

2 . 2 Clearances in Existing Codes and Standards 5 2.3 Temperatures Developed in Heating Systems

2.4 Limiting Safe Temperatures on Combustible Surfaces 9 2.5 Data for Model Validation 11

3. THEORETICAL BASIS FOR THE MODEL 11

3.1 Radiative Heat Transfer 12

3.2 Convective Heat Transfer 14

3.3 Conductive Heat Transfer 15

3.4 Solution of the Equations for an Arbitrary Protection System . 16

4. COMPUTER IMPLEMENTATION OF THE MODEL 18

5. COMPARISON OF THE MODEL PREDICTIONS WITH EXPERIMENTAL DATA 19

6. MODEL CAPABILITIES AND EXAMPLES 20

6.1 Heat Transfer From Appliance to an Unprotected Wall 21

6.2 Heat Transfer From Appliance to a Sheet Metal Protected Wall . 22

6.3 Heat Transfer From Appliance to a Masonry Protected Wall ... 23

7. USES FOR AND LIMITATIONS OF THE MODEL 23

8. REFERENCES 25

Appendix A: Program Listing of STOVE 37

PROGRAM STOVE 38

SUBROUTINE INPUT 41

DOUBLE PRECISION FUNCTION FVAL 46

SUBROUTINE HEATS 47

SUBROUTINE HEAT 48

DOUBLE PRECISION FUNCTION CFIGS 49

DOUBLE PRECISION FUNCTION CFIGP 50

DOUBLE PRECISION FUNCTION HCONV 51 CHARACTERS FUNCTION CMET 5 2 SUBROUTINE PSUM 5 i CHARACTER*60 FUNCTION PMATL 54
ii

COMMON BLOCK FOR PROGRAM STOVE 55

Appendix B: Data Input for STOVE 56
Ill

LIST OF TABLES

Table 1. Sample Output From STOVE 28

LIST OF FIGURES

Figure 1. Heat Transfer From Hot Appliance to Cooler Wall Surface ... 29

Figure 2. Node Model Representation of Stove / Protector / Wall System . 30

Figure 3. Program Layout For Program STOVE 31

Figure 4. Comparison of Calculated Wall and Protector Surface Temperatures

With Experimental Results 32

Figure 5. Predicted Wall Surface Temperatures for Heat Transfer From Appliance Surface to an Unprotected Combustible Wall Surface ... 33

Figure 6. Predicted Wall Surface Temperatures for Heat Transfer From Appliance Surface to a Combustible Wall Protected With a Double

Aluminum Sheet Wall Protector (Painted Black) 34

Figure 7. Predicted Wall Surface Temperatures for Heat Transfer From Appliance Surface to a Combustible Wall Protected With a Double

Aluminum Sheet Wall Protector 35

Figure 8. Predicted Wall Surface Temperatures for Heat Transfer From Appliance Surface to a Combustible Wall Protected With a Solid Masonry

Wall Protector With A Ventilated Air Space 36
NOMENCLATURE

radiant exchange configuration factor dimensionless

radiant exchange configuration factor dimensionless

convection heat transfer coefficient kW / m

2 • K

thermal conductivity- kW / m • K

characteristic length m

Nusselt number dimensionless

Prandtl number dimensionless

thermal resistance m

2 • K / kW

Raleigh number dimensionless

total thermal resistance - E m

2 • K / kW

heat transfer rate kW/m2

temperature K

characteristic horizontal dimension m

characteristic vertical dimension m

emissivity dimensionless

Stephan- Boltzmann constant kW / m

2 • K*
STOVE: A Predictive Model for Heat Transfer

From Solid Fuel Appliances

1

Richard D. Peacock and Richard A. Dipert

Abstract

A computer implementation of a model to predict temperatures on wall and wall protector surfaces exposed to the heating of an appliance such as a solid fuel heating appliance is described. A

steady state heat transfer model with flexibility to describe a generalized method of protection for a combustible wall surface is

presented along with a computer program implementing the model.

Good agreement was found comparing the model predictions with data

previously collected during full scale experiments conducted to

evaluate the effectiveness of generic methods of wall protection

in reducing temperatures on combustible wall surfaces.

Extensive references of research related to solid fuel heating

safety are included.

Key words: Chimneys; fire models; fire safety; fire tests; flues; heat

transfer; heating equipment; literature reviews; radiant energy; stoves; wood.

1. INTRODUCTION

The U.S. Consumer Product Safety Commission and the U.S. Department of

Energy, as part of a program to investigate safety risks involved with the use

of solid fuel burning appliances, have sponsored experimental research at the

Center for Fire Research (CFR) at the National Bureau of Standards (NBS) to

identify hazards associated with solid fuel heating. The studies were conducted to provide information to improve safety practices for the use of the
2

appliances, and to provide data upon which to base improved codes and

standards

During the first years of the program, an accident survey, literature

review, and codes and standards analysis were performed to establish accident

patterns , to determine the types of risks involved with the use of wood

burning appliances, and to ascertain the adequacy of existing codes and

standards in addressing these risks [1-3]. 1 Overwhelmingly, conditions

related to installation, operation, and maintenance were responsible for the

fire incidents studied. Only a small percentage of the fires was attributed

to product design or product defects. Thus, safe installation and use of wood

burning appliances is a critical requirement for preventing fire accidents

involving the equipment. Much of the criteria for the installation and use of

wood burning appliances are based upon data developed over forty years ago and

do not provide information on materials of construction, or appliances

available in the current market.

The present program at CFR includes research on:

• clearances to combustibles from appliances and chimney

connectors [4]

• methods of protection to allow reduced clearances to walls and

l Number in brackets refer to literature references listed in

section 8 at the end of this report.
ceiling surfaces exposed to radiant heating by appliances and

chimney connectors [5];

• temperatures developed in and around fireplaces with and without

fireplace inserts installed [6,7];

• intensity and duration of chimney fires in factory-built and

masonry chimneys [8]

• temperatures on combustible material surrounding chimney connectors passing through walls and / or connecting to chimneys [9]

and;

• prediction of temperatures on surfaces of combustible walls

exposed to heating from a typical radiant heating appliance.

This report, one of a series of reports providing information from the

experimental program on wood burning safety at NBS , presents the results of

the development of a computer based implementation of a model to predict

temperatures on a wall surface exposed to heating from a radiant heating

appliance such as a wood stove. The resulting computer program allows the

user to specify thermal protection to reduce temperatures on the wall surface
4

2. REVIEW OF PREVIOUS WORK

2.1 Fire Incidents Involving Wood Burning Appliances

Recent statistics on fires and injuries related to wood burning

appliances are alarming:

Change

From

Previous Dollar

Year Fires Year Deaths Loss

1978 66,800 250 $134 million

1979 70,700 +14% 210 $175 million

1980 112,000 +58% 350

1981 130,100 +16% 290 $265 million

1982 139,800 +7% 250 $257 million

1983 140,600 +0 . 6 % 280 $296 million

Source

U.S. Consumer Product Safety Commission [10, 11]

There were more fires in solid fuel burning equipment, and a larger

percentage increase over previous years, than were reported for any other kind

of heating equipment -- including gas, electric, and oil burning

appliances [10-11].

This marked increase is attributed to the growing installation and use

of wood burning stoves in homes throughout the United States and the fact that

most homes are made of combustible construction. Clearly, accidental fires

from wood burning appliances are an increasingly important problem.
5

2.2 Clearances In Existing Codes and Standards

Recommendations for minimum acceptable clearances to combustible

materials for the installation of chimney, chimney connectors, and appliances

are specified in the various model building codes and recommended practices

manuals. Reference [12] is typical of the specifications found in the codes.

For simplicity, a single, hopefully conservative clearance is given for each

type of appliance installed without protection. No allowance is made for the

size, heat output, heat transfer characteristics or other features unique to

individual models. Similarly, only a few, specific methods of protection

employed to allow reduction of these clearances are recommended.

Typically, 0.91 m of clearance is specified between radiant heaters and

unprotected combustible construction. For residential solid fuel chimneys,

typically 51 mm of clearance is required. Chimney connectors for solid fuel

burning residential appliances require a clearance of at least 0.46 m to

combustible materials. However, as with appliances, these clearances may be

reduced by the use of appropriate protection applied either to the appliance

or to the combustible surface.

The experimental basis for these code requirements is not, in many

cases, quite so clear. Several experimental studies have been carried out to

determine minimum acceptable clearances to combustible materials. Voigt [13],

in a 1933 publication, recommends a minimum clearance of 0.30 m for chimney

connectors 0.23 m in diameter. A more extensive study, performed by

Underwriters Laboratories in 1943 [14]

presents minimum safe clearances for
6

both unprotected surfaces and surfaces protected by various methods.

Distances at which a maximum temperature rise of 50° C above room temperature

is reached are presented as a function of the temperature of the exposed face

of a heat producing appliance. The relative protection afforded by various

materials used as heat barriers between the appliance and combustible surfaces

is also examined. Lawson, Fox, and Webster [15] and Lawson and Simms [16]

have studied the heating of wall panels and wood by radiation. With

experimentation and theoretical predictions, they present safe clearances

between flue pipes and wall surfaces as a function of the pipe diameter and

the pipe surface temperature. To maintain a maximum wall temperature of

100°C, 0.15 m pipe should not exceed 350°C in surface temperature at a

clearance of 0.46 m [15]. Loftus and Peacock [5] present the results of

research studying clearances and methods of protection for wall and ceiling

surfaces exposed to radiant heating appliances. A number of recommended

methods of protection to reduce temperatures on combustible wall and ceiling

surfaces to acceptable levels were found. In the study, appliance surface

temperatures from 300 to 450°C were used.

These experimental studies established limits for two important parameters: appliance surface temperature and clearance to combustibles for

unprotected and protected surfaces. Maximum appliance surface temperatures

for the appliances studied ranged from 300 to 450° C; average appliance surface

temperatures from 200 to 250°C. Minimum safe wall clearances for unprotected

surfaces ranged from 0.31 to 0.91 m. Most of the current code provisions are

only adequate for maximum appliance surface temperatures up to 300 to 350° C.
7

2.3 Temperatures Developed in Heating Systems

Tests made with prefabricated porcelain- enameled metal chimneys for

solid or liquid fuel furnaces [17,18] established a limiting temperature rise

of 190°C on the outer surface of the chimney for a flue gas temperature of

537°C. With this limitation, wood framing space 51 mm or more away from the

chimney was considered safe. Satisfactory insulation of the chimneys to

reduce the outer surface temperatures to acceptable levels was obtained with

asbestos paper plies totalling about 45 mm in thickness. In the same study,

some asbestos cement pipe coverings were also found to reduce heat

transmission to the extent required for safety of nearby combustibles.

To establish performance requirements for lightweight prefabricated

chimneys, tests were conducted with lined and unlined masonry chimneys having

102 mm thick walls [19,20]. Hazardous conditions on wood framing spaced 51 mm

away from the chimney were noted with a continuous flue gas temperature of

482° C for the unlined chimney and 592° C for the lined chimney. However, these

hazardous conditions were not reached in the lined chimney tests until after

13 hours. In order to study operating conditions with typical fuels, a number

of firing tests [21] were conducted with heating appliances known to give high

flue gas temperatures, using wood and soft coals as fuels. With a coalfired, jacketed type heater, gas temperatures ranging from 648 to 704°C were

measured for an hour or more in the flue at the ceiling level above the

heater
8

Lawson, Fox, and Webster [15] presented results of tests to measure

surface temperature of flue pipes. Measured for a variety of flue systems

using solid fuels -- mostly coal and coke -- they report temperatures of about

150°C under "normal" conditions and temperatures as high as 815°C for over

fire conditions.

Fox and Whittaker [21] report temperatures on metal flues of several

heating appliances operated over a range likely to encountered in normal use.

Maximum flue pipe surface temperatures ranged from 704 to 815 °C at the appliance flue outlet, 360 to 510° C at a distance of 0.91 m from the appliance flue

outlet, and 287 to 326°C at a distance of 1.8 m from the appliance flue

outlet

Shoub [17] concluded that combustible materials will be ignited if

maintained in continued contact with a masonry chimney of 120 mm wall

thickness with flue gas temperatures of 400° C.

In tests for the Department of Energy [4]

temperatures ranging from 297

to 436°C during normal operation and 377 to 693°C during over fire conditions

were noted on the surfaces of several wood burning appliances when tested to

prescribed test methods [22]. A total of 11 different short term tests,

ranging from 1.9 to 25.6 hours duration, were conducted to establish normal

firing conditions in wood burning appliances [23]. An examination of the

data from these tests shows spikes occurring at the beginning and end of tests

and, apparently, whenever the door to the stove was opened. These sharp increases in temperature were attributed to a "high fire" in the morning and to
9

the rapid increase in active flaming when the door was opened for refueling

the fire. The average stove surface temperature rise for normal burning

ranged from 177 to 218°C, flue gases from 140 to 269°C, inner chimney wall

surface 119 to 241° C, and the outer chimney wall surface 14 to 48° C.

2.4 Limiting Safe Temperatures on Combustible Surfaces

Listings of heat producing appliances and methods for setting clearances

between appliances and combustible surfaces are based upon Underwriters

Laboratories listings [22]:

• maximum temperature rise of 65 °C above room temperature on exposed

surfaces; and

• maximum temperature rise of 50° C above room temperature on unexposed

surfaces, such as beneath the appliance, floor protector, or wall

mounted protective device.

These requirements are based upon the fact that while the ignition

temperature of wood products is generally quoted to be on the order of 200°

[24], wood that is exposed to constant heating over a period of time may

undergo a chemical change resulting in a much lowered ignition temperature and

increased potential for self - ignition.

Mitchell [25] presents data on wood fiberboard exposed to temperatures

as low as 109°C that resulted in ignition after prolonged exposure. MacLean
10

[26,27] reports charring of wood samples at temperatures as low as 93° C. He

concludes that wood should not be exposed to temperatures appreciably higher

than 66 °C for long periods. McGuire [28] suggests that the maximum safe

temperatures on the surface of a combustible material adjacent to a constant

heat source should be no more than 100° C.

Clearly, the ignition of wood at moderately elevated temperatures is a

complex phenomenon; the time of exposure is indeed an important parameter

[29,30]. While exact limits recommended in the literature vary due to

exposure time and details of the tests conducted, the numerous documented

fires involving the ignition of wood members near low pressure steam pipes

[31] suggest an upper temperature limit for wood exposed to long-term lowlevel heating should not be appreciably higher than 100°C.

Nearby combustible materials other than wall and ceiling surfaces, such

as chairs or draperies must also be kept a sufficient distance from

combustible materials to prevent ignition of the materials. The testing

standards and model codes treat all combustibles with the same requirements.

Thus, the 0.91 m clearance requirements in NFPA 211 and maximum temperature

rise requirements in the Underwriters Laboratories testing standards apply

equally well to other combustibles as well. Similarly, a temperature limit of

100°C is more than adequate to protect most combustibles used in furnishings.
11

2.5 Data for Model Validation

Much of the available literature related to wood heating safety provides

a significant amount of data that can be used to compare theoretical

predictions with experimental measurements. In the above literature,

references [4], [5], and [9] provide measurements of appliance surface

temperatures and wall surface temperatures and provide a full description of

the experimental setup to be modeled. Reference [22] provides acceptable

limits on combustible surface temperatures for use in predicting minimum

clearances , maximum appliance surface temperatures , minimum acceptable

protector thermal properties, and the like. These references will provide the

majority of data for the comparison of theoretical predictions with measured

temperatures on surfaces of appliances , on protector systems , and on

combustible walls.

3. THEORETICAL BASIS FOR THE MODEL

Figure 1 presents a schematic diagram of a heating appliance / wall

system with an arbitrary protection system between the appliance and the

wall. Heat transfers from the hot stove surface through any intervening

protection to the wall surface, through the wall, and to the cooler surroundings. A few assumptions, reasonable to the system being modeled, simplify the

model considerably:
12

• The stove is operating at steady state conditions (thus, we assume

the stove has been operating for a period of time and has reached

a steady operating condition)

• Stove is at a constant uniform surface temperature.

• Heat transfer through air spaces in the system takes place by

radiation and convection only.

• Heat transfer through solids in the system takes place by conduction only.

With these assumptions, a one - dimens ional , steady state model of the

stove / protector / wall heat transfer is appropriate. The only loss in

generality of the predictive capability of the model is the inability to

predict any time dependent behavior of the system. Since the intended purpose

of the model is to study the fire safety of the stove / protector / wall

system under worst case conditions, this loss is acceptable. By assuming

steady state conditions with a constant stove temperature, the worst case

conditions will be modeled.

3.1 Radiative Heat Transfer

For heat exchange between two surfaces, the net radiative heat transfer

between surfaces 1 and 2 is given by [32]:
13

q -

4 4

a (T

x

- Tp

1 - e. 1 - e, + +

12

(1)

F :

, the configuration factor for radiative exchange between surface 1 and

surface 2, is defined as the fraction of the radiation leaving surface 1 which

is intercepted by surface 2. Compilations of configuration factors are

available in the literature [33,34]. For the stove / wall protector geometry,

the following equations are appropriate. The configuration factor for a

differential element to a plane parallel rectangle with the normal to the

element passing through the comer of the rectangle is given by [33]:

F = — dA 2n

(1+X2 )'

( 1+Y2

)

tan

-1

(1+X2 )' +

tan

-1

(1+Y2

) 2^ ( 2 )

where X = (width of rectangle) / (distance from rectangle to element) and Y =

(height of rectangle) / (distance from rectangle to element) . Since the

configuration factor for a surface equals the sum of configuration factors for

any subdivision of the surface, the configuration factor for any point (X^-.Y^

on the wall (or first protector) surface can be defined from equation (2) as
14

F

12 - FdA<Vxs'VV - F

dA ( VVMs'VV + WVWVW ' FdA ( WVVH

S> (3)

For radiant heat exchange between two identical, directly opposed rectangles (such as two protective surfaces of the same size), the configuration

factor is given by [33]

12 ttXY In

'(1+X2

) (1+Y2 1 + X

2 + Y2 *] + X(1+Y2

) H

tan"

1 —

( 1+Y2

)

+ Y ( 1+X2

) ^ tan"

1 —r - X tan'

1 X - Y tan

1 Y

(1+X2

)^

(4)

3.2 Convective Heat Transfer

For convective heat transfer between two surfaces separated by an air

space, the net heat exchange by convection is given by

q = h (T

x

- T

2

) (5)

where h is the convective heat transfer coefficient. For free convection at
15

the surface of a vertical surface (such as the wall, appliance, or protector

surface), h can be found from the equations [35]

m h L

NU

L

" “IT

0.387 Ra,

1/6

0.825 + E + (0.492/Pr)

9/16“] 8/27 ( 6 )

3.3 Conductive Heat Transfer

For solids, the net heat exchange by conduction is given by

i - -r (T

i

- V (7>

While for some materials, the thermal conductivity, k, is a function of

temperature, for most materials, the assumption that k is a constant leads to

inconsequential loss in generality. For instance, for aluminum, the thermal

conductivity changes by only 25% over a temperature range from -170°C to well

over 2000°C
16

3.4 Solution of the Equations for an Arbitrary Protection System

At steady state, the heat transferred from the appliance to the outside,

figure 2, is equal to the heat transferred through any element or group of

elements within the system, or

< T

s

- V 1 TOTAL ^OTAL( T

i

R.

- w

l

( 8 )

Equations (1), (5), and (7) can be expressed as in equivalent resistance forms

as

(Conduction) R.

l

_L_

K

(9)

(Convection) R. =

h

( 10 )

1 - e, 1 1 - e.

(Radiation) R. „ (T|l + 7 Tj) ( 11 )

For the current problem, these equations can be combined into two as

R.

1 (Solids) K

( 12 )
17

(Airspaces) R. = — a (T 2 +

i

) (T "+'t"7

h

+ 1 - e 1 1 - e 2 —

- + t

- + r

-

1 12 2

(13)

Thus, the solution method with a given appliance temperature, Ts

, and a

given temperature of the surroundings, T0 , begins by assuming temperatures for

the intermediate surfaces, calculating individual resistances from equations

(12) and (13) to determine the total resistance, R^j^ , calculating the total

heat flow rate from equation (8)

and comparing the total heat flow rate to

the individual heats. If the calculated individual rates are sufficiently

close to the calculated total heat flow rate, the steady state solution has

been obtained. If any of the individual heats are different from the total

heat, new estimates for each of the intermediate temperatures are made and the

process is repeated until sufficient agreement has been found. Reference [36]

provides a number of methods for making best guess estimates for the next

iteration toward the solution. For the current problem, a simple linear

search is used where one variable at a time is changed until a local optimum

is found.

A number of literature sources are available to allow determination of the

physical data required for the input (for instance, for the thermal conductivity and emissivity) . References [32] and [33] provide extensive listings

of thermal and material properties for common materials.
18

4. COMPUTER IMPLEMENTATION OF THE MODEL

Included as Appendix A is a listing of the FORTRAN (written in ANSI

standard FORTRAN 77) program implementing the model as described above. The

general structure of the program is illustrated in figure 3.

Program input (detailed in Appendix B) takes the form of different key

words with arguments to specify values which depend upon the key word. In

most cases, the order of the key words is unimportant. A description of each

of the input key words and values which go on the same line are presented

below:

STOVE

AIRSPACE

FOR

XWALL

YWALL

PROTECTOR

<height> <width> <emissivity> <temperature>

<thickness> <emissivity>

<variable> — <lower> <upper> <increment>

<x position>

<y position>

<thickness> <height> <width> <k> <emissivity> <temperature>

A sample input for the program follows:

FOR:

STOVE:

AIRSPACE:

ALUMINUM SHEET:

AIRSPACE:

ALUMINUM SHEET:

AIRSPACE:

GYPSUM WALLBOARD:

F/G INSULATION:

BRICK OUTSIDE:

AIRSPACE:

END:

TSTOVE = 473.15 673.15 10.

0.9 0.5 0.5 473.15

0.91 0.9

0.00254 3.0 3.0 177. 0.9

0.0254 0.9

0.00254 3.0 3.0 177. 0.9

0.0254 0.9

0.0127 3.0 3.0 0.17 0.9

0.0916 3.0 3.0 0.038 0.9

0.0916 3.0 3.0 0.72 0.9

273.15
19

This input specifies a series of calculations to be done for a stove temperature ranging from 200° C to 400° C ( 473.15 to 673.15 K in the input above) for

a wall protection system consisting of two aluminum sheets spaced 25 mm

(0.00254 m in the input above) apart and placed 25 mm from an insulated

outside wall of a house. A clearance of 0.91 m from the appliance to the first

aluminum sheet is specified. A sample output from the program, using this

sample data set, is presented in table 1. Calculated temperatures on all

surfaces from the stove to the outdoors are shown along with the specified

sizes and thermal properties of the materials used for the walls and protectors. Execution time, of course, depends upon the computer in use. On a

typical desk top personal computer, execution of the above test case required

less than 1.5 minutes.

5. COMPARISON OF THE MODEL PREDICTIONS WITH EXPERIMENTAL DATA

Figure 4 presents a comparison of calculated temperatures on the

surfaces of wall protectors and on the surfaces of combustible walls with

experimentally measured values taken from references [4] and [5]. To assess

the predictive capabilities of the model, a range of conditions from the

experimental studies were simulated. Wall materials used in these

experimental studies ranged from uninsulated gypsum wallboard to a fully

insulated stud wall with a brick facing on the exterior. A number of

different wall protection methods were taken from reference [5], varying from

a simple sheet metal protector to a sheet metal / insulation board / air spacr

composite protector or a ventilated brick protector. A simple cross plot of
20

the calculated values and the experimental values illustrates the agreement of

the model's predictions with experimental data obtained in earlier studies.

Agreement of the calculated values with the experimentally measured values,

stated as

( ( ^calculated " Measured ) / Calculated ) * ^0

with temperatures expressed in absolute, averaged within less than 1 percent.

Individual agreement, however ranged from 5 percent low (calculated values

lower than experimental) to 4 percent high. Much of the disparity in the

comparison can be explained by the choice of ambient conditions for the

experimental tests. All the data in the two reports were described in terms

of temperature rise above ambient conditions. Since the experimental

calculations are based upon absolute temperatures, some assumptions had to be

made for the ambient temperatures in the surroundings during the tests. A

variation in ambient temperature of 15° C could change the calculated surface

temperatures on the wall surfaces by as much as ±10 percent. Thus, the

agreement illustrated in figure 5 is excellent in light of the possible

variation in the calculations depending upon the assumed ambient temperature.

6. MODEL CAPABILITIES AND EXAMPLES

A theoretical model for predicting the heat transfer between the

appliance and the wall surfaces can be a useful tool not only in the design of

appliances and wall protection devices but also in the design of future

experiments to study clearances and reduced clearances for wood burning
appliances. This section presents some examples of the use of the model in

predicting temperatures and clearances from combustibles for both protected

and unprotected wall surfaces.

21

6.1 Heat Transfer From Appliance to an Unprotected Wall

Figure 5 shows calculated wall surface temperatures as a function of

appliance / wall clearance for a medium size appliance (an appliance 0.5 by

0.5 m on the side parallel to the wall surface) adjacent to an unprotected

wall surface for appliance surface temperatures from 150 to 350° C. For these

calculations, the outside air temperature (temperature of the surroundings)

was assumed equal to 0°C. The wall consisted of 12 mm gypsum wallboard, a 92

mm stud space with glass fiber insulation, and a 92 mm common brick facing on

the outside of the wall exposed to the outdoors. At an appliance clearance of

0.91 m, appliance surface temperatures greater than about 300 °C would lead to

temperatures on the wall in excess of the recommended limit [22] of 50°above

room ambient temperature at a point on the wall directly centered behind the

appliance. Since, in an earlier study [4], average appliance surface

temperatures of about 200 °C were noted, a sufficient margin of safety is

indicated for an appliance this size.
22

6.2 Heat Transfer From Appliance to a Sheet Metal Protected Wall

Figures 6 and 7 show calculated wall surface temperatures as a function

of appliance / wall clearance for a medium size appliance (an appliance 0.5 by

0.5 m on the side parallel to the wall surface) adjacent to a protected wall

surface for appliance surface temperatures from 150 to 350° C. As before, the

outside air temperature was assumed equal to 0°C. The wall protector

consisted of two sheets of aluminum (2.5 mm in thickness) separated by a

ventilated 25 mm air space. The wall protector was spaced from the wall by a

ventilated 25 mm air space. The wall consisted of 12 mm gypsum wallboard, a

92 mm stud space with glass fiber insulation, and a 92 mm common brick facing

on the outside of the wall exposed to the outdoors. With the surfaces of the

protector painted black and at an appliance clearance of 0.91 m, appliance

surface temperatures greater than about 300° C would lead to temperatures on

the wall in excess of the recommended limit of 50° C above room ambient

temperature -- in fact, about the same as the case with no protection.

However, when the surfaces of the protector are left unpainted (shiny aluminum

surfaces), appliance surface temperatures higher than 350°C are required to

raise the temperature of the wall surface above acceptable limits.

Conversely, the clearance of the appliance to the wall could be reduced from

0.91 m to 0.3 m with an average appliance surface temperature of 200° C.
23

6.3 Heat Transfer From Appliance to a Masonry Protected Wall

Figure 8 shows calculated wall surface temperatures as a function of

appliance / wall clearance for the same appliance (an appliance 0.5 by 0.5 m

on the side parallel to the wall surface) adjacent to a protected wall surface

for appliance surface temperatures from 150 to 350°C. Again, the outside air

temperature was assumed equal to 0°C. The wall protector consisted of a 92 mm

thick solid brick wall was spaced from the wall by a ventilated 25 mm air

space. The wall consisted of 12 mm gypsum wallboard, a 92 mm stud space with

glass fiber insulation, and a 92 mm common brick facing on the outside of the

wall exposed to the outdoors. With the surfaces of the protector painted

black and at an appliance clearance of 0.91 m, appliance surface temperatures

greater than about 300° C would lead to temperatures on the wall in excess of

the recommended limit of 50°C above room ambient temperature -- again not

significantly lower than in wall surface temperatures than for the unprotected

wall. Note, however, one of the major thermal characteristics of a masonry

wall protection system -- high thermal mass -- is not accounted for in a

steady state prediction.

7. USES FOR AND LIMITATIONS OF THE MODEL

A model was developed to predict temperatures on protected and unprotected wall surfaces exposed to heating from a (primarily) radiant heating

appliance. A one - dimens ional , steady state model of appliance / protector /

wall heat transfer showed agreement within an average of less than 1 perccmt
24

when compared to experimental results from earlier laboratory studies. A

range of building materials typical of residential construction, along with a

number of different wall protection methods were simulated in the comparison.

As a guideline to the range of applicability of the model, the variations of

the thermal properties used in the comparisons were

k: 0.038 to 177 W/m K

e

0.1 to 0.9

airspace thickness: 0.1 to 1.0 m

solid thickness: 0.0025 to 0.1 m

Improvements in the program implementation of the model are possible.

The simple linear search for the solution of the equations is certainly not

the most efficient method. A number of search methods have been described in

the literature [36]. An n-dimensional simplex search where the next guess for

a given variable depends upon the values of the other n-1 variables would

improve the execution speed of the program. Additional improvements would be

realized with any of a number of acceleration methods, also available in the

literature [36]. Of course, a more complicated, harder to understand and

modify program would result.
25

8 . REFERENCES

[1] Peacock, R. D., A Review of Fire Incidents, Model Building Codes, and

Standards Related to Wood-Burning Appliances, Nat. Bur. Stand. (U.S.),

NBSIR 79-1731 (April 1979).

[2] Peacock, R. D., A Review of Fire Incidents Related to Wood-Burning

Appliances, Wood Energy Institute, Proceedings of Wood Heating Seminar

IV, Portland, Oregon, March 21-24, 1979, 43-46.

[3] Shelton, J. W. , Analysis of Fire Reports on File in the Massachusetts

State Fire Marshal's Office Relating to Wood and Coal Heating Equipment,

contract to the National Bureau of Standards (U.S.), NBSGCR 78-149

(November 1978).

[4] Peacock, R. D., Ruiz, E. , and Torres-Pereira, R. , Fire Safety of Wood

Burning Appliances, Part 1: State of the Art Review and Fire Tests,

Volume I and II, Nat. Bur. Stand. (U.S.), NBSIR 80-2140 (November 1980).

[5] Loftus, J. J., and Peacock, R. D. , Clearances and Methods of Protection

for Wall and Ceiling Surfaces Exposed to Radiant Heating Appliances,

Nat. Bur. Stand. (U.S.), NBSTN 1205 (December 1984).

[6] Maxwell, T. T. , Dyer, D. F. , Maples, G., and Burch, T., An Investigation

of Creosoting and Fireplace Inserts, contract to the National Bureau of

Standards (U.S.), NBSGCR 81-365 (December 1981).

[7] Terpstra, W. R. , Jorgenson, M. L. , and Dosedlo, L. J., Investigation of

Fire Hazards of Fireplace Inserts in Factory-Built and Masonry

Fireplaces, contract to the National Bureau of Standards (U.S.), NBSGCR

82-368 (January 1982).

[8] Peacock, R. D., Intensity and Duration of Chimney Fires in Several

Chimneys, Nat. Bur. Stand. (U.S.), NBSIR 83-2771 (December 1983).

[9] Loftus, J. J., and Peacock, R. D., Evaluation of Thimble - Chimney

Connector (Wall-Pass Through) Systems for Solid Fuel Burning Appliances,

Nat. Bur. Stand. (U.S.), NBSIR 84-2969 (November 1984).

[10] Kale, D. , Fires in Woodburning Appliances, U. S. Consumer Product Safety

Commission (December 1982)

[11] Harwood, B. , and Kale, D., Fires Involving Fireplaces, Chimneys and

Related Appliances, U. S. Consumer Product Safety Commission (September

1981)

[12] Standard for Chimneys, Fireplaces, Vents and Solid Fuel Burning Appliances, NFPA 211-1984, National Fire Protection Association, Quincy,

Massachusetts (February 1984)
26

[13] Voigt, G. Q. , Fire Hazard of Domestic Heating Installations,

Nat. Bur. Stand. (U.S.), NBS Research Paper RP596 (September 1933).

[14] Neale, J. A., Clearances and Insulation of Heating Appliances, Underwriters Laboratories, Inc., UL Bulletin of Research No. 27 (February

1943).

[15] Lawson, D. I., Fox, L. L. , and Webster, C. T., The Heating of Panels by

Flue Pipes, Fire Research Special Report No. 1, Fire Protection Association, London, England (March 1952)

[16] Lawson, D. I., and Simms, D. L. , The Ignition of Wood by Radiation,

British Journal of Applied Physics, Vol 3, 288-292 (September 1952).

[17] Shoub, H. , Survey of Literature on the Safety of Residential Chimneys

and Fireplaces, Nat. Bur. Stand. (U.S.), NBS Misc. Pub. 252 (December

1963) .

[18] Prefabricated Metal Chimneys, National Bureau of Standards, Fire

Research Section, unpublished reports to the Federal Public Housing

Authority (1941-1945).

[19] Thulman, R. K. , Temperatures Developed in Chimneys for Low Cost Houses,

Nat. Bur. Stand. (U.S.), Tech. News. Bull. 328 (August 1944).

[20] Thulman, R. K. , Performance of Masonry Chimneys for Houses, Housing and

Home Finance Agency (U. S.), Housing Research Paper No. 13 (November

1952).

[21] Fox., L. L.

and Whittaker, D., Some Measurements of Temperatures of

Metal Flues of Domestic Heating Appliances, Journal of the Institution

of Heating and Ventilation Engineers, Vol. 23, 183-192 (August 1955).

[22] Standard for Room Heaters, Solid Fuel Type - - UL 1482, First Edition,

Underwriters Laboratories, Inc., Northbrook, IL (August 1979).

[23] Loftus , J. J., Evaluation Tests on Metal Factory-Built Insulated

Chimneys Used for Venting Solid Fuel Burning Appliances,

Nat. Bur. Stand. (U.S.), letter report to the U. S. Consumer Product

Safety Commission (April 1985)

[24] Schaffer, E. L. , Smoldering Initiation in Cellulosics Under Prolonged

Heating, Fire Technology, Vol. 16, No. 1, 22-28 (February 1980).

[25] Mitchell, N. D., New Light on Self-Ignition, NFPA Quarterly, Vol. 45,

No. 2, 165-172 (October, 1951).

[26] Maclean, J. D., Effect of Heat on Properties and Serviceability of

Wood: Experiments on Thin Wood Specimens, Forest Products Laboratory

Report No. R1471, Madison, WI (1945).
27

[27] Maclean, J. D., Rate of Disintegration of Wood Under Different Heating

Conditions, American Wood-Preservers Association (1951).

[28] McGuire, J. H. , Limiting Safe Temperature of Combustible Materials, Fire

Technology, Vol 5., No. 3 (August 1969).

[29] Ignition and Charring Temperatures of Wood, Forest Products Laboratory

Report No. 1464, Madison. WI (January 1958).

[30] Shelton, J. W. , Wood Heat Safety, Garden Way Publishing, Charlotte, VT

(September 1979).

[31] Matson, A. F. , Dufori, R. E., and Breen, J. F. , Performance of Type B

Gas Vents for Gas -Fired Appliances, Part II, Survey of Available

Information on Ignition of Wood Exposed to Moderately Elevated Temperatures, Underwriters Laboratories, Inc., UL Bulletin of Research No. 51,

Northbrook, IL (May 1959)

[32] Incorpera, F. P., and DeWitt, D. P. , Fundamentals of Heat Transfer, John

Wiley & Sons, New York, NY (1981).

[33] Siegel, R. , and Howell, J. R. , Thermal Radiation Heat Transfer, McGrawHill Book Company, New York, NY (1981).

[34] Hsu, Chia-Jung, Shape Factor Equations for Radiant Heat Transfer Between

Two Arbitrary Sizes of Rectangular Planes, Canadian Journal of Chemical

Engineering, Vol. 45, 58-60 (February 1967).

[35] Churchill, S. W. , and Chu, H. H. S., Correlating Equations for Laminar

and Turbulent Free Convection from a Vertical Plate, Int. J. Heat Mass

Transfer, Vol. 18, 1323 (1975).

[36] Beveridge, G. S., and Schechter, R. S., Optimization: Theory and Practice, McGraw-Hill Book Company, New York, NY (1970).
28

Table 1. Sample Output From STOVE

DOUBLE ALUMINUM PLATE, ALL SURFACES PAINTED BLACK

NUMBER OF NODES IN CALCULATION: 10

POINT ON WALL: (X): 0.000 (Y) : 0.000

SERIES OF CALCULATIONS FOR VARIABLE TSTOVE: 473.150 673.150 20.000

I MATERIAL HEIGHT

(m)

WIDTH

(m)

THICK

(m)

EMISS K

(W/m-K)

TEMPERATURE

(°C)

0 STOVE 0.50 0.50 0.90 200.00

1 AIRSPACE 0.91 0.90

2 ALUMINUM SHEET 3.00 3.00 0.00 0.90 177.000

3 AIRSPACE 0.03 0.90

4 ALUMINUM SHEET 3.00 3.00 0.00 0.90 177.000

5 AIRSPACE 0.03 0.90

6 GYPSUM WALLBOARD 3.00 3.00 0.01 0.90 0.170

7 INSULATION 3.00 3.00 0.09 0.90 0.038

8 BRICK OUTSIDE 3.00 3.00 0.09 0.90 0.720

9 AIRSPACE 0.00 1.00 0.00

0: STOVE / AIRSPACE

1: AIRSPACE / ALUMINUM SHEET

2: ALUMINUM SHEET / AIRSPACE

3: AIRSPACE / ALUMINUM SHEET

4: ALUMINUM SHEET / AIRSPACE

5: AIRSPACE / GYPSUM WALLBOARD

6: GYPSUM WALLBOARD / INSULATION

7: INSULATION / BRICK OUTSIDE

8: BRICK OUTSIDE / AIRSPACE

9: AIRSPACE

TSTOVE (

'0 ) ( 1) ( 2) ( 3) ( 4) ( 5) ( 6) ( 7) ( 8) ( 9)

(°,O (°<C) C 'C) (° C) (° C) (°'C) C 'C) (°<C) (°C) (°C)

473. 150 200 .0 33 .1 33 .1 31 .6 31 .6 30 .1 29 .3 3 .1 1.7 0.0

493. 150 220 .0 38 .7 38 .7 37 .0 37 .0 35 .3 34 .4 3 .6 2.0 0.0

513. 150 240 .0 44 .7 44 .7 42 .8 42 .8 41 .0 39 .9 4 .2 2.3 0.0

533.,150 260 .0 51 .1 51 .1 49 .0 49 .0 47 .0 45 .7 4 .7 2.6 0.0

553.,150 280 .0 57 .8 57 .8 55 .6 55 .6 53 .4 51 .9 5 .4 2.9 0.0

573.,150 300 .0 64 .8 64 .8 62 .5 62 .5 60 .1 58 .5 6 .0 3.2 0.0

593.,150 320 .0 72 .2 72 .2 69 .7 69 .7 67 .2 65 .4 6 .7 3.6 0.0

613.,150 340 .0 79 .9 79 .9 77 .3 77 .3 74 .6 72 .6 7 .4 3.9 0.0

633.,150 360 .0 87 .8 87 .8 85 .1 85 .1 82 .3 80 .1 8 .1 4.3 0.0

653.,150 380 .0 96 .0 96 .0 93 .2 93 .2 90 .3 87 .8 8 .8 4.7 0.0

673.,150 400 .0 104 .3 104 .3 101 .5 101 .5 98 .5 95 .8 9 .6 5.0 0.0
Figure

1.

Heat

Transfer

From

Hot

Appliance

to

Cooler

Wall

Surface

29

Aauaiji|0 ioh o

c

cc aoejjns aouBjiddv ;oh
igure

2.

Node

Model

Representation

of

Stove /

Protector /

Wall

System

w

o>ccDo

<1> -oOc 3

COIc <NI

h-" i epou pue

l-\ epou jo eoejjeiu! ib

ejruejediuej eoBjjns = !j.

<D

C ° s®s o w w z '-5

ftI I T- I— v.l CL 0

•cr

wu

I.-! epou pue

S-! epou jo eoBpejui jb

ejnjBjedtuej eoBjjnsrUj.

-ct

n

0) Ooc
STOVE 1

INPUT 1

FVAL

PMATL
Figure

4.

Comparison

of

Calculated

Wall

and

Protector

Surface

Temperatures

With

Experimental

Results

32

CM r- i— i—

(Oo) aanivyBdiABi 30Vdans

asivnnonvo

25

50

75

100

125

150

175

200

MEASURED

SURFACE

TEMPERATURE

(°C)
3 3

•o«

4JO

a> 4JOMCDC

a]oM

ffl O

cd 4-13

in©c

cda<SOMu

a) CMs

tduHM

cda> KMO<4-1 n©U

cdM0) §•0) H <DO © cd O CM

cd

H

cm 3

Tj

w

m i-i

r—\ •-1 ^

T-l 3

*d E*

©

l—

T) XI © i-i M JJ 5 3 d rQ © S u o

PM

U

in©3

bo

co o

co

in

c\j o

CM

10 o

(Do) 3Hn±VH3dW31 T1VM

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CLEARANCE

(m)
Figure

6

.

Predicted

Wall

Surface

Temperatures

for

Heat

Transfer

From

Appliance

Surface

to

a

Combustible

Wall

Protected

With

a

Double

Aluminum

Sheet

Wall

Protector

(Painted

Black)

34

00 CO CM C\J

o

O)

o

d

o

(Oo) 3HnJLVH3dlAI3± TIVM

0.2

0.3

0.4

0.5

0.6

0.7

0.8

CLEARANCE

(m)
Figure

7.

Predicted

Wall

Surface

Temperatures

for

Heat

Transfer

From

Appliance

Surface

to

a

Combustible

Wall

Protected

With

a

Double

Aluminum

Sheet

Wall

Protector

O

O

o o o o o o o

lO o in o LO o in

CO CO C\J CNJ T— 1—

(Do) 3aniva3diAi3i hvm

3 5

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CLEARANCE

(m)
Figure

8

.

Predicted

Wall

Surface

Temperatures

for

Heat

Transfer

From

Appliance

Surface

to

a

Combustible

Wall

Protected

With

a

Solid

Masonry

Wall

Protector

With

A

Ventilated

Air

Space

36

o o o o o o o

m o m o in o in

CO CO CM CM T” T~

(Oo) 3UniVb3dVM31 TIVM

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CLEARANCE

(m)
Appendix A: Program Listing of STOVE
12

3

45

6

78

g10

li12

13

1415

16

17

18

19202122

23

2425

26

2728

29

30

3132

33

3435

36

3738

39

40

4142

43

4445

46

4748

49

505152

53

5455

56

5758

59

6061

62

63

6465

66

67

6869

70

12

3

45

6

7

8

91011

12

13

14

1516

17

18

192021

22

23

2425

26

2728

29

3031

32

33

3435

3637

38

39

4041

42

43

4445

46

4748

49

505152

53

545556

5758

59

6061

62

636465

66

6768

69

70

PROGRAM STOVE

Cc @@@@@@@@

c @@@@ @ @ c @@@@ @@@@@@ @@@@@@ @@§ @ @@@@@@ c @@@@@@@@ @@@@ @@@ @ @@@ @ @ @@@

c @@@(s @@@@ @@@ @ @@@ @ @@@@@@

c @ @@@@ @@@@ @@@ @ @§@@ @

c @@@@@@@@ @@@@ @@@@@@ @@ @@@@@@

C

C

C THIS PROGRAMS CALCULATES AN ENERGY BALANCE ON A STOVE / WALL SYSTEM

C ASSUMING STEADY STATE CONDITIONS, WITH AN ARBITRARY NUMBER OF WALL

C PROTECTORS BETWEEN THE STOVE AND THE WALL

C INCLUDE ’ STOVE. CMN’ CHARACTER CMET*5, MATL*60 ,VERSN*7 LOGICAL THRU1 , NOTYET , THEEND DATA VERSN /’86.0108’/

C

C INITIALIZE EVERYTHING TO DEFAULT CONDITIONS, READ INPUT FOR CASE

C QEPS=0. 00001 EPS=0 . 0001

TSTEP1=2. TSTEP2=2

10 CALL INPUT (THEEND)

IF (.NOT. THEEND) THEN XSTOVE=WSTOVE/2

YSTOVE=0

IF ( . NOT . FULPRT ) THEN WRITE (6,11) (I ,FMATL(MATL(I) ,MATL(I+1) )

, 1=0, N-l) ,N,MATL(N) WRITE (6,12) VNAME, (1,1=0, N) WRITE (6,8) • ’,(’ CC) ',1-0, N) WRITE (6,8) (’ ’ ,1—1,N) END IF NCALCS-MAX ( INT ( ( VUPPER-VLOWER ) / VINCR+0 . 5 ) +1 , 1

DO 100 ICALC=1 , NCALCS VARVAL=VLCWER+VINCR* ( ICALC- 1

C

C SET NEXT VALUE OF VARIABLE TO BE INCREMENTED

C

IF (IVAR.EQ. 1) THEN XWALL-VARVAL

ELSE IF (IVAR.EQ. 2) THEN YWALL=VARVAL

ELSE IF (IVAR.EQ. 3) THEN

T ( 0 )=VARVAL ELSE IF (IVAR.EQ. 4) THEN

L ( I SUB ) -VARVAL

IF (1SUB.EQ. 1) ZSTOVE-VARVAL

ELSE IF (IVAR.EQ. 5) THEN WIDTH ( ISUB ) =VARVAL

IF (ISUB.EQ.0) WSTOVE=VARVAL XSTOVE=WSTOVE/2

ELSE IF (IVAR.EQ. 6) THEN

HEIGHT ( ISUB )=VARVAL

IF (ISUB.EQ.0) HSTOVE-VARVAL

ELSE IF (IVAR.EQ. 7) THEN K ( I SUB ) -VARVAL

ELSE IF (IVAR.EQ. 8) THEN ENNIS ( ISUB )=VARVAL END IF C

C INITIALIZE THE COUNTERS TO ZERO

C ITER=0

C

C INITIALIZE TEMPERATURE GUESSES TO WORST CASE CONDITIONS

C
7172

73

7475

76

7778

79

808182

838485

86

8788

89

9091

92

93

9495

96

979899

100 101 102

103

104 105 106

107 108 109

110 111

112

113

114 115

116

117 118

119

120

121 122

123

124 125

126

127

128 129

130 131 132

133

134 135 136

137 138 139

140

71

72

73

747576

7778

79

8081

82

83

8485

86

87

8889

909192

93

9495

96

9798

99

100 101 102

103

104 105

106

107

108 109

110 111

112

113

114 115

116

117 118

119

120 121

122

123

124 125

126

127 128

129

130

131 132

133

134 135

136

137

138

139

140

DO 20 1=1, N-l

20 T(I )=T(N)

TDIFF=T(0)-T(N)

TGOAL=T(N)

C

C DETERMINE NEXT GUESS FOR TEMPERATURES

C DO 30 1=1, N-l

30 T( I )=T( I )+TDIFF/N

C

C CALCULATE TOTAL RESISTANCE AND HEAT FLOW FROM GUESSED TEMPERATURES

C CALL HEATS

40 INNER=0 C

C CALCULATE WITH NEWLY GUESSED TEMPERATURES AND HEATS

C

DO 60 1=1,

TINC=ABS ( TDIFF/ N/ TSTEP1

TINCI=TINC QSIGN=DSIGN ( 1 . DO , Q( I

) -QTOTAL

C

C GO THROUGH INNER ITERATION LOOP AT LEAST ONCE FOR SOME FORCED

C IMPROVEMENT

C THRU1=. FALSE.

50 IF (.NOT. (ABS( (Q( I )-QTOTAL) /QTOTAL) . LE. QEPS. AND. THRU1) ) THEN INNER=INNER+1

THRU1=.TRUE.

IF (ABS ( (Q( I

) -QTOTAL ) /QTOTAL ) . GT . QEPS ) NOTYET= . TRUE

IF (MATL ( I ).NE. ’AIRSPACE’ ) THEN

C

C HEAT TRANSFER IS CONDUCTION, CALCULATE TEMPERATURE

C

T ( I )=T ( I- 1

) -QTOTAL*R( I

ELSE

C

C HEAT TRANSFER IS BY CONVECTION & RADIATION, SEARCH FOR TEMPERATURE

C T(I )=T(I)+QSIGN*TINC

C

C RECALCULATE THE HEAT FLOW AND COMPARE TO TOTAL HEAT

C CALL HEAT(I)

IF (DSIGN(l.D0,Q(I)-QTOTAL) .NE.QSIGN) THEN

TINCI=TINCI/TSTEP2

TINC=TINCI QSIGN=DSIGN ( 1 . DO , Q( I

) -QTOTAL

ELSE

TINC=TINC*2. END IF GO TO 50 END IF END IF C

C RECALCULATE TOTAL HEAT WITH THE NEW TEMPERATURES AND PROCEED

C CALL HEATS

60 CONTINUE

C

C IF DEBUG IS ON, PRINT OUT A SIM1ARY OF THE ITERATION

C ITER=ITER+1

IF (DEBUG. AND. NOTYET) THEN WRITE (6,7) ITER, INNER WRITE (6, ’ ( IX, A,F7 . 2) ' ) ’STOVE TEMPERATURE: ’ ,T(0)-273. 15 WRITE (6, ’ (1X,A,F8.2,A,F8.3)’ ) 'TOTAL HEAT: ’.QTOTAL,

2 ’ TOTAL RESISTANCE: ’ , RTOTAL WRITE (6,3) DO 70 1=1,
141 142

143

144 145

146

147

148

149

150 151

152

153

154 155

156

157

158

159

160

161 162

163

164 165

166

167 168

169

170 171

172

173

174 175 176

177 178

179

180

181

182

183

184 185

186

187 188

189

190

191 192

193

194 195

196

197 198

199 200

201 202

203

204 205

206

207 208

209

210

141

142

143

144 145

146

147 148

149

150 151 152

153

154 155

156

157 158

159

160 161

162

163

164 165

166

167 168

169

170

171

172

173 174

175 176

177

178

179

180 181

182

183

184 185

186

187 188 189

190 191

192

193

194 195 196

197 198

199 200 201

202

203

204 205

206

207 208

209

210

70

C

C

CC

80

C

C

C

90

100

12

3

45

6

7891112

IF (MATL(I).EQ. ’AIRSPACE’. AND. I. EQ.l) THEN WRITE (6,5) MATL(I) ,T(I)-273.15,R(I),Q(I),CF(I) ELSE IF (MATL(I).EQ. ’AIRSPACE' .AND. I. NE.l) THEN WRITE (6,1) MATL( I ) ,T(I )-273 . 15,R(I),Q(I),H(I),CF(I) ELSEWRITE (6,2) MATL(I) ,T(I)-273.15,R(I),Q(I)

END IF CONTINUE

TDIFF=T(N)-TGOAL WRITE (6, ’ (1X,A7,F10.3,A)’ ) ’ TDIFF: ’ ,TDIFF,

2 CMET(TDIFF/TGOAL,EPS)

WRITE (6,6) 'QMET: ’

, (Q(I)-QTOTAL,

2 CMET ( (Q ( I

) -QTOTAL ) / QTOTAL , EPS )

, 1=1 , N

END IF TDIFF=T(N)-TGOAL

T(N)=TGOAL

IF ANY OF THE INDIVIDUAL HEATS HAVEN’T CONVERGED ON THE FINAL VALUE, CONTINUE WITH THE PROCESS UNTIL ALL ARE EQUAL

NOTYET=. FALSE. DO 80 1=1,

IF (ABS((Q( I) -QTOTAL) /QTOTAL) .GT.EPS) NOTYET= . TRUE

CONTINUE

IF (ABS (TDIFF )/TGOAL. GT.EPS) NOTYET= . TRUE

IF (NOTYET) GO TO 40

THE SOLUTION HAS BEEN FOUND, PRINT IT OUT

IF ( . NOT . FULPRT ) THEN WRITE (6,9) VARVAL, (T(I )-273 . 15, 1=0 ,N) ELSE

WRITE (6.4) TITLE WRITE (6, ’(IX, A, 13)’) ’ITERATIONS: ’.ITER WRITE (6, ’ ( IX , 3A,F8 . 3

)

’ ) 'VARIED VARIABLE: ’ , VNAME, ’ = ’, 2 VARVAL WRITE (6, ’ ( IX , A,F7 . 2) ' ) 'STOVE TEMPERATURE: ’ ,T(0)-273. 15 WRITE (6, ’ (1X,A,F8.2,A,F8.3)’ ) ’TOTAL HEAT: ’.QTOTAL,

2 ’ TOTAL RESISTANCE: ’ , RTOTAL WRITE (6,3) DO 90 1=1,

IF (MATL(I).EQ. ’AIRSPACE’. AND. I. EQ.l) THEN WRITE (6,5) MATL(I) ,T(I)-273.15,R(I),Q(I),Q(I)

ELSE IF (MATL(I).EQ. ’AIRSPACE’ .AND. I. NE.l) THEN QCONV=(T(I-l)-T(I))/CONV(I)

QRAD=(T(I-1)-T(I))/RAD(I) WRITE (6,1) MATL(I),T(I)-273.15,R(I),Q(I),QCONV,QRAD

ELSEWRITE (6,2) MATL(I) ,T(I)-273.15,R(I),Q(I) END IF CONTINUE

WRITE (6,4) 'TEMPERATURES ARE OF COOLER SIDE OF NODE’ END IF CONTINUE GO TO 10 END IF STOP FORMAT ( IX , A10 , 2X ,F10 . 2 , 3X, F10 . 3 , 2X.F10 . 3 , 3X, F10 . 3 , 3X ,F10 . 3

FORMAT ( IX, A10 , 2X.F10 . 2 , 3X, F10 . 3 , 2X ,F10 . 3

FORMAT ( ’ 0MATERIAL TEMPERATURE RESISTANCE HEAT CONV

2ECTION RADIATION ’ , /

FORMAT ( ’ 0’ ,A) FORMAT ( IX, A10 , 2X ,F10 . 2 , 3X, F10 . 3 , 2X ,F10 . 3 , 16X ,F10 . 3

FORMAT ( IX, A7 , 4 (F10 . 3 , A5, : ) , / , 10( 8X , 4 (F10 . 3 , A5 , :),/)) FORMAT ( ’ OITERATION : ’,13,' INNER LOOP: ’,13) FORMAT (’ ’ ,A10,20(A7, : )) FORMAT (’ ’ ,F10.3,20(F6.1,1X, :)) FORMAT ( ’ 0’ , / , 20( ’ ’,16,’: ’,A,/)/) FORMAT (’ ’ , A10 , 20 (

’ (’ ,12, ’)’,:)

END
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r SUBROUTINE INPUT (THEEND)

Cc @@@@ @ c @@@@ mmrn @@@@@@ §§@ s @@@@@@

c @@@@ e @@@ @@@ @ @@@ @ @@@@

c @@@@ @ m@ @m @ @@@ s @@@g

c @@@@ @ m@ mmrn @@@ @ @@§@

C

C mmrn § @@@ @@§ @m

mm

C

C PURPOSE: INPUTS DATA DESCRIBING THE STOVE / WALL PROTECTION SYSTEM

C TO BE MODELED

C

INCLUDE ’ STOVE. CMN’ PARAMETER (NVAR=8) CHARACTER VAR(NVAR)*6 , IN*80 ,KEYWD*80 INTEGER VLEN(NVAR) LOGICAL THEEND , HAVEX , HAVEY DATA (VAR(I )

, VLEN(I )

, 1=1, NVAR) /’XWALL ’,5,’YWALL ’ , 5

,

’ TSTOVE’ , 6, 2 'THICK ',5, 'WIDTH ' , 5, 'HEIGHT' , 6

, 'K ’,1,'EMMIS ’,5/ C

C LOOK FOR A KEYWORD OR END OF FILE

C THEEND= . TRUE

HAVEX=. FALSE. HAVEY=. FALSE. TITLE=’ STOVE / WALL PROTECTOR HEAT TRANSFER MODEL'

N=0 IVAR=0

VNAME=’ ’ 10 READ (5, ’ (A80)’ ,END=30) IN

THEEND=. FALSE. IS=INDEX( IN, ' : ’) IF (IS.GT.l) THEN KEYWD=IN( 1: IS-1)

IF (KEYWD.NE. 'END' ) THEN

C

C XWALL ... X POSITION OF POINT ON THE WALL

C

IF (KEYWD.EQ. 'XWALL') THEN ICHR=IS+2 XWALL=FVAL ( IN , ICHR) HAVEX= . TRUE

C

C YWALL . . . Y POSITION OF POINT ON THE WALL

C ELSE IF (KEYWD.EQ. 'YWALL' ) THEN ICHR=IS+2 YWALL=FVAL ( IN , ICHR) HAVEY=.TRUE. C

C AIRSPACE ... AN AIR SPACE BETWEEN TWO SOLID PROTECTORS

C ELSE IF (KEYWD.EQ. 'AIRSPACE' ) THEN N=N+1

MATL(N)=' AIRSPACE’

ICHRt=IS+2 V1=FVAL(IN, ICHR)

V2=FVAL(IN, ICHR) V3=FVAL ( IN , ICHR

IF (V2.EQ.0. .AND.V3.EQ.0. ) THEN

T (N)=V1 EM1IS (N)=l.

HEIGHT(N)=0. ELSE

L (N)=V1

EM1IS(N)=V2

IF (EFMIS(N).EQ.O.) EPMIS(N)=1.0

T (N)=V3
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HEIGHT (N)=HEIGHT(N-1) WIDTH ( N

) =WIDTH( N- 1

END IF C

C STOVE . . . THE HOT STOVE SURFACE

C ELSE IF (KEYWD.EQ. ’STOVE’ ) THEN MATL(0)=’ STOVE’ ICHR=IS+2 EMMIS ( 0

) =FVAL ( IN , ICHR

IF (EFMIS(O).EQ.O.) EMIS(N)=1.

HEIGHT ( 0 )=FVAL (IN , ICHR) WIDTH ( 0 )=FVAL ( IN , ICHR

T (0 )=FVAL(IN, ICHR) C

C FOR . . . SPECIFIES A SERIES OF CALCULATIONS TO BE DONE

C ELSE IF (KEYWD.EQ. ’FOR’ ) THEN

IVAR=0

ISUB=0 DO 20 1=1 , NVAR

J=I NDEX ( IN , VAR( I ) ( 1 : VLEN ( I ) )

IF ( J .NE . 0 . AND . IN( J~1 : J-l) . EQ. ’ ’) IVAR=I

20 CONTINUE

IR=0 ICHR=IS+2

IF (IVAR.EQ. 0 ) THEN WRITE (6,1) IN GO TO 10 C

C IF IT'S A VARIABLE WITH SUBSCRIPT, MAKE SURE ONE’S THERE C

ELSE IF (IVAR.GE.4) THEN

IL=INDEX( IN , ’ (

’

IR=INDEX( IN , ’ )’

IF ( IL . EQ . 0 . OR . IR . EQ . 0 . OR . IL . GT . IR) THEN WRITE (6,2) IN GO TO 10 END IF ISUB=FVAL(IN, ICHR) END IF ICHR=IR+1 VLOWER=FVAL ( I N , ICHR

VUPPER=FVAL ( IN , ICHR

VINCR=FVAL( IN , ICHR)

IF ( (VLOWER . NE . VUPPER. AND . VINCR.EQ. 0

2 .OR. (VLOWER. EQ. VUPPER. AND. VINCR.NE.0)

3 .OR. (VUPPER.GT.VLOWER.AND.VINCR.LT. 0)

4 .OR. ( VUPPER.LT. VLOWER. AND. VINCR.GT.O)) THEN WRITE (6,4) IN GO TO 10 END IF VNAME=VAR ( IVAR

VNAME ( VLEN ( IVAR )+ 1 : VLEN ( I VAR ) +1+IR- IL )=IN ( IL : IR

C

C DEBUG . . . TURN DEBUG PRINT ON OR OFF C

ELSE IF (KEYWD.EQ. ’DEBUG’ ) THEN

IF (INDEX (IN, ’OFF’ ) .NE. 0) DEBUG=. FALSE.

IF (INDEX (IN, ’ON’ ) .NE.O) DEBUG= . TRUE

C

C PRINTOUT . . . SPECIFY LEVEL OF PRINTOUT

C ELSE IF (KEYWD.EQ. ’PRINTOUT’ ) THEN

IF (INDEX(IN, ’FULL’ ) .NE.O) FULPRT= . TRUE

IF (INDEX(IN, ’FULL’ ).EQ.O) FULPRT= . FALSE

C

C TITLE . . . SPECIFY A TITLE FOR THE PRINTOUT C

ELSE IF (KEYWD.EQ. ’TITLE’ ) THEN
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TITLE=IN ( IS+2 : 80

C

C IF IT’S NOT ONE OF THE RECOGNIZED KEYWORDS, ASSUME A SOLID PROTECTOR

C ELSE

N=N+1 ICHR=IS+2

MATL(N)=IN( 1 : IS-1

L(N)=FVAL(IN, ICHR)

HEIGHT(N)=FVAL(IN, ICHR) WIDTH ( N

) =FVAL ( I N , ICHR

K(N)=FVAL(IN, ICHR)

EffllS ( N )=FVAL ( IN , ICHR

T (N)=FVAL(IN, ICHR)

IF (L(N).EQ.O. .OR.HEIGHT(N) .EQ.0. .OR. WIDTH(N) .EQ. 0 . .OR. 2 K(N) . EQ. 0 . . OR.EMIIS(N) . EQ. 0 . ) THEN WRITE (6,3) IN N=N-1 GO TO 10 END IF END IF GO TO 10 END IF END IF C

C DATA HAS BEEN READ IN, CHECK CONSISTENCY OF DATA INPUT

C

30 IF (THEEND) THEN RETURN

ELSE IF (N.LE.l) THEN WRITE (6,*) 'DATA INPUT ERROR, TOO FEW NODES SPECIFIED.' ELSE

IF (DEBUG. AND. IVAR. NE.0) THEN

IF (IVAR.LT.4) THEN WRITE (6,5) VAR ( IVAR)

, VLOWER, VUPPER , VINCR

ELSEWRITE (6,6) VAR(IVAR),ISUB, VLOWER, VUPPER, VINCR

END IF END IF DO 40 1=1,

IF (DEBUG) CALL PSUM(I)

IF (MATL( I ) .EQ. ’AIRSPACE’ ) THEN

IF ((L(I).LE.O. .AND.I.NE.N) .OR. (HEIGHT(I) .LE.0. .AND.I.NE.N)

2 .OR. (HEIGHT(I) .NE. 0. .AND. I .EQ.N) .OR.EMMIS(I) .LE. 0. ) THEN WRITE (6, ’(IX, A, 13)’) ’INCORRECTLY SPECIFIED AIR SPACE.’,

STOP ’INPUT DATA ERRORS, AIR SPACE’ END IF ELSE

IF (L(I ) .LE.0 . .QR.HEIGHT(I) .LE. 0. .OR.WIDTH(I) .LE. 0. .OR. 2 K(I ) . LE . 0 . . OR.Et“MIS(I ) .LE.0.) THEN WRITE (6, ’(IX, A, 13)’) 'INCORRECTLY SPECIFIED PROTECTOR

STOP ’INPUT DATA ERRORS, SOLID PROTECTOR' END IF END IF

40 CONTINUE

IF (XWALL.LT. 0. .OR. YWALL.LT. 0. ) THEN WRITE (6,*) ’INCORRECTLY SPECIFIED POINT ON WALL.’ STOP 'DATA INPUT ERRORS, XWALL & YWALL’ END IF

IF (T(O).LE.T(N)) THEN WRITE (6,*) 'INCORRECTLY SPECIFIED ENDPOINT TEMPERATURES.’ STOP 'DATA INPUT ERRORS, T(0) & T(N)

END IF IF (T(O).LE.O. .OR.WIDTH(O). LE.0. .OR. HEIGHT(O) .LE.0. .OR.EmiS(O)

2 .LE.0.) THEN

WRITE (6,*) ’INCORRECTLY SPECIFIED STOVE PARAMETERS.' STOP 'DATA INPUT ERRORS, STOVE’ END IF END IF

IF (MATL(N).EQ. ’AIRSPACE’ ) HEIGHT (N)=HEIGHT(N-1)
44

421 1 ZSTOVE=L ( 1

1 211

422 1 HSTOVE=HEIGHT ( 0

212

423 1 WSTOVE=WIDTH ( 0

1 213

424 |C 214 425 |c IF NOT POSITION HAS BEEN SPECIFIED, USE MIDPOINT OF STOVE 1 215

426 jc 1 216

427 1 IF (.NOT. HAVEX) THEN 1 217 428 XWALL=WSTOVE/2. 1 218

429 END IF 1 219

430 1 IF (.NOT. HAVEY) THEN 1 220

431 YWALL=HSTOVE/2. 1 221

432 1 END IF 222

433 |c 1 223

434 jc IF NO INCREMENT HAS BEEN SPECIFIED, MAKE ONE UP 224 435 jc 1 225

436 1 IF (IVAR.EQ.O) THEN 1 226

437 IVAR=1 1 227

438 VLOWER=XWALL 228

439 VUPPER=XWALL 1 229

440 1 VINCR=1 .

1 230

441 1 END IF 1 231

442 |c 232

443 jc PRINT OUT A DESCRIPTION OF THE STOVE / WALL SYSTEM AS SPECIFIED 1 233

444 jc 234

445 WRITE (6,11) TITLE, N+l.XWALL, YWALL 1 235

446 1 IF (IVAR.GT.0. AND.IVAR.LT. 4) THEN 1 236

447 WRITE (6,5) VAR ( IVAR )

, VLOWER , VUPPER , VINCR 1 237

448 1 ELSE IF (IVAR.GT.4) THEN 238

449 1 WRITE (6,6) VAR(IVAR) ,ISUB, VLOWER, VUPPER, VINCR 1 239

450 1 END IF 1 240

451 WRITE (6,12) 241

452 1 DO 50 1=0,

1 242

453 IF (I.EQ.O.OR.I.EQ.N) THEN 243

454 1 IF (MATL(I).EQ. ’STOVE’) THEN 244 455 1 WRITE (6,13) I,MATL(I),HEIGHT(I),WIDTH(I),EMlIS(I),T(I)-273. 15

245

456 1 ELSE IF ( MATL( I ).EQ. ’AIRSPACE’) THEN 246

457 1 WRITE (6,14) I,MATL(I),L(I),Ef*JIS(I),T(I)-273.15 247

4 58 1 ELSE 1 248

459 1 WRITE (6,15) I ,MATL(I )

, HEIGHT(I ), WIDTH( I) ,L(I ) , EMUS ( I ) ,K(I

249

460 1 2 T(I )-273 . 15 250

461 1 END IF 1 251

462 1 ELSE 1 252

463 1 IF (MATL(I).EQ. 'STOVE') THEN 1 253

464 1 WRITE (6,13) I ,MATL(I )

, HEIGHT (I ), WIDTH( I) ,EM1IS(I

254 465 1 ELSE IF ( MATL( I ).EQ. ’AIRSPACE’) THEN 255

466 1 WRITE (6,14) I,MATL(I),L(I),EmiS(I) 1 256

467 1 ELSE 1 257

468 1 WRITE (6,15) I ,MATL(I )

, HEIGHT(I )

, WIDTH( I) ,L(I ), EMMIS(I) ,K(I

1 258

469 1 END IF 1 259

470 1 END IF 1 260 471 | 50 CONTINUE 1 261

472 1 RETURN 262

473 |c 1 263

474 jl FORMAT (’OSYNTAX ERROR ON "FOR” STATEMENT, ILLEGAL OR NO VARIABL| 264 475 1 2E SPECIFIED.’,/,’ ’,A79,//) 1 265

476 \z FORMAT ('OSYNTAX ERROR ON ’’FOR’’ STATEMENT, SUBSCRIPT REQUIRED FO| 266

477 1 2R VARIABLE SPECIFIED.’,/,’ \A79,//) 1 267 478 1

FORMAT (’OSYNTAX ERROR ON STATEMENT, UNRECOGNIZED KEYWORD.',/, 1 268

479 2

’

’

, A79, //) 269

480 1

FORMAT (’OSYNTAX ERROR ON "FOR" STATEMENT, RANGE AND INCREMENT l| 270

481 1 2NCONSISTENT .’,/,’ \A79,//) 1 271 482 | 5 FORMAT (

’ 0SERIES OF CALCULATIONS FOR VARIABLE ’ ,A, ’

: ’.3F10.3) 1 272

483 1FORMAT <0SERIES OF CALCULATIONS FOR VARIABLE \A,’(’,I2, 1 273

484 2 ’): ’ .3F10.3) 1 274 485 |ll FORMAT (’1’ ,A, //

1 275

486 1 2 ’ NUMBER OF NODES IN CALCULATION: ’,12,/,’ POINT ON WALL: (X)

276

487 1 3 F10.3,T41, ’

Y ) : ' ,F10.3) 1 277

488 1 12 FORMAT (’01 MATERIAL HEIGHT WIDTH THICK EMISS| 278

489 1 2 K TEMPERATURE’,/, 1 279

490 1 3 ' (m) (m) (m) 1 280
45

491 | 4 (W/m K) CC)’,/,’ , , 7 BV~, ),n I 281

492 j 13 FORMAT ( IX, 12 , 2X, A, T26, IX, F6 . 2, T35, F6 .2 ,T51 ,F6 . 2, T70 , F7 . 2 ) j 282

493 | 14 FORMAT ( IX, 12 , 2X, A, T43,F6 .2, T51 ,F6. 2, T70 , F7 . 2) | 283

494 j 15 FORMAT ( IX. 12 , 2X, A, T26, IX, 4 (F6. 2, 2X) , F8 . 3 , 2X, F8 .2) j 284

495 | END | 285
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DOUBLE PRECISION FUNCTION FVAL (IN.ICHR)

C

c @@@@@@@@ @638 c @@@@ 888

c @§@@ e@@ @ @@@@@@ 888

c @@@@@@@@ @@@ @ @ 888

c 6@@@ @@@ e @@@@@@ 888

c @@@@ @@@(3 @ @@@ 888

c

0 @@@@ m @@@@@@ 888

c ARGUMENTSIN: STRING CONTAINING (MAYBE) NUMBER

c ICHR: (INPUT) BEGINNING CHARACTER POSITION

c (OUTPUT) NEXT CHARACTER POSITION

C

C PURPOSE: DECODE NEXT NUMBER IN STRING AS A DOUBLE PRECISION VALUE

C

IMPLICIT DOUBLE PRECISION (A-H.O-Z) CHARACTER IN* (* )

, FORMAT*10

IL=LEN(IN) IFIRST=ICHR

DO 20 I=IFIRST, IL IF ( (IN(I : I ) .GE . ’ 0’ . AND . IN( I : I) .LE. ’ 9’ ) .OR. IN(I : I ) . EQ. ’

.

2 .OR. IN(I : I ) .EQ. ’+’ .OR. IN(I : I ) . EQ. ' ) THEN

C

C THERE IS A NUMBER ON THE CARD, FIND OUT WHAT IT IS C DO 10 J=I , IL

C

C IF WE FIND THE END OF THE NUMBER, READ IT FROM THE LINE

C

IF ( ( INC J : J) .LT. ’ 0’ .OR. INC J: J) .GT . ' 9’ ) . AND. INC J: J) . NE . ’

.

2 .AND.INCJ: J) .NE. ’+’ . AND. INC J: J) . NE . ’ ) THEN WRITE (FORMAT, 30) J-I READ (IN(I : J- 1 > .FORMAT) VAL FVAL=VAL

ICHR=J RETURN

END IF

10 CONTINUE

C

C IF WE GET TO THE END OF THE LINE WITHOUT FINDING END OF NUMBER,

C JUST READ THE NUMBER

C WRITE (FORMAT, 30) IL-I+1 READ (INC I :IL), FORMAT) VAL FVAL=VAL

ICHR=J RETURN

END IF

20 CONTINUE

C

C IF NO NUMBER IS ON THE CARD, JUST RETURN A 0. C FVAL=0

RETURN

C

30 FORMAT (’ (F’,12. 2, ’ .0)’

END
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SUBROUTINE HEATS

C

c @@@@ 8 c @888 8 8 c @888 8 @88888 @88888 888888 @88888

c @8888888 8 @88 8 8888 888

c @880 8 @88888 @88888 @888 @88888

c 8888 8 8 8 @88 8888 888

c @888 8 @88888 @88888 8888 @88888

c

C ARGUMENTS : NONE

CC PURPOSE: CALCULATES TOTAL HEAT AND TOTAL RESISTANCE THROUGH WALL

C PROTECTORS

C

INCLUDE ’ STOVE. CMN’ C

C JUST SUM UP RESISTANCES TO MAKE UP TOTAL RESISTANCE

C RTOTAL=0

DO 10 1=1,

CALL HEAT (I)

1 0 RTOTAL=RTOTAL+R ( I

C

C TOTAL HEAT IS JUST DELTA T / TOTAL RESISTANCE

C QTOTAL= ( T ( 0

) - T ( N ) ) /RTOTAL RETURN

END
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SUBROUTINE HEAT ( I

C

c sees e

c sees @ e

c sees @ eeeeee eeeess

c @@@@@@@@ @ eee @ sees

c ssse e eeeeee eeeeee sees

c sees § § e ess esse

c esse @ seeeee essees esse

C

C ARGUMENTS: I: ELEMENT NUMBER

C

C PURPOSE: CALCULATES HEAT THROUGH ELEMENT NUMBER I C INCLUDE ’ STOVE. CMN’ DATA SIGMA / 5.67D-8 / IF (MATL(I) .NE. ’AIRSPACE’ ) THEN

C

C MATERIAL IS A SOLID, CONDUCTION ONLY

C R(I)=L(I)/K(I)

ELSE IF (MATL(I).EQ. ’AIRSPACE' .AND. I. EQ.l) THEN

C

C MATERIAL IS AND AIRSPACE NEXT TO STOVE, CALCULATE FOR POINT ON WALL

C XNOTS=XWALL- (XSTOVE-WSTOVE* . 5

YNOTS=YWALL-YSTOVE ZNOTS=ZSTOVE

CF ( I

) =CFIGS (XNOTS , YNOTS , ZNOTS ) -CFIGS (XNOTS-WSTOVE , YNOTS , ZNOTS

2 +CFIGS (XNOTS-WSTOVE , YNOTS-HSTOVE , ZNOTS

3 -CFIGS (XNOTS, YNOTS-HSTOVE, ZNOTS) RAD (I )=1 . / (CF(I )*SIGMA*HHIS(I )*(T(I-1)**2+T(I)**2)

2 *(T(I-1)+T(I))) RMTEMP=293 . 15 RLOSS= ( T ( I - 1

) -T ( I ) ) / ( ( T ( I ) **4 -RMTEMP**4 ) *SIGMA*QHIS ( I

2 *(1-CF(I) )

R(I)=1./(1. /RAD(I)-1. /RLOSS) ELSE IF (MATL(I).EQ. ’AIRSPACE’ .AND. I. NE.N) THEN

C

C MATERIAL IS AN AIRSPACE, BUT NOT NEXT TO STOVE

C CF(I)=CFIGP(HEIGHT(I) ,WIDTH(I ) ,L(I)

H(I )=HCONV(T( 1-1) , T(I ), HEIGHT (I )

CONV(I)=l./H(I)

RAD(I )=1 . / (CF (I )*SIGMA*EMMIS( I )*(T( I-l)**2+T( I )**2)

2 *(T(I-1)+T(I)))

R(I)=l./(l./CONV(I)+l./RAD(I))

ELSE

C

C MATERIAL IS AN AIRSPACE AND LAST ELEMENT ... THE GREAT OUTDOORS

C CF(I)=1

H(I )=HCONV(T( 1-1) , T(I )

, HEIGHT (I )

CONV(I)=l./H(I)

RAD(I)=1./(CF(I)*SIGMA"EEWIS(I)*(T(I-1)**2+T(I)**2)

2 *(T(I-1)+T(I)))

R(I)=l./(l./CONV(I)+l./RAD(I))

END IF Q(I)=(T(I-1)-T(I))/R(I) RETURN

END
49

644 1 DOUBLE PRECISION FUNCTION CFIGS (A,B,C) 1 1 645 |c 1 2 646 |c eeeeeeee 8880 0800 1 3 647 |c 8 8880 8 8 4 646 ic 0 8008 888888 0888 880800 688880 5 649 jc 8 8888 8888 000880 868 1 6 650 jc 8 8888 8888 8880 8 668088 1 7 651 |c 8 8888 8088 0880 88888080 680 8 652 ic 08888800 8888 0008 8 8860 866888 9 653 ic 80066688 10 654 ic 1 11 655 ic ARGUMENTS: A: WIDTH OF RECTANGLE 12 656 ic B: HEIGHT OF RECTANGLE 1 13 657 |c C: DISTANCE TO POINT OF CALCULATION 14 658 ic 1 15 659 ic PURPOSE: CALCULATES RADIATION CONFIGURATION FACTOR FOR A PLANE 16 660 |c ELEMENT TO A PLANE PARALLEL RECTANGLE. 1 17 661 ic 1 18 662 ic SOURCE: THERMAL RADIATION HEAT TRANSFER, SEIGEL & HOWELL. 19 663 ic 1 20

664 1 IMPLICIT DOUBLE PRECISION (A-H.O-Z) 1 21

665 PI=3. 14159 22

666 1 X=A/C 1 23

667 Y=B/C 24 668 CFIGS=1

/(2*PI)* (X/ SQRT ( 1+X**2) *ATAN(Y/SQRT ( 1+X**2 )

25

669 1 2 + Y/SQRT(1+Y**2)*ATAN(X/SQRT(1+Y**2) )26

670 RETURN 27

671 1 END 1 28
50

672 1 DOUBLE PRECISION FUNCTION CFIGP (A,B,C) 1 673 |C 2 674 jc @@@@@@@@ mm mm 3 675 \C @ @@@@ @ @ 4 676 jc @ @@@@ mmm mm @@@@@@ @@@@@@ i 5 677 |c @ mm mm @m e 6 678 jc @ @@@@ mm mm @ @@@ e 7 679 jc @ @@@@ mm mm @@@@@@@@ @@@@@@ i 8 680 jc @@@@@@@@ mm mm @ @@@@ @g@ ! 9 681 jc @@@@@@@@ @@@ 10 682 jc 11 683 jc ARGUMENTS : A: WIDTH OF RECTANGLE 12 684 jc B: HEIGHT OF RECTANGLE 13 685 jc C: DISTANCE BETWEEN RECTANGLES 14 686 jc 15 687 jc PURPOSE: CALCULATES RADIATION CONFIGURATION FACTOR FOR TWO 16 688 jc IDENTICAL, PARALLEL, DIRECTLY OPPOSED RECTANGLES. 17 689 jc 18 690 jc SOURCE: THERMAL RADIATION HEAT TRANSFER, SEIGEL & HOWELL. 19 691 jc 20 692 IMPLICIT DOUBLE PRECISION (A-H.O-Z) 21

693 1 PI=3. 14159 22

694 X=A/C 23 695 1 Y=B/C 24 696 1 CFIGP=2

/ (PI*X*Y)*(LOG( (

1+X*X)*( 1+Y*Y) )/

1+X*X+Y*Y) )**0 . 5 + 25

697 2 X*SQRT(1+Y*Y)*ATAN(X/SQRT(1+Y*Y) ) + 26

698 1 3 Y*SQRT(1+X*X)*ATAN(Y/SQRT(1+X*X) ) - 27 699 1 4 X*ATAN(X) - Y*ATAN(Y)) 28

700 1 RETURN 29

701 1 END 30
51

702 1 DOUBLE PRECISION FUNCTION HCONV(Tl,T2,L) 1 1 703 |C 1 2

70*. |c gggg g 1 3 705 |c gggg g 4 706 ic gggg g gggggg gggggg gggggg ggg g 1 5 707 ic gggggggg g ggg ggg g g ggg ggg g 1 6 708 ic gggg g g ggg g g ggg ggg g 1 7 709 ic gggg g g ggg ggg g g ggg gggg 8 710 ic gggg g gggggg gggggg g ggg gg 1 9 711 ic 10 712 ic ARGUMENTS: Tl: TEMPERATURE OF HOTTER SURFACE 1 11 713 ic T2: TEMPERATURE OF COOLER SURFACE 1 12

714 ic L: HEIGHT OF SURFACES 13 715 ic 1 14 716 ic PURPOSE: CALCULATES FREE CONVECTION HEAT TRANSFER COEFFICIENT FOR j 15 717 ic A VERTICAL SURFACE. 1 16 718 ic 1 17 719 ic SOURCE: FUNDAMENTALS OF HEAT TRANSFER, INCORPERA & DEWITT. ! 18 720 ic 1 19 721 IMPLICIT DOUBLE PRECISION (A-H.O-Z) 20

722 1 DOUBLE PRECISION K,NU,L,NUSELT 21

723 1 DIMENSION C(3 , 5) 1 22

724 1 DATA ((C(I, J),J=1,5),I=1,3) / 23 725 1 2 -. 381021E-2, . 132063E-3 , -.117332E-6, .687499E-10, -

. 127680E-13

24

726 3

, - . 167333E-4 , .143076E-6, - . 249135E-10 .781850E-13, -

. 127693E-1625

727 4

, - . 501195E-5, . 468550E-7 , .881329E-10, - . 117315E-13

. 307192E-17 j 26

728 1 5 / 1 27 729 1 TF=(Tl+T2)/2 28

730 1 DELTAT=(T1-T2) 1 29

731 1 K=C ( 1 , 1 )+C ( 1 , 2

) *TF+C (1,3) *TF*TF+C ( 1 , 4) *TF** 3+C (1,5) *TF**4 30 732 ALPHA=C ( 2 , 1 )+C ( 2 , 2

) *TF+C ( 2 , 3

) *TF*TF+C ( 2

4)*TF**3+C(2, 5)*TF**4 i 31

733 1 NU=C(3 , 1)+C(3 ,2)*TF+C(3 , 3 )*TF*TF+C(3 , 4)*TF**3+C(3 , 5)*TF**4 1 32

734 1 PR=NU/ALPHA 33 735 RA=9 . 8* ( 1 . / TF ) *ABS ( DELTAT ) *L**3 / ( NU*ALPHA

34 736 1 NUSELT=(0. 825+0. 387*RA**(l./6. ) / ( 1. +(0. 492/PR)**(9. /16

)) 35

737 1 2 **(8./27. ))**2 36

738 1 HCONV=NUSELT*K/L 37 739 RETURN 1 38

740 1 END 1 39
741 1 CHARACTER*5 FUNCTION CMET (VALUE , EPS

1 1 742 |C 2

743 jc gggggggg 3 744 |c g gggg g 4 745 ic g gggg ggggggg gggggg gggggg 1 5 746 ic g g g ggg g ggg gggg 6 747 ic g gggg g g ggg gggggg gggg 7 748 ic g gggg g g ggg g gggg 8 749 ic gggggggg g g ggg gggggg gggg 9 750 ic 10 751 ic ARGUMENTS: VALUE: NUMBER TO BE EVALUATED 11 752 ic EPS : ACCEPTANCE CRITERION FOR VALUE 12 753 ic 13 754 ic PURPOSE: FUNCTIONS RETURNS A CHARACTER INDICATION OF WHETHER THE 14 755 ic VALUE IS WITHIN LIMITS. USED FOR DEBUG PRINTOUT 15 756 ic 16 757 IMPLICIT DOUBLE PRECISION (A-H,0-Z) 1 17 758 i IF (ABS (VALUE ) . LE . EPS ) THEN 18 759 CMET=’ (IN) ' 19 760 i ELSE 20 761 CMET=' (OUT)

21

762 i END IF 22

763 i RETURN 23 764 i END 1 24
765 s'JssxTiXt ?s-jy.;:- 766 |C 767 jc 88888088

768 jc gggg § 763 jc e§eg § 8B8BB8 gee § ggggggg

770 jc ggg §g ggg see gee § g g g gg 771 fix If* |L §ee§ 000000 ggg g § g ggg 772 jc gggg §:§§ gee g g g ggg 773 jc gggg gggggg gggggg g g ggg "5 C A3SO*STS: : SURFACE BOBER PCS SCM4ARY PSISTOUT

776 C

777

778

773

76C 781 76

783

76*

7 85 786

787

7 86 789

79C 7s:

732

753

73* 735

~S€

PURPOSE : rSETTS XT ALL TEE VARIAELZS 3 THE CMOS SLOCK. D5E0 fce debog mncm.

DdLMS * STOPS. CMS* '•SHE (6,13) I ,ISMLCI) , 1(1) ,S(I) ,L(I) ,£CI),H(I) ,CFCD .2M-CS Cl)

• cgbv; : : . sad c ; . seight

i

.kebthci ) ,xstovs , yscots , zstote

3 KSTC7VE,BSITCWS,»<ALL VKALL. KJOIAL , QTCIAL .

RECURS

FCEKfeC . CCURSZ5T VAXES ECS SPACE M2. MATERIAL IS A . . 2

3A

57

8

3

ISKFSRAXRE : . FLO . 3 . 1*1, RSSISIASCE :

; ,F10.3. . lEICKSESS : .FID. 3.1*1. 3HE93&L CCSiOXTiWiTX : * ,512.5, !, E F10.3.T61, ’ CXSFIGQRATTCE ?ACTOR: 1 ,310.3,

emissive:?: ,?ic.3,:*i, _vlividual ezai: ei:.3, . COST . R3STS1WCS :

'

, E1C . 3 , , ’SAD. RESISTANCE : EM. 3. , ESISEC : XSTC7S:

-STMTE: XnAX:

ETCIAL

.fio.3,:*i, ’tmnB: -• ,no.3,/,

.?10.3,T31,'XSTOBE: ' ,E II. 3 MSI. MSXTE: .E1D.3, .

. E10 . 3 , 131 , HSTOVE :

’ ,F1D.3,/, .E10.3.T31. TnALL: MF1C.3,/,

.F3II.3,T31, 'QT0T6L:’ ^ - .FIO.3,161, 5: 110 )
798

799

800 801

802

803

804 805

806

807 808 809

810

811 812

813

814 815

816

817 818

819

820 821

822

823

824 825 826

827 828 829

830

831 832

12

3

456

78

910

1112

131415

16

1718

192021

2223

2425

262728

29

30

3132

33

3435

CHARACTER*60 FUNCTION PMATL (MATL1 ,MATL2

c @@@@@666 886

c eeee 8 8 886

c 6888 8 6686866 888688 888

c @@@86666 8 6 886 @ 8888 888

c 8666 6 @ 868 @@@@@@ 6866 686

c 8868 8 8 668 8 888 6868 886

c 8888 8 6 @@@ 888886 8686 888

ARGUMENTS: MATL1: DESCRIPTION OF MATERIAL CLOSER TO APPLIANCE

MATL2 : DESCRIPTION OF MATERIAL FURTHER AWAY FROM APPLIA

PURPOSE: CREATES A CONCATENATED DESCRIPTION OF TWO MATERIALS FOR

PRINTOUT

NCE

CHARACTER*40 MATL1.MATL2

PMATL=MATL1 DO 10 1=40, 1,-1

IF (MATL1 (I : I ) . NE . ' ’) THEN PMATL (1+1: 1+3)=’ /

’ GO TO 20 END IF

10 CONTINUE

PMATL=’ ’ 20 DO 30 1=40, 1,-1

IF (PMATL(I : I ) . NE . ’ ’) THEN PMATL (1+2 : 60)=MATL2 RETURN

END IF

30 CONTINUE

PMATL=MATL2 RETURN

END
o

o

55

CCt-tON BLOCK FOR PROGRAM STOVE

1 | IMPLICIT DOUBLE PRECISION (A-H.O-Z) I 1 2 |C j 2

3 j PARAMETER (MAXPRO=20) | 3

* |C | 4 5 | DOUBLE PRECISION L,K j 5

6 | CHARACTER MATL*40 ,VNAME*10 , TITLE*80 j 6

7 j LOGICAL DEBUG, FULPRT | 7 8 j COMMON /NSTOVE/ T(0 iMAXFRO) ,R(0 :MAXFRO) ,L(0 :MAXFRO) ,K(0 :MAXPRO) , | 8

9 | 2 H(0 :MAXPRO) , CF(0 :MAXPRO) ,EIWIS(0 :MAXPRO) ,Q(0 :MAXPRO) , | 9

10 | 3 CONV(0 :MAXPRO) ,RAD(0 rMAXPRO) ,HEIGHT(0:MAXPRO) ,WIDTH(0:MAXPRO) , | 10

11 j 4 XSTOVE , YSTOVE , ZSTOVE , WSTOVE , HSTOVE , XWALL , YWALL , RTOTAL , QTOTAL , N , j 11

12 | 5 IVAR, ISUB,VLCWER,VUPPER,VINCR,DEBUG, FULPRT | 12

13 j COMMON /CSTOVE/ MATL ( 0 : MAXPRO )

, VNAME , TITLE | 13

14 |C | 14
Appendix fi: Data Input for STOVE
57

The data input for stove takes the form of six different key words with

arguments to specify values which depend upon the key word. In most cases,

the order of the key words is unimportant, except as noted below. A description of each of the input key words and values which go on the same line are

presented below:

STOVE

AIRSPACE

FOR

XWALL

YWALL

PROTECTOR

<height> <width> <emissivity> <temperature>

<thickness> <emissivity>

<variable> — <lower> <upper> <increment>

<x position>

<y position>

<thickness> <height> <width> <k> <emissivity> <temperature>

BOLDFACE type are required key words. Words in <brackets> specify numeric

inputs as follows

<emissivity> specifies the emissivity of the cooler surface of the

material. If specified for an airspace, it is the emissivity

of the surface adjacent to the airspace at the farther

distance from the stove.

<height> specifies the height of the stove or protector in meters.

<increment> specifies the amount to increment the variable <variable> in

the FOR statement for each calculation to be performed. The

first calculation is done with <variable> equal to the value

<lower>; the second calculation is done with <variable> equal

to the value <lower> + <increment> and so forth until the

value of <variable> is greater than or equal to the value of
58

<k>

<lower>

<temperature>

<thickness>

<variable>

<upper>. The units for the number are the same as those for

the variable <variable>.

specifies the thermal conductivity of the solid protector in

W/m-K.

specifies the beginning value of the variable <variable> in

the FOR statement for each calculation to be performed. The

first calculation is done with <variable> equal to the value

<lower>; the second calculation is done with <variable> equal

to the value <lower> + <increment> and so forth until the

value of <variable> is greater than or equal to the value of

<upper>. The units for the number are the same as those for

the variable <variable>.

specifies the temperature of the stove surface, protector, or

airspace in K. Temperatures are only specified for the stove

surface (surface number 0) and for the outermost surface or

airspace (surface number N)

specifies the thickness of the material (for a protector) or

the distance between surfaces (for an airspace)

specifies the variable to be incremented in each calculation

to be done. The first calculation is done with <variable>

equal to the value Clower>; the second calculation is done
<width>

<x position>

<y position>

59

with <variable> equal to the value <lower> + <increment> and

so forth until the value of <variable> is greater than or

equal to the value of <upper>. Legal variables which may be

used are: T(0) -- the stove temperature, width(i), k(i)

xwall , ywall , emissivity(i) , height(i) , l(i).

specifies the width of the stove or protector in meters.

specifies the x position of the point on the wall at which the

calculation is to done in meters.

specifies the y position of the point on the wall at which the

calculation is to done in meters
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instruction s)

4. TITLE AND SUBTITLE

1. PUBLICATION OR

REPORT NO.

NBSIR 8b-3300

2. Performing Organ. Report No. 3. Publication Date

February 1987

STOVE: A Predictive Model for Heat Transfer from Solid-Fuel Appliances

5. AUTHOR(S)

Richard D. Peacock and Richard A. Dipert

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s) National Bureau of Standards

Department of Commerce

Gaithersburg, MD 20899

7. Contract/Grant No.

8 . Type of Report & Period Covered

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

10. SUPPLEMENTARY NOTES

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

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here) A computer implementation of a model to predict temperatures on wall and wall

protector surfaces exposed to the heating of an appliance such as a solid fuel

heating appliance is described. A steady state heat transfer model with flexibility

to describe a generalized method of protection for a combustible wall surface is

presented along with a computer program implementing the model. Good agreement was

found comparing the model predictions with data previously collected during full scale

experiments conducted to evaluate the effectiveness of generic methods of wall

protection in reducing temperatures on combustible wall surfaces. Extensive references

of research related to solid fuel heating safety are included.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

chimneys; fire models; fire safety; fire tests; flues; heat transfer; heating

equipment; literature reviews; radiant energy; stoves; wood

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

(_Xj Uni imited

| | For Official Distribution. Do Not Release to NTIS 66

H Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

15 . Price 20402.

[ X] Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $ 13.95

USCOMM-DC 8043-P60