Damage to cellulosic solids by thermal radiation

Damage to Cellulosic Solids by Thermal Radiation D. L. SIMMS Fire Research Slation, Boreham Wood, Herts. (Received ?uly 1962) This paper examines the different ways in which thermal radiation can produce damage in cellulosic materials. The criteria suggested by various authors as necessary for the onset of the different hinds of thermal damage have been considered. Over a wide range of conditions, fixed temperature criteria have been shown to be adequate lor correlating the experimental results. Exceptions to, and some of the limitations of, this approach are discussed.

Notation c is the specific heat of the solid co is the specific heat of the gases passing through the char layer d is the depth of penetration of char E is the effective activation energy e is the exponential function f is the frequency factor F~ denotes unspecified functions H is the Newtonian cooling constant

h=U/K

I is the intensity of irradiation Ip is the intensity of irradiation at the peak of the pulse K is the thermal conductivity of the solid k is the thermal diffusivity of the solid - K/pc

l is the thickness of the slab l o is the depth where there is a reversal in the direction of flow of the volatiles m is the mass flow of volatiles in the solid in the positive x direction per unit area M . N are constants Q is the heat of reaction per unit mass of reactant q is the rate of generation of heat per unit volume by exothermic chemical reactions R is the universal gas constant T is the absolute temperature T, is the absolute temperature of the volatiles in the solid Tc is the absolute temperature at a critical condition To is the absolute ambient temperature T, is the absolute temperature at which thermal destruction occurs

t is the time of irradiation tp is a characteristic time defining the time scale of the pulse radiation taken as the time at which the intensity is a maximum t~ is the time at which thermal destruction occurs u is the absorption of radiant heat per unit volume x is a linear coordinate normal to the surface is the attenuation coefficient f~ is the rate constant of the chemical reaction 7 = k (kt) '/2 the cooling modulus of a semi-infinite solid p is the density of the solid ..'~ is the total energy in the pulse Oc is a charring temperature Oi is a threshold temperature 0...... is the maximum temperature reached in the solid 0,~ is the mean temperature at ignition Or is the surface temperature at ignition to is the concentration of reactant mass per unit volume too, to1, toc are the initial, final and critical concentrations respectively of the reactant ,k is a shape function z = x / l denotes dimensionless distance r = f t ; dimensionless time 0 = T R / E; dimensionless temperature

Introduction RADIANT heat is the most important means of heat transfer in a well-established fire and potentially one of the great dangers from nuclear explosions. An understanding of its role in the 303

304

D.L.

initiation and development of fires involving cellulosic materials, the most commonly occurring combustible, is therefore essential. There are a number of different forms of thermal damage by radiation. The first is charring, that is, the conversion of wood or similar cellulosic material into charcoal. The second form is ignition, where the volatiles are produced from the heated surface at a rate sufficient to form a flammable mixture with the surrounding air. The rate of heating may be high enough for flame to appear in the volatile stream and flash down to the surface--this is called spontaneous ignition; the volatiles m a y also be ignited by an independent source of ignition such as a flame or electric spark placed in the volatile s t r e a m - this is called pilot ignition, unless the flame is in contact with the surface when it is called surface ignition. A material that ignites m a y or m a y not continue to burn; the condition where flaming persists on the surface of the material after the removal of the incident radiation is called continued burning. The third form is thermal destruction, where either charring or flaming persists till the irradiated material is destroyed or it disintegrates. The present paper examines a number of experimental and theoretical studies of these various types of thermal damage 1-15. It does this by setting out the differential equations for the thermal and chemical histories of the solid*. From these equations several dimensionless groups are obtained; the roles that the more important of them play in the derivation of the appropriate groups for correlating experimental results are discussed. It is shown that for each type of thermal damage, it may be necessary or possible, depending on the values of the dimensionless groups, to use different approximations; two of particular importance in the * F l a m e first appears in the stream of volatiles i s s u i n g f r o m the solid a n d f e a t u r e s o f their release are k n o w n t o affect the threshold conditions for ignition and continued burning m o r e than the ignition time~h P r e s u m a b l y the reason w h y a definition o f the onset o f ignition in t e r m s of t h e conditions in the s ol i d is sufficient for m o s t p r a c t i c a l purl~oses is b e c a u s e , once volatiles are produced, their rate o f production, over w h a t is a relatively small range o f temperatures in the s o l i d , is always sufficient t o s u p p o r t a flame, p r o v i d e d the heating c o n d i t i o n s are n o t near t o the threshold for ignition. T h e fact that certain c o n d i t i o n s m u s t obtain in the g a s e o u s p l u m e b e f o r e ignition occurs m a y be r e s p o n s i b l e f o r t h e o b s e r v e d differcmce in the times t o ignite a given material w h e n the areas irradiated differ: this effect m e a n s that experimental results s o m e t i m e s h a v e t o be c o r r e c t e d b e f o r e being applied to a lar g e a r e a Is.

Simms

Vol.

6

thermal balance equation are semi-infinite solids (thick materials) and slabs with linear temperature gradients (thin materials). The different criteria suggested for defining the onset and occurrence of thermal damage are then examined. Each type m a y be associated with a different criterion, and even if the same criterion may be used, with a different value for it. Various experimental results are then correlated on the basis of the analysis presented. Although the discussion is restricted to thermal damage to cellulosic solids, much of the analysis is applicable to other organic combustible solids, particularly those in which damage occurs in the solid, and to skin in so far as this can be treated as a material with constant thermal properties. Heat and Chemical Balances in the Solid The heat balance in the dry solid* is derived from : (a) The external heating, which is usually in the form of radiationS; this m a y be absorbed in an infinitesimally thin surface layer if the material be opaque, or over a range of thicknesses if the diathermancy of the material be important. The former is a special case of the latter (Appendix I). (b) The conduction transfer in the solid, which is taken to be normal to the heated surface; the thermal conductivity is here assumed to be independent of temperature and distance from the surface~. (el The thermal capacity of the solid; again this is assumed to remain unaltered during exposure~. (d) The convective transfer by the volatiles moving within the solid (Appendix II). (e) The chemical generation of heat b y decomposition of the solid (Appendix I I I ) . (f) The surface cooling; this is assumed to be * T h e p r e s e n c e o f w a t e r i n the s o l i d modifies the heat transfer within it in a c o m p l e x m a n n e r . S o m e moisture diffuses a w a y f r o m the h o t surface a n d m a y then c o n d e n s e within the s o l i d . s o m e is e v a p o r a t e d f r o m the h o t surface whilst its oresence m o d i fies t h e t h e r m a l p r o p e r t i e s o f t h e solid. A d i s c u s s i o n o f the effect o f the Presence o f water o n h e a t flow at the rates o f heating d i s c u s ~ d in this paper is g i v e n b y L . Y . CMEN 1~ as well as b y C . C . WILLIAMS 5 a n d R . GARDON6. t F o r simplicity, all the s u r f a c e s i n t h e f o l l o w i n g d i s c u s s i o n are a s s u m e d to b e non-reflecting. ;tVery little i n f o r m a t i o n appears t o b e a v a i l a b l e o n the variation of these p r o p e r t i e s o v e r the range o f temperature considered here.

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Damage to cellulosic solids by thermal radiation

Newtonian for mathematical simplicity, though problems with non-linear cooling can be solved in a number of ways including an electrical analogue method 18 and by a series expansion method 19. In properly designed experiments, the external heating takes place over an area on the surface which is linearly much greater than the depth to which the material is effectively heated and the heating is normal to the surface'-'". This, and the above considerations, lead to the differential equation for one-dimensional heat flow for a diathermanous, self-heating material. K ~-'T

-ax'-'

I 'c

3T ~t

- q - u + mc,,

?T,. ax ....

[1]

The boundary conditions are: ax

H ( T - T,,) at x = 0

KaT =-H(T-T.) ~x

reaction is almost certainly more complex than a first order reaction; with diathermancy each component of the spectrum should strictly be considered separately; the heat transfer effects of the volatiles emerging from behind the charred outer layer are neglected; the density, thermal conductivity and specific heat also change with temperature. Nevertheless, equation 8, the heat balance equation, and equation 6, the chemical balance equation, are too complicated for analysis in the general case. even if the simplest assumptions are made about the form of I. Dimensional analysis is therefore used to consider what further simplifications m a y be made. The equations can be put into dimensionless form by defining: z = ~ / l dimensionless distance r = f t dimensionless time ~-~= T R / E dimensionless temperature

. . . . [2]

at x = l

. [3] "" "

and the initial condition is

305

Then -a: ~ =

o; + ~, ~;c~--!-

a;- ....

T = T O when t = 0 The term for radiation absorption, obtained from equations 44 and 48 as u = ~Iph ( t / t , ) e -'x

The term for chemical heating Appendix I I I is q = Qao, / at with a o ~ / a t = -lo~ e -E/nT

u, ....

given in . . . . [5]

(:,/It,) \ e p 4 !

...

where

(-). = R T . / E

....

Or

o)

~¢o

"'"

and u/%=l at r = 0 from which it follows that

. . . . [7]

R T = F ' [R~,~ ~I, Ill k x It, e ' K-'fr-" z'

c~o~

K o:r-ax=.=, t,c aTat - ~I,,X (t/t~). e-'X+ Q ~ [ . . . [8] Dimensional Analysis Even the above formulation simplifies the problem considerably, notably: the chemical

[11]

a (o,/o,,,) _ 1o, e-,~o

. . . . [6]

Equation 6 is also the differential equation governing the chemical decomposition. Inserting equations 4 and 5 in equation 1 and neglecting mass convection within the solid (Appendix II) leads to

[91

+O~=I(O(') I l l ( ( . ) _ ( % ) _ at z = 0 or 1 .. [10]

[4]

and the initial condition is = to,, at t = 0

-x

is

pcE'

PO~o= F ,

fRr,

- [ E

It

]

pclE'

. . . . [13]

ft~

....

[14]

....

[151

Equation 14 gives the temperature distribution within the solid, and equation 15 the changes in chemical constitution. Equations equivalent to 14 and 15 m a y be formed by combining any pair of groups of terms to form another pair.

306

D . L . Simms

If in the convection within the solid, T = T,, and l 0 can be identified with l, as in a material with an impervious membrane at a depth l, or ½l as in symmetrical heating, equations 14 and 15 apply unmodified, that is, the same parameters appear in equations 14 and 15 whether T=T,, or ~Tv/~x=O, although the functional relations are different. Simplification of General Analysis Expressions such as equation 14 are of little practical use, but as it is usually possible to neglect one or more terms, useful simplifications m a y be made. For example, the effect of diathermancy is determined by those terms involving 2; if the effect of diathermancy can be neglected (Appendix I ) - - a s with opaque materials--such terms have to be omitted from the heat balance equation 14. However, any groups that can be formed out of the excluded terms which do not contain 2, the property concerned, must be retained, that is, in equation 14 the terms 2l, 2I~R/Epcf are excluded, but I ~ / E p c f l . their ratio, which does not contain a, is retained. It is often more useful, however, to combine this group with the group ft, as I, tpR/Epcl or E R / E p c l , sometimes referred to as an 'energy modulus'.

E=Fa

'K'

l ' f l ~' t,cE ' Epcl' lt~ ....

[161

This is the equation for an opaque material and the same result would, of course, be obtained by reverting to, and modifying, the original differential equation and boundary conditions.

Separation of chemical and heat balance equations If internal chemical heating can be neglected ( A p p e n d i x I I I ) , all terms containing Q, E, R and f must be deleted from the heat balance equation 14 and it is ( T - T o ) , the temperature rise, not the absolute value of T, which is the relevant parameter; the same result m a y be obtained directly by deleting q from equation 1. Equations 14 and 15 can then be treated separately, a valuable simplification, and the

Vol. 6

dependent variable becomes temperature, dependent only on the conventional conduction parameters for an inert, diathermanous material

The energy modulus now becomes

I~t,,/ pcl ( T - To) or E / pcl ( T - To) and equation becomes

17 rearranged in terms of it

pcl ( T _ To) = F:. -- ,

,

,

,

..

For an opaque, inert material, i.e. eliminating terms in 2, equation 18 can be reduced to

p c l i T - To) =F"

-;- ' - Ix ' kt l-'' - 7

".

Role o[ dimensionless groups Each group in equations 14 to 19 m a y be regarded as the ratio of two terms, each of which can usually have a physical meaning attached to it. Two of particular importance in equation 19 are discussed below. Degrees o] transience--The term k t / l ~, the Fourier number, m a y be written as

(K / l) ot pcl8 rate of conduction of heat away from surface rate of retention of heat This is a dimensionless time variable and hence is a measure of the 'age' of a problem. If kt/l=' is small, the conducted heat will not have penetrated far, and the material is effectively of infinite depth. If k t / l 2 is large, then the rate of retention of heat is relatively small and the material is approaching conditions where conductivity is no longer a relevant factor since it is effectively thin.

Thickness of the specimen--The term H I / K , the Biot number, is essentially the ratio of surface to internal resistance. Equation 19 m a y be simplified and, in certain cases, solved in terms of combinations of this parameter and the Fourier number k t / l 2. Two approximations are important, the semi-infinite ~olid (corresponding

December 1962

Damage to cellulosic solids by thermal radiation

to thick materials) and the slab with the linear temperature gradient (corresponding to thin ones). For the semi-infinite solid, the thickness of the specimen is by definition of no importance, and, by eliminating l from the Fourier and Biot numbers, namely (Hl/K)O'xkt/I 2, the appropriate parameter becomes H °-t/ Kpc. Equation 19 then becomes

pc~kt~),~ ( r - To)

t : F,

[ K ' t, Kpc ]

. [201

Further, if H'-'t/Kpc is small, surface heat losses m a y be neglected 2~. For the slab in which kt/l" is large enough for a quasi-stationary state to exist, the thermal conductivity must not appear in the parameter containing time. By eliminating K from the product of the Fourier and Biot numbers, the working parameter becomes Ht/pcl and the mean temperature rise can be expressed in terms of this parameter and the energy modulus. Equation 19 then becomes

pc;(r-r0)

=fs

' t. ' ~ c /

The mean temperature rise, 0,,,, is obtained b y deleting the term in x/l,

[tHt]

. . . . [22]

If the heat losses are large, then the energy required to produce a certain level of thermal damage increases with exposure time. This point has been made by several workers 8-12 who realized that the energy modulus 2/pcl (T-To) increased with time of exposure tp or t for this reason. Nevertheless, their analysis made no attempt to include its effect by using terms allowing for these losses in correlating experimental data. Their choice of kt/l 2 or ktp/l 2, as a parameter in determining the energy requirements for thermal damage, can only be meaningful if the Fourier number is not large.

Threshold Conditions for Thermal Damage It is now necessary to consider definitions of observable thermal damage; several criteria have been suggested as necessary or sufficient for thermal damage to occur.

307

(I) The simplest hypothesis ~ 1.,, 1~ is to assume that a given type of thermal damage occurs when the temperature of the solid (usually the surface temperature) reaches a certain fixed value. The mathematical expression of this may take either of two forms: R T / E or T equal to some given value If the chemical heating and convection in the solid are neglected, the parameter R T / E cannot be retained in equation 16 and equation 17 or 18 must be used. Further, only if experimental data for materials with different activation energies, E, are used can these two forms be distinguished. F. M. SAUERs argued that the ignition temperature and, in effect, the charring temperature, varies with the method of measurement and should not be used. Equally, however, the decomposition of cellulose involves more than one reaction and a comprehensive analysis would have to include terms such as E,f 1, E..,I2 . . . . etc. The use of a single E and f in equation 6 and as used by Sauer 8,~ m a y thus only be appropriate over a certain temperature range. A similar argument to this is used by S. B. MARTIN,W. LAI and C. P. BUTLERl°-1~" who accordingly replaced R T / E by T-T,,. Sauer's s criterion, in fact, is a fixed temperature one, since he correlated his experimental data by use of the dimensionless group R T / E ; this is disguised by his correlation which used materials having similar values* of E. Assuming a zero-order chemical reaction leads theoretically to infinite temperatures -°-", because mathematically there is no limit to the heat available: in a mathematical model with such a reaction, there m a y be little significance in the value chosen for the fixed temperature, because of the large increases in temperature that occur very rapidly when the reaction within the solid begins (Figure I). This m a y be one reason, i.e. the reaction is near zero-order, why the empirical concept of a fixed charring or a fixed ignition temperature is successful in m a n y problems. On the other hand, the flammable gases do not ignite on the surface and must take a finite time to travel to the point where ignition occurs1% If this time is comparable with the * N o exoeriments

been reported.

using materials with different values o f E have

308

D.L.

time of the thermal heating, a fixed temperature criterion will not apply. (2) A criterion of a critical rate of evolution of volatiles, N, for continued burning was assumed by C. H. BAMFORI), J. CRANK and D. H. MALAN~ in the form of I

f_ (aco / at) dx ~ N

. . . . [23]

o

This criterion is, in principle, easy to apply for a semi-infinite solid or for a symmetrically heated slab, otherwise lo is dependent on the heating conditions. This criterion could be used for other forms of thermal damage.

(b)

t 09 m t..

D

Y

(P I---

Time Figure I. Characteristic t e m p e r a t u r e rise w i t h time." (a) E x o t h e r m i c reaction begins," (b) T h e r m a l d a m a g e s us tained

(3) Sauer 8 assumed that charring begins at any depth when the volatile content there, ¢o, falls to a certain value ¢Oc. Williams '~ found that a damage function of the form given in equation 24 gave an adequate correlation for charring, but commented that it was extremely complicated to use. t

J-_e -~/~ dt = ~). . . . .

[24]

0

This was based on a suggestion by F. C. HENRIQUES 23 for correlating thermal damage to skin. L. Y. CHEN1. found that the hypothesis is too insensitive to be tested because of the heavy dependence of to on the value of E, which is very large and not known accurately. (4) Similarly, a weight loss criterion s has been used

S (COo- co) dx = m

. . . . [25]

Simms

Vol.

6

(S) For thin materials a possible criterion for continued burning would be that the mean temperature has to reach a certain value. The tentative justification for this is that, after heating ceases, the temperature distribution in the material becomes more uniform and if this uniform level approximates to the mean temperature at ignition, volatiles are produced at a rate given by equation 23 so that flaming can continue. Obviously, this mean temperature criterion cannot be applied to thick materials.

Application of Analysis

Charring and weight loss problems Williams ~ assumed that charring occurs at a fixed temperature and found an adequate correlation between his measured and predicted depth of charring, d, for short times; his analysis neglected heat losses from the surface and used kt/l'-' as one parameter and a modified energy modulus as the other, namely, It/pcd (To-T,). Sauer's analysis was based on that of Williams: he s correlated his charring data in terms of the groups* It/Topc(kt) 1/2, Id/kTo although in his experiments the times were long. Heat losses from the front surface cannot then be neglected, as Sauer s himself noted, for he pointed out that these caused the value of the group It/Topc (kt) ~/2 to increase with increased time of exposure. Where only heat losses from the rear surface can be neglected, the more appropriate parameters to use would be

It~pc (kt) 1/2 (To- To) or E/#c (kt)'/: (To- To) and H x / K as in equation 20. For the same reasons, the correlations produced for other experimental results where the intensity of radiation is not constant, are also inadequateg-iL

Spontaneous ignition Ignition time--constant

intensities---E.

K.

LAWRENCE4 attempted to find whether the fixed temperature criterion was sufficient or whether a criterion based on a critical rate of production of volatiles was also necessary. He assumed that the irradiated solid was opaque, and showed that there was no significant chemical *Present n o t a t i o n .

December 1962

Damage to cellulosic solids by thermal radiation

heating for the values of the chemical kinetic constants assumed by him (Appendix III). He then calculated from equation 23 that the rate of production of volatiles at ignition was always more than twice the critical level (2.5 x 10 -~ g cm-'-' s -t) suggested by Bamford, Crank and Malan ~, as necessary for continued burning~. Lawrence succeeded in correlating his results in terms of ignition occurring when the surface temperature reached 500 °C,; he assumed therefore that the rate of production of volatiles was never a critical factor. However, Bamford, Crank and Malan 1 also showed that the rate of production of volatiles increased progressively at first but then diminished very sharply because the volatile content of the solid rapidly became exhausted. At rates of heating near the threshold for ignition, therefore, the supply of volatiles m a y be exhausted before the surface temperature reaches 500°C and Lawrence's conclusion of a fixed ignition temperature is invalidated; the chemical balance equation 15 cannot always be neglected and a chemical criterion, such as one based on equation 23 is then necessary. This conclusion may be confirmed from Lawrence's value of the ignition temperature. The rate of heat loss from a semi-infinite solid at 500°C in equilibrium is approximately 0.6cal cm -~ s - ' ; this equilibrium condition corresponds to the critical intensity of radiation at which ignition is just possible -~. Lawrence worked well above this level of radiation. In other experiments ~'~, the lowest level at which spontaneous ignition was obtained was about 1 ealcm -: s - ' and the difference between the critical intensity predicted from the equilibrium heat losses and the minimum intensity found in practice has been shown to be due to the limited supply of volatiles*. In some experiments specimens of oak were subjected to preliminary heating within the range of temperatures 120 ° to 180°C for different periods and then exposed to various intensities of radiation. The minimum intensity t N o value is a v a i l a b l e for the rate o f e v o l u t i o n of volatiles necessary before ignition can occur, b u t it c~.n b e n o less than for c o n t i n u e d b u r n i n g w h e r e all the volatiles are a b s o r b e d by the flame as they are emitted bY the surface, :~K. AKITA o b t a i n e d a similar v a l u e 1. w h e n using h o t air heating. a n d radiation. * W h e n the w o o d surface is observed t o glow, it is an a l m o s t invariable sign that ignition will n o t take place. T h e surface is then a b o v e 6 0 0 ° C a n d the rate of p r o d u c t i o n of volatiles m u c h reduced.

309

at which ignition was just possible was progressively raised by an amount related to the loss in weight of the solid during the preliminary heating 24. At intensities of radiation well above the critical, it was found possible to correlate experimental results using a fixed temperature criterion ':', and neglecting convection in the solid, chemical heating and diathermancy. The thin materials ignited and continued to burn so that the mean temperature criterion was applicable, and the appropriate parameters for constant intensities of radiation are, from equation 22, x~/iwlO,,, and Ht/t~cl. Also, if the materials are diathermanous, the heat is absorbed in depth, reducing the thermal gradients. This does not change the mean temperature rise, but the difference between the mean and surface temperatures will be much less than a calculation negelecting diathermancy would show. With the thick materials, a surface temperature criterion was applicable, and the appropriate parameters for constant intensities of radiation are, from equation 20, X/pc(kt)l/20F and H2t/Kpct. Again, since the surface temperature of a semi-infinite solid is lower for diathermanous materials than for blackened ones, which are opaque s, diathermancy m a y be responsible for some of the scatter found 1~. A fixed temperature criterion for spontaneous ignition is thus adequate for correlating results where ignition occurs, but a criterion based on equation 15 is necessary to explain why ignition does not always occur at intensities above the critical value. Threshold conditions--When the intensity varies with time, as in a pulse of radiation, correlation of the threshold condition for ignition may be of more practical importance than the ignition time t~. When diathermancy, chemical heating and internal convection are neglected, that is, when the problem can be treated as the heating of an opaque, inert material, equation 19 m a y be used. Writing 0 for (T-T,,), the temperature rise tAn

analytical solution-c t o this condition

is readily obtained ~' as

p c . ( k t l t t_ OF - - (1 --exD 7 2 e r i c "D

310

D . L . Simms

pclO

, [ , l ~ , 1..,

...

.

The maximum values of both the surface and the mean temperature are of the form

pctO.....

=F10[ HI _

ktv] '

....

[27]

Vol. 6

(Appendix I) can be obtained 13 and is shown in Figure 2. Semi-infinite solid. The thickness l must be eliminated when discussing a semi-infinite solid. This, and writing OF for the front surface ignition temperature, reduces equation 28 to

~"J

1

The function F is, of course, different in the two cases. Similarly, the threshold condition is pclO~

. . . . .

The functional relationships for two special cases can be obtained and correlated with experimental results. Slab with linear temperature gradient. The thermal conductivity, K, must be eliminated when discussing the mean temperature of a slab thin enough for the gradient across it to be linear. This, and substituting 0,,,, the mean temperature for 0,, reduces equation 28 to pclO,,~

- F ~ o [Ht,~] -" [ vcl j

....

[29]

H t p / p c l is a dimensionless group representing the ratio of the energy lost to the energy absorbed at ignition. An analytical solution for the mean temperature rise for the pulse given in equation 45

In the absence of a solution in terms of elementary functions, a modified Schmidt method was used to produce one and this is shown in Figure 3. Correlation of threshold d a t a - - T h e experimental results consist of two sets of threshold values of E for various values of t,, for the slab and for the semi-infinite solid. The results for the slab with the linear temperature gradient are plotted in Figure 2, using the dimensionless variables of equation 29, and are compared with the analytical solution; the results for the semiinfinite solid are plotted in Figure 3 using the dimensionless variables of equation 30 and are compared with the computed solution. The value chosen for 0,,, was 525°C, as obtained previously '~. The theoretical curve is below the experimental line for the slab by a factor of less than 15 per cent for large values of H t , / p c l and by less than 30 per cent for J

~0

Experimentat

O0

0

I /"

~

o Ignition • No ignition 0.5

1"0

1.5

2'0

2Htp/tOCl

Figure 2.

Threshold energy in pulse ]or ignition of thin materials (slabs with linear temperature gradient)

December 1962

Damage to cellulosic solids by thermal radiation

5"0

~

°°

,

I ~

I

~

311

Q

~o o

2"5

"

~ m ~ | - -

~

Theoretical threshold

o Ignition ~ Ignition [] Ignition 0"2

, 0"4

* No • No • No

ignition' ignition ignition

Oak Cedar Fibre insu[atin(

0-6

0"8

Figure 3. Threshold ~,nergy in pulse for ignition of thick materials (semi-infinite solids)

small values, and the theoretical curve is less than 15 per cent below the experimental line for the semi-infinite solid. Because the area irradiated in the laboratory is small, the energy required for ignition is greater than for a large area~5; a correction for this would bring the results closer to the theoretical lines. Unfortunately, the data available, although showing the effect is greatest near the threshold condition, do not permit an estimate of its magnitude. The theoretical lines m a y therefore represent the conditions for large areas better than the data suggest.

Pilot ignition In pilot ignition the volatiles are ignited by a small flame near the surface. The ignition time 2'~ varies with the position of the flame for a given intensity of radiation. It is therefore not possible to correlate all results in terms of one correlation temperature, although adequate correlations are possible at any one position 2~ and an analysis of the type given in this paper needs to be supplemented by a study of conditions in the volatile stream.

Surlace ignition In this type of ignition, the pilot flame is placed in contact with the surface, which is irradiated until the flame begins to spread; Bamford, Crank and Malan 1 then say the surface is

'critically hot'. In presenting their results, they commented that, at high intensities, the energy required for surface ignition appeared to tend to a constant value. Their specimens were semiinfinite, and an approximation is given elsewhere for high intensities 2 which suggests that if the results are plotted in terms of two param e t e r s - e n e r g y , ~, and the product of the square root of the ignition time and the intensity of radiation, It ~/~-they should lie on a straight line if surface ignition occurs at a fixed temperature. Their results for short times are replotted in Figure 4 using these parameters; the graph is sufficiently near to linear to suggest that surface ignition occurs at a fixed temperature.

Continued burning Saueff and Butler, Martin and Lai ]°-t2 studiec~ the continued burning of alpha-cellulose papers --manufactured with a 2 per cent carbon content so that they were opaque. Specimens were. irradiated until they ignited and continued to burn after the radiation was removed; this they defined as sustained ignition*. Their results are * T h e f l a m e , w h i c h a p p e a r s o n the f r o n t s u r f a c e b e f o r e c o n t i n u e d b u r n i n g m a y b e sa;d t o h a v e b e e n established, contributes s o m e heat o f its o w n a n d p r e v e n t s h e a t loss f r o m t h e f r o n t s u r f a c e . Its i n c l u s i o n in the a n a l y s i s w o u l d mean that the b o u n d a r y c o n d i t i o n s h a v e t o b e c h a n g e d w h e n the flame appears w h i c h w o u l d lmake the analYsis even m o r e c o m p l i c a t e d . B a m f o r d , C r a n k a n d M a l a n ' a s s u m e ~ t h a t since the first p e r i o d , t h a t is t h e p r e - i g n i t i o n p e r i o d . is s h o r t , t h e c h a n g e i n b o u n d a r y c o n d i t i o n s c a n b e neglected. T h e y w e r e a l l a l y s i n g r e s u l t s for surface i g n i t i o n , whe~'e ignitiotr t i m e s a r e u s u a l l y s h o r t and this assumption is justifiable. Also. in the present experiments, its c o n t r i b u t i o n 2 , 2. ( a b o u t 0"7 eal c m -~ s -~) is generally small c o m l m r e d w i t h the intensity o f radiation used (1 t o 20 cal crn -~ s 1).

312

D . L . Simms

enabling the corresponding value for the Newtonian cooling constant, H, to be estimated. The values for the ignition temperature are then adjusted to give the best fit between the experimental results and the theoretical line. Sauer's results are shown in Figure 5. The mean temperature found in this way is 650°C. This is rather higher than the temperature of about 525°C found for spontaneous ignition 4,14,~ but Sauer ~ stated that the critical

-~s5 x

50

.oc_45

/

~ as ~

Vol. 6

ar

B'0

"T

r

g

/

•~ 20

is

/x / / /

/

0'8 0"07 0'10

/

It ~ catcrn-2s -'~ Figure 4. Sur[ace ignition (data ot Bare,oral, Crank and Malan x) plotted in terms of a range of values of k t / l 2, but where k t / 1 2 > l , i:e. thin materials, an equation based on equation 22 must be used. For constant intensities of radiation, terms in t~ have to be deleted and equation 22 becomes = F I , [ Ht]

. . . . [31]

An analytical solution to this equation is readily obtained as

2nt[,_ pclO,,,

pcl [

( '22" 1 .... Ea21 exp

- pcl ] J

which is shown plotted in Figure 5. Correlation of data on continued burning t i m e s - - W h e n H t / p c l tends to zero, equation 32 becomes

x polos,

>

1

....

[aa]

Hence, from values of the measured energy modulus when 2 H t / p c l is small, estimates of the effective ignition temperature may be made,

0"25 0"5 1"0 2"5 2Ht/pcl Figure 5. Correlation of continued burning times fo~ thin materials (slab with linear temperature gradient --data ot Sauer~). Range o] intensities 3 to 15 cal cm -~- s -]. Range o] thicknesses 0.006 to 0.008 cm. Range of ignition times 0.3 to 4.0 s. Correlating temperature 650°C exposure time was chosen such that ignition occurred about 80 per cent of the time. In the other experiments, the ignition time is taken at the 50 per cent level. Thermal destruction The form of equation 33 suggests that the amount of energy required to cause a given level of thermal damage would be reduced as the intensity of radiation increases but in certain experiments increases have been found. G. MIXTER and L. J. KROLAK29 irradiated a material, stated to be 9 oz sateen, until it had 'no opacity'. H. C. HOTTEL"~° mentioned that the material is naturally diathermanous. For an opaque material, decreasing the exposure time reduces the effective thickness of the material, since k t / l 2 is smaller, and this decreases the energy required to produce a given front face temperature. However, in view of the 'no opacity' criterion adopted by Mixter and Krolak 29 it is more appropriate to

December 1962

Damage to cellulosic solids by thermal radiation

examine conditions at the rear face, namely, as a first approximation to regard thermal destruction as occurring when the rear face reaches a fixed temperature; this suggests that for an opaque solid the required energy should increase as the exposure time decreases. However, even if the material is effectively diathermanous over the whole range of exposure used, the energy required m a y still be shown to increase as the exposure time decreases. A criterion similar to that given by Sauer s for charring, namely, the volatile content falls to a fixed value, ~Oc, m a y be assumed for thermal destruction. Integrating equations 6 and 7 gives

(~')"I- fRTc2

log ~ !

EI/pcl x

e-~1"%

..

.[84]

This assumes that for short exposure times 2 H t / p c l ~ 1 which means that equation 38 may be written as It 0 = T - To = pcl

Substituting equation 41 into equation 39 and deleting the constant terms gives I (32 e+~(%-T) t ~rl;

Eliminating T ~ - T~ by using equation 40, then E log I C£. R T y × pc[ + constant

E

Rro >R~->> 1

....

[36]

such that e-~/"L >> e-Emr0

Although T~ increases linearly with time of irradiation (equation 35), large variations in I can be associated with small variations in T~ since the exponential term in T~ is much more powerful than T~2. Equation 38 can be reduced to .

.

[39]

.

If T~, the fixed temperature at which thermal destruction occurs when there is no delay due to a chemical reaction, is not very different from T~, then T~=T~+ ~I ( t - t s )

...

.

[40]

and ~

e-~/"%

x e +F"

×1/

,

.0 u

(%-rp/uT~

5

eStruct,on temper

[38]

1 02 T~2e-Era*. . . . .

e-~/n%

'Destruct,Ion' temperature influenced by r e a c t t ~ ~

. . . . [37]

Then for the critical value, T~, equation 34 can be reduced to

.

. . . . [43]

The means of the results given by Mixter and Krolak for the total destruction of fabrics are plotted in Figure 6 in terms of equation 43; although the scatter is large the results do lie about a straight line. At the lower intensities of radiation, it m a y be assumed that only the attainment of a given mean temperature is necessary for thermal destruction and from these results a value of Ts m a y be obtained. The value calculated for E is about 20 000 cal/mol which is in reasonable agreement with those given elsewhere*. ~,n 5 o

I OC e -F/RT .

. . . . [42]

. . . . [35]

pcl

and that E

31:~

. ..

[41]

316

17 18 Incident energy, Z

19

20 cat/cm z

Figure 6. Variation of critical energy for thermat destruction with intensity of radiation

The increase in incident energy to produce a given degree of thermal damage with increasing intensity of radiation, although small, is consistent with the assumption of a chemical reaction with an effective activation energy of an acceptable magnitudeS'. * H a d E a v a l u e o f less than, say, 10000 c a l / m o l , it would have suggested a physical rather than a chemical explanation for Mixter and Krolak's results~L t S . B. MARTIN a n d R . W . RAMSTADsl, K . AKITA 1' a n d TADA~ MORIYAs~ fOUnd that the spontaneous ignition U~mperature increases with increasing intensity; a similar explanation to t h e one given here would explain their results.

314

D . L . Simms

Conclusions If chemical heating is negligible compared with the external heating, and if the onset of thermal damage is rapid, then, provided conditions in the volatile stream can be ignored, equations defining chemical criteria for thermal damage may be neglected and materials may be assumed to have 'thermal damage temperatures'. Experimental results for the onset of charring, for spontaneous ignition (both for ignition times and threshold conditions), for pilot and surface ignition and for continued burning have been correlated in this way. This method is not applicable at very high rates of heating when the rate of chemical reaction in the solid presents a limiting condition and at low rates of heating when the supply of volafiles may be exhausted.

VoL 6

sensitive to the maximum intensity--in most building fires the intensity of radiation changes slowly--and consequently the maximum intensity represents the maximum hazard, and partly because the pulse of constant intensity is easiest to achieve and results using it are the easiest to analyse. For a constant intensity, A is taken as unity for the duration of the pulse, when t < t~. The second is the pulse similar in form to that of a nuclear explosion:'~; a function amenable to analytical treatment which fits the curve of a nuclear explosion ]'~ approximately is given by

IX (t/ t,)=d'I. (t/ t,) ~-e-"'/'p . . . . [45] :~

1"0,

0

0.8

,'--

o-6

The work described in this paper forms part of the programme of the Joint Fire Research Organization of the Department of Scientific a:nd Industrial Research and Fire Offices" Committee; the paper is published by permission of the Director of Fire Research. The experimental results on which this paper is based were obtained over a number of years and too many of the authors" colleagues assisted with the work ]or all to be named. It is more than duty, however, to acknowledge the help and assistance of Miss Margaret Law and Messrs R. W. Pickard and P. L. Hinkley. The author would also like to thank Dr P. H. Thomas for his continued help and criticism both of the work itself and with the writing of this paper. Dr K. Akita of the Fire Research Institute v] Japan very kindly sent an English translation of Chapter 6 of his work ~ which deals with ignition of materials by high intensity radiation. APPENDIX I ABSORPTION OF RADIATION Radiation Pulse A pulse varying in time may be described functionally as I = I ~ (t/tp) . . . . [44] The first intensity/time curve of importance is the impulse which is constant in time; this is partly because the thermal damage time is very

,_N .% 0"4 0.2 0 Z

o

2"0

.~'0

Dimensiontess

6"0

time,

(t/tp)

8"0

Figure 7. Pulse shape--nuclear explosion. Curve I, nuclear explosion'S'%" 2, equation 45; 3, equation 47 The total energy delivered by such a pulse is ~

-

te'I,t,

....

[461

Equation 45 is a better fit than an equation of the form 34 I~t ( t / t . ) = e l . (t/t.) e-'/'. . . . . [47] with which it is compared in Figure 7. Absorptivity Materials, which are not totally absorbing, reflect some of the incident radiation in amounts which vary with the wavelength of the incident radiation and the nature of the surface and its colour. The amount changes during the exposure; the surface darkens slowly at first and then more rapidly. Corrections allowing for this change may be made for some conditions 15. A certain amount of the incident radiation is scattered by the smoke emitted from the surface' but this effect has been neglected.

December 1962

Damage to cellulosic solids by thermal radiation Diathermancy

There is general agreement that wood is diathermanous but its importance in determining the temperature rise is uncertain. It is conventionaP -7 to assume that the energy absorbed, u, is given b y the Lambert-Beer attenuation law u =

~I e -~x

. . . . [48]

where I is the net incident flux falling on the face x = 0. This assumes that the sole attenuating factor is absorption. With highly reflecting diathermanous materials, where there is scattering in depth, u cannot be expressed as simpl V as in equation 48. Williams:' found that the temperature rise in the irradiated solid was predictable in terms of an opaque solid. He concluded that the effect of diathermancy was small for an irradiation period of up to five seconds over a range of intensities of radiation (0.26 to 3.5 calcm -2 s -1) from a graphite furnace operating at 2000°K. The peak wavelengths from such a furnace are between 1.1 and 1.7/t. Williams suggested that wood had a high reflectivity at just these wavelengths. Some measurements 35 at the National Physical Laboratory confirmed this. Gardon 6 argued that the reflectivity is high because the diathermancy is high, the bulk of the reflected radiation being radiation scattered back from the interior of the wood. He claimed that Williams's experimental technique did not justify his conclusions. Williams did not measure surface temperatures, he extrapolated from internal measurements by thermocouples; this could be done only some time after irradiation had started. Gardon himself claimed that only in the early stages is the profile influenced by diathermancy and that what happens during this period could not be inferred from Williams's measurements. His own experiments showed that wood is partially diathermanous to solar radiation and that the effect of diathermancy decreases with time. If charring does not begin, the effect lasts for about two seconds. Gardon also found that the agreement between his temperature measurements and the predicted values was not complete. Owing to the numerous uncertainties in his measurements and the variability and inhomogeneity of wood, the reasons

315

for the discrepancies could not be elucidated. A. F. ROSERTSON3s measured the effect of diathermancy on the temperature distribution in irradiated wood, taking into account cooling losses from the surface; his experimental results agreed with his theoretical calculations and showed clearly that the natural surface of wood is practically transparent but that blackened surfaces are opaque. APPENDIX II CONVECTION W I T H I N T H E SOLID* The last term in equation 1 is the convective heat transfer; if the breakdown of the primary solid reactant is wholly into gaseous material, the flow of volatiles m at a depth x is given by ~0

m = -

| (a,~ / ~t).

dx

....

[49]

¢

The value of lo depends on m a n y factors, such as the frictional resistance of the material and the effect of pressure, if any, on the reaction rate. Similarly, the difference between T and Tv depends on the heat transfer within the pores of the material. The maximum value of m is that occurring at the surface and is the rate of loss of weight per unit area. Clearly, whilst this convective term m a y be of considerable importance in discussing the combustion of wood, it is effectively zero prior to charring: provided ignition is not long delayed after the decomposition becomes rapid, it may be neglected. APPENDIX III T H E IMPORTANCE OF CHEMICAL HEATING Few experiments to discover the type of chemical degradation that occurs at high rates of heating have been reported. S. B. MARTIN and A. BROIDO38 showed that the products of thermal decomposition are determined by the rate of heating; the higher the rate of heating the greater the destruction caused to the material and the greater the quantity of tars produced. A few measurements have been made of the temperature rise of the irradiated surface; inspection of such records as are available shows little if any sign of the point of inflection in *The treatment given here is t h a t of P. H. "tHOMAS a:,

316

D.L.

the heating curve '~'6,16 that would reveal significant chemical heating before ignition. Williams ~ found that his measurements of temperature profiles of oven-dried samples of wood exposed to intensities of radiation of about 3.5 cal cm -~ s - ' from a graphite resistance furnace could be correlated by heat transfer theory neglecting chemical heating; the irradiation times in his experiments were usually less than five seconds. His temperature profiles showed no sign of inflection due to chemical heating; he never measured surface temperature values, these were obtained by extrapolating from internal measurements. Gardon 6 concluded that even after the initiation of damage, i.e. ignition, thermal effects due to chemical reactions are minor compared with those due to the external heating. He found that the internal temperature profiles as measured by fine wire thermocouples were comparatively unaffected by chemical reactions; the front surface temperature did, of course, increase once ignition had occurred. However, in Gardon's experiments, like those of Williams, the specimens were exposed for a few seconds only. Gardon did find an inflection in the surface temperature/time curves of blackened specimens at between 400 ° and 500°C which he suggested might be due to thermal convection eddies; Martin and Ramstad '~1 commented that these are more likely to be due to changes in the chemical reactions occurring*. They suggested that below about 400 ° to 500°C the reactions are endothermic but above this exothermic. The experiments suggest that the reactions occurring at these rates of heating are different from those found at lower rates of heating and imply that the values of the chemical kinetic constants will also be different. This would mean that within the range of experimental conditions in this paper (say 1 to 15 cal cm -2 s-') the net effect of chemical heating would be relatively small. Sauer's results 9 for continued burning and results for charring have been correlated successfully without introducing a term allowing for *A possible s a d simpler explaoation is that the blackening agent used by Gardon (Indian ink) came away from the surface very ~li~htlv~it certainly sealed the surface well enough to prevent ignition is some of the author's experiments.

Simms

Vol.

chemical heating ( F i g u r e 5). The results '5 for the spontaneous ignition of semi-infinite solids are too scattered to detect any sign of an effect due to chemical heating, whilst Akita '4 found a fixed temperature criterion adequate for alI but very high-intensity radiation. With the slabs 1'~ there was some sign that, at the lower intensities of radiation, ignition occurred sooner than predicted from the intensity of the incident radiation, assuming an ignition temperature of 525°C. At long times too, the error of assuming Newtonian cooling would be expected to increase the ignition time, i.e. to act in the opposite direction to chemical heating, and this suggests that chemical heating is playing some part. Lawrence', using values of 3S 000 cal/mol for the activation energy E , calculated that chemicaI heating would be negligible in a semi-infinite solid before 500°C. He found, however, that if E were 25000cal/mol, then chemical heating might be significant. Any attempt to calculate the value of the chemical heating relative to the external heating depends upon the accuracy with which the chemical kinetic constants and the reactions themselves are known. Until these are known with more accuracy, calculated estimates of chemical heating will be too uncertain to be useful. However, for the purpose of dimensional analysis, the rate of chemical heating m a y be assumed to be q = Q&0 / ~t . . . . [501 The rate of reaction' is assumed to be first order, i.e. - Oto/Ot=Bto . . . . [51] with the condition to=to 0 at t = 0 In an effectively zero-order reaction, i.e. with negligible loss of primary reactant, q = Qfltoo

The rate constant/3 is customarily assumed tc~ be of the Arrhenius form, i.e. /3=fe-~/RT . . . . [S2]

References ' B A M F O R D , C. H . , CRANK, 'The combustion of wood'.

J.

and

MALAN,

D.

H.

Proc. Camb. phil. Soc.

December 1962

Damage to cellulosic solids by thermal radiation

1946, 42, (Part 2), 166-82 2 LAWSON, D. I. and SIMMS, D. L. 'The ignition of

wood by radiation'. Brit. ]. appl. Phys. 1952, 3 (9), 288-92; (12) 394-6 :~ HOPKINS, H. C. 'The study of temperature in inflammable solids exposed to high intensity thermal radiation'. S. M. Thesis, Department of Chemical Engineering, Massachusetts Institute of Technology. Cambridge, Mass., 1952 i LAWRENCE, E. K. 'Analytical study of flame initiation'. S. M. Thesis, Department Of Chemical Engineering, Massachusetts Institute of Technology. Cambridge, Mass., 1952 -~ WILLIAMS, C. C. 'Damage initiation in organic materials exposed to high-intensity thermal radiation'. Massachusetts Institute of Technology. Fuels Research Laboratory. Tech. Rep. No. 2. Cambridge, Mass., 1953 6 GARDON, R. 'Temperature attained in wood exposed to high-intensity thermal radiation'. Massachusetts Institute of Technology. Fuels Research Laboratory. Tech. Rep. No. 3. Cambridge, Mass., 1953. 7 HOTTEL, H. C. and WILLIAMS, C. C. 'Transient heat flow in organic materials exposed to highintensity thermal radiation'. Industr. Engng Chem. (lndustr.), 1955, 47 (6), 1136-43 SAUER, F. M. 'The charring of wood during exposure to thermal radiation--correlation analysis for semi-infinite solids'. U.S. Department of Agriculture. Forest Service. Division of Fire Research. Berkeley, Calif., August 1956 ~' SAUER, F. M. 'Ignition of black alpha-cellulose papers by thermal radiation'. U.S. Department of Agriculture. Forest Service. Division of Fire Research. Berkeley, Calif., September 1956 i, MARTIN, S. B. and LAI, W. 'Ignition by thermal radiation'. Proceedings of the First Fire Research Correlation Conference, p 84. National Academy of Sciences--Nat. Res. Counc. Publ. No. 475. Washington, 1957 II BUTLER, ('. P., MARTIN, S. B. and LAI, \V. 'Thermal radiation damage to cellulosic materials. Part II. Ignition (if alpha cellulose by square wave exposure'. U.S. Naval Radiological Defense Laboratorv Research and Development Tech. Rep. U S N R D L - T R - 1 3 5 . San Francisco, 1956 ~'-' MARTIN, S. B. and LAI, W. 'Thermal radiation damage to cellulosic materials. P a r t III. Ignition of alpha-cellulose by pulses simulating nuclear weapons air bursts;. U.S. Naval Radiological Defense Laboratory Research and Development Tech. Rep. U S N R D L - T R - 2 5 2 . San Francisco, 1958 13 THOMAS, P. H., SIMMS, D. L. and LAW, MARGARET. 'On the correlation of the threshold for ignition by radiation with the physical properties of materials'. Department of Scientific and Industrial Research and Fire Offices' Committee. Joint Fire Research Organization F. R. Note No. 381 / 1958 ~t AKIT*, K. 'Studies on the mechanism of ignition of wood'. (English summary.) Rep. Fire Res. Inst. Japan, 1959, 9 (1-2), 99-106. [Detailed review by \V. G. COURTNEY. Fire Res. Abstr. Rev. 1962, 4 (l and 2), 109-15] x.~ SIMMS, D. L. 'Ignition of cellulosic materials by

317

radiation'. Combustion C~ Flame, 1960, 4 (4), 293300 i6 SIMMS, D. L. 'Experiments on the ignition process of cellulosic materials'. Combustion 6~ Flame, 1961, 5 (4), 369-75 17 CHEN, L. Y. 'Transient heat and moisture transfer through thermMly-irradiated cloth'. Massachusetts Institute of Technology. Fuels Research Laboratory. Tech. Rep. No. 7. Cambridge, Mass., 1959 ls LAWSON, D. I. and McGuIRE, J. H. 'The representation of distribution resistance and shunt capacitance circuits by lumped networks'. Department of Scientific and Industrial Research and Fire Offices' Committee. Joint Fire Research Organization F . R . Note No. 196/1955 19 JAEGER, J. c. 'Conduction of heat in a solid with a power law of heat transfer at its surface'. Proc. Camb. phil. Soc. 1950, 46 (4), 634-41 20 THOMAS, P. H. 'Some conduction problems in the heating of small areas on large solids'. Quart. J. Mech. 1957, 10 (Part 4), 482-93 2~ LAWSON, D. I., Fox, L. L. and WEBSTER, C. T. 'The heating of panels by flue pipes'. Department of Scientific and Industrial Research and Fire Offices' Committee. Fire Research Special Report No. 1. H.M. Stationery Office: London, 1952 22 HicKS, B. L. 'Theory of ignition considered as a thermal reaction'. J. chem. Phys. 1954, 22 (3), 414-29 2:~ HENRIQUES, F. C. 'Studies of thermal injury, V - the predictability and the significance of thermallyinduced rate processes leading to irreversible epidermal injury'. Arch. Path. (Lab. Med.), 1947, 43, 489-502 2t SIMMS, D. L. and ROBERTS, VALERIE E. 'Effect of prolonged heating on the subsequent spontaneous ignition of oak'. J. Inst. Wood Sci. 1960 (5), 29-37 .25 SIMMS, D. L. and HIRD, D. 'On the pilot ignition of materials by radiation'. Department of Scientific and Industrial Research and Fire Offices' Committee. Joint Fire Research Organization F . R . Note No. 365/1958 2~ SIMMS, D. L. 'The pilot ignition of materials by radiation'. Department of Scientific and Industrial Research and Fire Offices' Committee. Joint Fire Research Organization F. R. Note No. 496 / 1962 ~7 SIMMS, D. L. and HINKLEY, P. L. 'Protective clothing against flames and heat'. Department of Scientific and Industrial Research and Fire Offices' Committee. Joint Fire Research Organization. Fire Research Special Report No..3. H. M. Stationery Office : London, 1960 29 WEBSTER, C. T., \VRAIGHT, H. a n d THOMAS, P. H.

'Heat transfer from burning fabrics'. J. Text. Inst. 1962, 53 (1), T29-37 '-'9 MIXTER, G. and KROLAK, L. J. 'Critical energy of fabric as indicated by its persistence time under thermal radiation'. U.S. Atomic Energy. Commission. University of Rochester Report 3o HOTTEL, H. C. 'Introductory remarks with special reference to transport mechanism', pp 648-60. 'Radiation and high temperature behaviour of textiles'. Ann. N . Y . Acad. Sci. 1959, 82, 7 :u MARTIN, S. B. and RAMSTAD, R. W. 'Temperature profiles in thermally-irradiated cellulose accom-

318

D.L.

panying its spontaneous ignition'. U.S. Naval Radiological Defense Laboratory. Research and Development Tech. Rep. USNRDL-TR-353. San Francisco, May 1959 32 MORIYA, TADAO. 'On the apparatus for producing thermal radiation of high intensity'. (English summary.) Bull. Fire Prey. Soc. Japan, 1958, 7 (2), 33-7 .~3 Effects of Nuclear Weapons. U.S. Atomic Energy Commission : Washington, 1957 :' t COOK, G. B. 'The initiation of explosions in solid secondary explosives'. Proc. Roy. Soc. A, 1958, 246, 154-60

Simms

Vol. 6

.~'~ National Physical Laboratory (Private communication) 3n ROBERTSON, A. W. National Bureau of Standards (Private communication) :~z THOMAS, P. H. 'On the rate of burning of wood'. Department of Scientific and Industrial Research and Fire Offices' Committee. J o i n t Fire Research Organization F.R. Note No. 446/1960 as MARTIN, S. B. and BROIDO, A. 'The effect of potassium bicarbonate on the ignition of cellulose b y thermal radiation'. U.S. Naval Radiological Defense Laboratory. Research and Development Tech. Rep. USNRDL-TR-536. San Francisco, October 1961