TEMPERATURES OBTAINED IN TIMBERS 

WHEN THE SURFACE TEMPERATURE IS 

CHANGED AFTER VARIOUS PERIODS 

OF HEATING 

April 1946 

No. R1609 

UNITED STATES DEPARTMENT OF AGRICULTURE 

FOREST SERVICE 

FOREST PRODUCTS LABORATORY 

Madison, Wisconsin 

In Cooperation with the University of Wisconsin 
- - - - 

TEMPERATURES OBTAINED IN TIMBERS WHEN THE SURFACE 

TEMPERATURE IS CHANGED AFTER VARIOUS PERIODS OF HEATING* 

By J. D. MacLEAN, Engineer

1 Forest Products Laboratory, Forest Service 

United States Department of Agriculture 

Introduction 

Extension studies have been made at the Forest Products Laboratory to 

determine the rate of temperature change in both round and sawed timbers when 

they are heated in different mediums and also the more important variables 

that affect the rate of heat transfer. Results of these investigations have 

been discussed in various publications (1 to 11).2 

In previous papers (1-6, 8-11) discussing the rate of temperature 

change in wood, time-temperature curves have been presented that show tho 

approximate temperature obtained at different points within a timber when a 

given surface temperature is applied for any definite heating period. It is 

often desirable, however, to know what temperatures will be obtained at any 

given time when the surface has been subjected to a higher or lower temperature during the period under consideration. 

The purpose of this paper is to show how the approximate wood temperature may be determined at any time after the surface temperature is changed 

and to discuss the various fields in which this information may be used. 

Factors Affecting the Rate of Temperature Change 

The following factors were found to have an important effect on tho 

rate of temperature change: (1) heating medium, (2) moisture content; 

(3) direction of grain in which heat movement takes place, and (4) density 

or specific gravity. 

*To be presented at the Forty-second Annual Meeting of the American WoodPreservers' Association to be held at the Netherland Plaza Hotel, 

Cincinnati, Ohio, April 23, 24, 25, 1946. 

1 Maintained at Madison 5, Wis., in cooperation with the University of 

Wisconsin. 

2 Numerals underlined in parentheses refer to publications named in the list 

of references at the end of this paper. 

Report No. R1609 -1-
Experiments showed that under the same temperature, steam heated 

faster than liquids; liquids heated faster than hot platen, and hot plates, 

heated faster than dry air. Water heated faster than oils, and the rate of 

heating in air was increased as the humidity was increased. These differences were apparently caused by variations in surface contact, specific heat 

of the heating medium, and similar factors. 

Wood seasoned below the fiber saturation point (about 30 percent moisture) heated slower than green material. At and above the fiber saturation 

point, however, variations in moisture content do not appear to cause any 

further important changes in the rate of heating. It may, therefore, be 

assumed that green timbers will heat at about the same rate (for any particular species) when the moisture content is at or above the fiber saturation 

point. For practical purposes in making temperature calculations, timbers 

with an average moisture content below 20 percent may be considered as masoned, while those with a moisture content above 20 percent may be considered 

as green. In general, green material will heat about 10 to 25 percent 

faster than seasoned wood under the same conditions of heating. 

There is apparently no significant difference in the rate of heating 

in the radial and tangential directions, but the rate of heating is about 

2-1/4 to 2-3/4 times as fact in the longitudinal direction, or along the 

fibers, as in the transverse direction. Longitudinal heating does not need 

to be taken into consideration, however, unless the timbers are exceptionally 

short and the cross-sectional area is large in proportion to the length. 

For example, the effect of end heating on the temperature at the mid-portion 

of a timber 4 by 4 inches in cross-section and 4 feet long would not need to 

be considered; but if a timber of the same length and having cross-sectional 

dimensions of 12 by 12 inches were heated, the effect of end heating would 

be important, except for short heating periods. 

The density, or specific gravity, of the wood affects both the conductivity (rate at which heate units pass through the wood) and the diffusivity, which is a measure of the rate of temperature change. The diffusivity, 

which may be considered a constant over normal ranges of temperature, varies 

inversely as the product of the density and specific heat, and durectkt as 

the conductivity. Heat conductivity is, in general, analogous to electrical 

conductivity, while temperature difference is analogous to voltage. Through 

a misunderstanding of the differences between heat conductivity and the rate 

of temperature change, it has been assumed by some that the heavier woods 

that conduct heat more rapidily will also heat faster or cool faster than the 

lighter woods that are known to have better insulating properties. This is 

contrary to what actually takes place, for although the lighter or low 

density woods are not such good heat conductors as the heavier woods, the 

rate of temperature rise when the wood is heated, or the rate of temperature 

drop in cooling, is more rapid in timbers of the lower density species. 

Report No. R1609 -2-
Temperature Changes That Occur When Wood Is 

Cooled After Heating or When the Heating Medium Temperature Is 

Increased During the Heating Period 

When the temperature of the central portion of a timber is lower than 

the surface temperature applied during ths heating period, a variable amount 

of temperature rise occurs at the interior (a) when the material is removed 

from the heating medium and exposed in the air at atmospheric temperature, 

(b) when it is in contact with the same medium as that used in heating but 

at a lower temperature, or (c) when it is placed in some other medium at a 

lower temperature. For example, in the application of the hot and cold bath 

treatment the partially-heated timbers are either cooled in a bath of the 

same preservative maintained at a lower temperature, or allowed to remain in 

the preservative while both the wood and preservative cool. When they are 

allowed to remain in the preservative the rate of cooling is slower and the 

average cooling temperature, over a given period, is higher than when the 

hot preservative is replaced with preservative at a lower temperature. 

Under these conditions the temperature rise at the interior of the timber 

would be higher than when the wood is cooled at a lower surface temperature 

for the same period. 

On the other hand, when timbers are heated in steam, liquids, or in 

air as in the dry kiln, a variable amount of time is usually required to 

raise the heating medium temperature to the maximum, Again in some heating 

operations it may be desirable to maintain a lower heating temperature for 

a time and then increase the temperature for a final period of heating. 

This will necessarily have a variable effect on the final wood temperature 

depending on the time the different temperatures are applied. 

Field of Application 

In the preservative treatment of wood it is important to know 

whether the temperatures and heating periods employed have been sufficient 

to sterilize the interior of the timbers if there is danger that infection 

is present. 

Laboratory experiments have shown that the temperature required to 

kill wood destroying fungi will depend both on the temperature and on the 

time the temperature is applied (12). As a result of these experiments it 

was concluded that it is not practical to attempt to sterilize wood by 

heating it to temperatures lower than 150° F., since the moot resistant 

fungus tested was not killed even after being heated at 140° F. for 12 hours. 

All specimens were sterilized, however, when the wood was maintained at a 

temperature of 150° F. for about 1-1/4 hours, and progressively shorter 

periods were required as the temperature was increased. 

Report No. R1609 -3-
When laminated timbers are glued they are commonly heated in kilns 

to a temperature that is sufficient to set the glue on all surfaces to which 

the glue is applied. Under these circumstances it is necessary to consider 

both the temperature and the time that the temperature is maintained. For 

such conditions it is of interest to know what temperature should be obtained 

at tho center before heating is discontinued, or to determine the rate of 

cooling (if the wood is heated somewhat above the specified minimum temperature) so that the length of the required heating period can be determined. 

Tho laminated timbers are sometimes heated throughout to the temperature of 

the heating medium and when this is done it may be desirable to compute the 

approximate rate of cooling so that sufficient time can be allowed for setting 

of the glue. 

Again, in the steaming and vacuum process the time the vacuum is 

applied should be limited by the temperature of the wood in the region where 

moisture is to be removed. When the temperature is too low to evaporate 

moisture effectively at the corresponding vacuum temperature, the vacuum 

should be discontinued to avoid unnecessary cooling of the wood, since the 

higher wood temperatures are more favorable for treatment. The approximate 

temperature changes that take place at any given distance from the surface 

may be readily computed for varoius vacuum periods, by the methods to be 

discussed. 

Factors Affecting Temperature Change During Cooling Period 

The amount of temperature rim that occurs at tho interior when 

partially heated timbers are cooled will depend upon such factors as the 

minim temperature reached at the center before cooling starts, the temperature of the heating medium (assumed as the surface temperature) the 

average cooling temperature, and whether the cooling mediun is the same as 

that used in heating. Under the same temperature conditions, timbers 

heated or cooled in air at a normal humidity will generally change temperature morc slowly than in a liquid or in an atmosphere at high humidity, 

such as can be maintained in a dry kiln. Radiation and evaporation of 

moisture will naturally have an important bearing on the rate of cooling in 

gases or in a vacuum. Cooling will also progress more slowly in still air 

or in a liquid that is not circulated during the cooling period since the 

heat is carried away more slowly under such conditions. For the same 

reason, timbers will cool more slowly when close piled while cooling as, for 

example, when left on trams after removal from the treating cylinder. 

A slow rate of cooling because of a gradual drop in the surface temperature, or cooling at high surface temperatures, naturally favors a 

greater rise in temperature at the interior during the cooling period when 

the timbers have not been heat3ed throughout to the maximum surface 

temperature. 

Report No. R1609 -4-
Timbers allowed to cool in the heating medium to any given surface 

temperature while the temperature of the medium is gradually reduced may,

for practical purposes, be assumed to be cooled at a temperature that is 

the average between the initial and final temperature of the heating medium 

for the cooling period in question. 

If timbers are first heated at a surface temperature Ub for a given 

time T1 and are then further heated at a lower temperature U2 for a time 

T-T1 (where T is the total heating period in hours), it is evident that the 

temperature U2 may be considered as a cooling temperature of U2 degrees

applied at the surface. 

Temperature Computations 

The same procedure can be followed in making temperature calculations 

whether the final temperature applied at the surface is higher or lower than 

the initial heating temperature. The method of making these computations 

after the surface temperature has been changed will be discussed in the 

following section, 

Method of Computing Temperatures 

As has been mentioned in earlier papers (1 to 6 and 8 to 11, inclusive) 

the rate of temperature change in a timber of any particular dimensions 

depends upon the diffusivity, which may be considered a constant for normal 

ranges of temperature. Average values of this factor have been determined 

in the laboratory experiments for woods of different densities heated in 

different heating mediums. 

Figure 1 shows the relation of diffusivity and specific gravity for 

green wood heated in steam and for air-seasoned and green wood heated in 

creosote. Data, for wood heated in water were not complete enough for 

plotting curves on this figure, but the data obtained indicate that it 

should be sufficiently accurate to assume green wood heated in water will 

heat about 90 percent as fast as when steam is used as the heating medium. 

In other words, the heating periods should be increased about 11 to 12 

percent over those required for heating with steam at the same temperature, 

to obtain a given temperature at any particular point in the timber. 

In previous publications (1 to 6 and 8 to 11 inclusive) timetemperature curves have been shown for both round and sawed timbers when 

heated by different methods with the surface temperatures assumed as constant during the heating period. The basic formulas for making these computations were given in several of them publications (1, 2, 10 and 11). The 

present paper, however, discusses the rate of temperature change that 

occurs at any time after the surface temperature is changed from the initial 

heating temperature Ub to a different surface temperature U2 where U2 may be 

either lower or higher than Ub. 

Report No. R1609 -5-
Equation 3, shown in the appendix, was derived for computing the temperature at any particular point in round timbers. Similarly, equation 6 

was derived for computing the temperature in sawed timbers. 

Definitions of the symbols used and a list of simple algebraic 

formulas derived from equations 3 and 6, that can be used with data from the 

curves, are also given in the appendix. 

Calculations involving the use of the basic equations 3 and 6 are 

tedious and require a large amount of work because of the type of equations 

employed and the number of variables that must be taken into consideration. 

The simple algebraic formulas given in the appendix and indicated by letters 

for the purpose of reference, may be readily used in conjunction with temperature data taken from the proper time-temperature curves shown in figures 2 

to 5, inclusive. This provides a simple method of making temperature computations and avoids the more difficult calculations from the basic equations 

3 and 6. For example, by using equation (A) (Appendix) only a simple 

arithmetical calculation is needed to find the temperature Uc at any time T, 

where Uc is the temperature at some particular point within a timber and T is 

the total time period under conaideration. In using equation (A) it is 

merely necessary to read temperatures from the proper time-temperature curve 

for the timber of the cross section under consideration (figs. 2 to 5, 

inclusive). 

It may be noted that equations 3 and 6 include the following factors: 

(1) Initial wood temperature = Uo (Taken as 60° F. in computing data 

for figures 2 to 5, inclusive) 

(2) Temperature of the heating medium during tho initial heating 

period = U1 (Taken as 200° F. in computing data for figures 2 

to 5, inclusive) 

(3) Diffusivity factor for transverse heating = h2 (Taken as 0.00025 

in computing data for figures 2 to 5, inclusive) 

(4) Heating period t1 (in seconds) = first heating period when surface 

temperature U1 is applied. 

(5) Total heating period t (in seconds), which includes both the time 

that the first surface temperature U1 and the time that the 

second surface temperature U2 is applied. The surface temperature U2 is, therefore, applied for the time t-t1. 

(6) a = radius of round timbers (equation 3), 

a and b = width and thickness of sawed timbers (equation 6). 

(7) r = distance of point p from the center of round timbers and 

(x,y) = coordinates of point p in sawed timbers. In both 

cases, p is the point at which the temperature is to be 

determined. 

Report No. R1609 -6-
Equations 3 and 6 each contain two converging series. The first 

series within the brackets is the same as that used in computing the timetemperature curves in figures 2 to 5, inclusive, for any period T when the 

surface temperature is U1 (1, 2). Similarly, the second series within the 

brackets is the same as that used in computing the data for the curves in 

figures 2 to 5, inclusive, when the heating period is T-T1. If the two 

series enclosed within the brackets (which involve the variables, time, 

dimensions, and diffusivity) are designated as (x1) and (x2), respectively, 

then (x1) and (x2) may be computed from the data plotted in figures 2 to 5 

when the the T1 and T are assumed. It is from this relation that equation 

(A), appendix, is derived. If (x1) and (x2) are substituted for these 

convergent series, equation (3) for round timbers could be written, 

Similarly, equation (6) for sawed timbers could be written, 

In this case, (x1) 

timber in question 

= where Um is the temperature read 

from the curve for the after heating for time T. 

Uo = 60° F., U1 = 200° F., and K = 2 for round timbers and = for sawed 

timbers. Substituting the numerical values given: 

where Un is the temperature 

read from the curve for the timber under consideration after heating f or time 

(T - T1) . 

If (x1) and (x2) are substituted in equation (3) for round timbers, 

Report No. R1609 -7-
Substituting the corresponding values of (x1) and (x2) in equation (6) for 

sawed timbers, 

which is the same general form as that shown for round timbers. 

Both of the foregoing expressions evidently reduce to the form, 

which applies for both round and sawed timbers and requires only the substitution of numerical values of the temperatures indicated. It should be 

borne in mind that Um and Un are read from figures 2 to 5 for the heating 

periods of T and T-T1, respectively, while U2, Ua or Ub may be any assumed 

temperatures . 

This formula (A) may be used in conjunction with the curves in 

figures 2 to 5 inclusive, for finding the wood temperature Uc when the 

initial wood temperature Ua, and surface temperatures Ub and U2 are assumed. 

Illustrative examples showing the application of formula (4) will be given 

later. Figures 2 to 5 (from which values of Um and Un are determined for 

heating periods of T and T-T1 hours) give time-temperature curves for the 

center and for a point midway between the center and surface of both round 

and sawed timbers of the dimensions indicated. These curves show the rate 

of heating when the surface temperature of 200° F. is applied for any time T. 

Additional time-temperature curves for distances of 1/2, 1, 2, 2-1/2, 3, 

3-1/2, and 4 inches from the surface and at the center of round timbers 

for various distances from the surface to the center of sawed timbers are 

given in a previous paper (6). Values of Um and Un may also be read 

directly from the curves in the latter paper for any of the distances from 

the surface mentioned, since they were prepared using the same diffusivity 

(0.00025), the same initial wood temperature (60° F.), and the came heatingmedium temperature (2000 F.) as were used for computing the curves shown in 

figures 2 to 5. 

Rate of Cooling 

Figures 6 to 19, inclusive, show values of Uc (the change in temperature during cooling) computed by means of equations (3) and (6) of the 

appendix, when the cooling temperature U2 is assumed as 80° F. These 

R1609 -8-
curves have been plotted as a guide in showing what temperatures should be 

obtained at the center of both round and sawed timbers before cooling starts 

to permit a subsequent rise in temperature that will be sufficient to 

sterilize the wood or to insure that it will reach or stay above a given 

temperature for a definite period, The curves also show the time required 

to reach the maximum temperature at the central portion of timbers of 

different dimensions after the surface heating has been discontinued and 

cooling has started. In addition, they show the time the temperature is at 

or above any temperature below the maximum reached. 

While it is desirable to consider the approximate diffusivity of the 

wood when calculations are made to determine the time T or T1 required to 

heat any particular point in a timber to a given temperature, a consideration of diffusivity is usually of less importance when the wood is cooled. 

If for example, the center is initially heated to any particular temperature 

lower than the surface temperature, the maximum temperature rise that occurs 

will be the same, regardless of the diffusivity. The effect of differences 

in diffusivity in this case is merely to change the rate of heating and 

cooling at various points in the timber, In other words, variations in 

diffusivity will affect the time T and T1 required to obtain any given 

temperature under the heating or cooling conditions assumed. 

The curves shown in figures 6 to 19 were computed on the assumption 

that the heating and cooling mediums were the same. When the wood is cooled 

in air or under other conditions that are favorable for a slower rate of 

cooling, the rise in temperature should be somewhat higher than that indicated by the curves shown in the figures, 

In general, it may be assumed that these curves represent the minimum 

increase in temperature that would occur during cooling when the center has 

been heated for the period T1 with the surface maintained at the temperature 

Ub. The temperatures obtained in the heating period T1 are shown at the 

point where the curves start, which is the time when the cooling; period is 

zero. Although the curves in figures 6 to 19 were based on a cooling temperature of 80° F. a variation of a few degrees higher or lower than 80° 

would not have a significant effect on the temperature changes at various 

periods of cooling. Since the rate of cooling will in many cases be somewhat slower than indicated, this provides for a reasonable amount of variation in cooling temperatures, The effect of applying different cooling 

temperatures can be easily investigated by means of equation (A). 

The purpose of figure 6 is to illustrate the temperature distribution 

between the center and surface of a timber after various periods of cooling 

and to show the effect of using different heating temperatures. A 10-inch 

diameter timber has been assumed with the center heated to 135° F. before 

cooling starts. In figure 6A the heating medium temperature Ub was taken 

as 200° F., while in figure 6B it was taken as 225° F. In both cases the 

initial wood temperature was taken as 60° F. 

R1609 -9-
The temperature distribution from the surface to the center at the 

time cooling starts is shown by the broken line curve from the surface temperature to the center temperature of 135° F. The curves are shown for only 

one half the diameter, since the temperature distribution is considered 

symmetrical with respect to the center. Although the temperature curves in 

figure 6 are plotted for a 10-inch diameter timber, the temperature distribution would be the sane, at the same proportional distance from the surface, 

for a timber of any other diameter. For example, the temperature at a distance of 1 inch from the surface of the 10-inch diameter timber is about 

200° F. (fig. 6B), as indicated by the broken line curve. The same temperature would be obtained in a 16-inch diameter timber at the same proportional 

distance of 1 x 16 or 1.6 inches from the surface, assuming the same wood 10 

and that the center temperatures are the same (in this case 135° F.). For a 

timber 8 inches in diameter the temperature of 200° F. (fig. 6B) would 

likewise be at a distance of 1 x 8 or 0.8 inch from the surface when the

10 

center temperature is 135° F. 

Temperature Changes in Round Timbers 

When longitudinal heating can be neglected, as in most timbers of 

commercial size, the symmetrical form of round sections, such as poles and 

piling, makes it possible to compute the temperatures in timbers of any 

diameter when the temperature distribution is known for any one diameter. 

The time required to reach the same temperature at the same proportional distance in any two timbers of diameters D1 and D2 inches will be 

directly proportional to the squares of the diameters or squares of the 

radii. To illustrate, assuming the same species and same heating conditions, 

if T10 represents the time required to reach a given temperature in a timber 

10 inches in diameter and T14 is the time required to reach the same 

temperature at the same proportional distance from the surface of a timber 

14 inches in diameter, then 

This relation will hold for the data plotted in figures 2 and 3 and also 

for those in figures 6 to 14, inclusive. 

From figure 6 it may be noted that the maximum temperature rise is 

at the center and the amount of temperature rise decreases rapidly as the 

surface is approached. The effect of using higher surface temperatures is 

shown by comparing the temperqature distribution curves in figure 6A with 

those in fibure 6B. Although the center temperature in both cases is the 

same, all intermetiate temperatures are higher when the higher heatingmedium temperature is employed. The rise in temperature during cooling is 

also higher when the higher heating-medium temperature is used. 

R1609 -10-
Figure 7 shows cooling curves for the center of timbers 8, 10, 12, 

14, 16, and 18 inches in diameter when heating temperatures of 200°, 225°, 

and 250° F. are used. The initial wood temperature was taken as 60° F. and 

the diffusivity as 0.00025, the values used for plotting the data in 

figures 2 to 5, inclusive. In computing the curves for figure 7 the center 

was assumed to be heated to a temperature that would rise (after cooling 

started) to slightly over 150° F. The required heating period was determined 

by assuming Uc = 151° F., by taking Un at the time of cooling (T-T1) when 

Uc would be approximately a maximum as indicated by figures 8 to 14, 

inclusive, and then solving for Um from equation A. In this case, Um is 

determined by using equation B derived from formula (A) (appendix). The method of finding Um, the temperature Ux to which the point under consideration must be heated before cooling starts, and the corresponding heating 

period when the other temperature conditions are known or assumed, is 

illustrated in example 1. 

Example 1 

The following conditions will be assumed: diameter of timber = 15 

inches; required temperature to be reached at the center after cooling 

starts = 155° F. = Uc; heating-medium temperature = 260° F. = Ub; initial 

wood temperature = 70° F. = Ua; cooling temperature = 65° F. = U2. From 

figure 7C, in which the heating conditions are nearest to those assumed in 

this example, it is found that the maximum temperature for a timber 15 

inches in diameter should be reached when the cooling period (T - T1) is 

about 5 hours. Assuming first that (T - T1) = 5 hours, Un is found from 

figure 2 for a timber 15 inches in diameter to be about 71.5° F. sub­ stituting in equation (B) of the appendix, 

From figure 2 it is found that a heating period (T) of about 13.4 

hours is required to reach a temperature of 135° F. Since T-T1 = 5 hours, 

T1 = (13.4 - 5) or 8.4 hours. From figure 2 the temperature reached after 

heating for 8.4 hours is found to be about 99.5° F. when the surface 

temperature Ub = 200° F. and the initial wood temperature Ua = 60° F. 

which were the values used in computing the data for fibures 2 to 5. The 

corresponding temperature Ux, obtained when Ub = 260° F. and Ua = 70° F. 

(assumed for this example) may be found from equation (C) of the appendix. 

From this equation, 

R1609 -11-
The center would, therefore, reach a temperature of 124° F. after 

heating at 260° F. for 8.4 hours, and after cooling for 5 hours at 65° F. 

the center temperature would rise to 155° F. In order to determine 

whether approximately the maximum temperature is reached after cooling far 

5 hours, cooling periods slightly less than and slightly more than 5 hours 

can be assumed, and the corresponding values of Uc can be determined in the 

Same manner as for the 5-hour cooling period. For example, for a cooling 

period of 4-1/2 hours Un = 68° F., approximately, Substituting in equation 

(B) gives Um = 131° F. From figure 2 it is found that a heating period 

(T) of about 12.75 hours is required to reach this temperature. 

Substituting in equation (A) of the appendix, 

which is only slightly more than 155° F. obtained after 5 hours cooling. 

A check for a somewhat longer period than 5 hours would easily show 

whether the temperature might rise further with increase in cooling period. 

Since, however, there is only a slight variation in the values of Uc for 

cooling periods of 4.5 and 5 hours, it is evident that the maximum rise in 

temperature occurs after cooling for approximately 5 hours. 

Since timbers of any diameter will have the same rise in temperature 

when the center temperature and the heating and cooling conditione are the 

same, curves similar to those shown in figure 7 could be plotted if desired, 

for various diameters with the curves stcarting at 124° F. The heating and 

cooling periods required for any given temperature will be proportional to 

the squares of the diameters as previously mentioned, 

Figures 8 to 11, inclusive, show the computed rate of temperature 

change at the center and midway between the center and surface of a timber 

10 inches in diameter when heated with surface temperatures of 200°, 220°, 

240°, and 260° F. and then cooled at 80° F. after the center has been 

heated to different temperatures. 

The approximate temperature changes for center temperatures within 

any of the 10-degree intervals shown may be easily determined by interpolating. For example, in figure 8 it is found that the maximum temperature 

rise is about 20° F. (140° - 120° F.) when the center been heated to 

120° F. when the center is heated to 130° F. the maximum temperature rise 

is about 17° F. (147° - 130° F.). If the center is assumed to be heated to 

125° F., the maximum temperature during cooling at 80° F. would then be 

determined as about 1/2(147° + 140°) = 144° F., approximately. The rise in 

temperature that occurs after heating is discontinued naturally decreases 

as the difference between the heating temperature and interior temperature 

decreases. For example, when the center is heated to a temperature close to 

that of the heating medium, practically no rise in temperature will occur 

during the coaling period. 

R1609 -12-
The heating periods required to reach tho different center temperatures are shown on each figure. From the heating periods given, it in 

evident that the time required for heating the wood to any desired temperature is reduced rapidly as the surface temperature Ub is increased. It may 

also be noted that when the center of a timber is heated to a given 

temperature before cooling starts, by using different heating medium 

temperatures, the maximum rise in temperature during the cooling period is 

higher for the higher heating temperature. 

The curves in figures 8 to 11 that are plotted for a timber 10 inches 

in diameter will apply equally well for any other timber of diameter D 

inches, since the time required to reach any temperature shown will be proportional to the squares of the diameters. For example, in figure 8 the 

temperature at the center of a 10-inch diameter timber before cooling starts 

is shown as approximately 135° F. after cooling for 3 hours when the center 

has been heated to 120° F. In order to reach the same temperature at the 

center of a timber 14 inches in diameter a cooling period of 196 x 3 or 100 5.88 hours would be required for the same wood and same heating conditions. 

This is the temperature shown in figure 13 for a 14-inch diameter timber 

after cooling for 5.88 hours. 

For convenience the multiplying factor is shown in table 1 for 

timbers ranging in diameter from 8 to 18 inches. 

To illustrate, figure 9 shows that after the center of a timber 

10 inches in diameter has been heated to 130° F. with the surface temperature of 220° F., the maximum rise in temperature is about 21° F., which is 

reached after cooling for about 2 hours. If a timber of the same wood and 

16-1/2 inches in diameter were heated at the center to 130° F. under the 

same heating conditions and then cooled at 80° F., the time required to 

reach the same maximum temperature rise would be computed as 2 x 2.72 = 

5.44 hours. 

If the diffusivity is other than 0.00025, the required time is 

readily found from the proportional relation shown by equation (E) of the 

appendix where h2 

a represents any given diffusivity. Table 2 has been

prepared so that tho ratios, are multiplying 

factors. For example, Tx = F1Th and Th = F2Tx in equation (E) or 

TD = fF1Td and Td = in equation (G) appendix. These factors will 

cover a sufficient range of diffusivities for general purposes, 

The relation of diffusivity, diameter of timber, and heating period 

is expressed by equation (G) of the appendix. This equation will be found 

convenient to use with the multiplying factors "f" given in table 1 and 

F1 or F2 given in table 2. 

R1609 -13-
Example 2 will illustrate how to compute tho temperature at any time 

T when the heating conditions, cooling temperature, and diffusivity are all 

different from those assumed in computing the various time-temperature 

curves. 

Example 2 

The following conditions will be assumed: Diameter of timber, D = 

16.5 inches. Center is to be heated to a temperature of 125° F. before 

cooling starts = Ux. Cooling temperature U2 = 5° F. Diffusivity of wood 

= 0.00028. Initial wood temperature Ua = 70° F. Heating medium 

temperature Ub = 235° F. Cooling period T - T1 = 5 hours. 

Find the required heating period T1 and the center temperature after 

cooling for 5 hours. 

The first step is to find U from equation (D) of the appendix. 

Substituting in this expression gives, 

This is the temperature that would be reached at the center in time T1 if 

the heating conditions were the same as those assumed in computing the 

temperature curves plotted in figure 2. Although the time temperature curve 

for the center of a timber 16-1/2 inches in diameter is not plotted in 

figure 2, the data for the 10-inch diameter timber can be conveniently used. 

In this case the multiplying factor f is = 2.72 as shown in 

table 1. From figure 2 the time required to reach a temperature of 106.7° F. 

in a 10-inch diameter timber is found to be about 4.15 hours (= Td in 

equation (G), appendix). This is the time required to reach a temperature 

Of 125° F. at the center under the heating conditions assumed in the example 

when the diffusivity is 0.00025, Since, however, the diffusivity is taken 

as 0.00028, by substituting in equation (G) of the appendix 

TD = T1 = (2.72) (4.15) = (f)(F1)(Td) = 10.1 hours, approximately. 

This is the value of T1 which was to be determined, 

The next step is to find the temperature Uc after cooling for 5 hours 

at a surface temperature of 5° F. Before adjusting for differences in 

diffusivity, T1 = (4.15)(2.72) = 11.3 hours. The cooling period of 5 hours 

is equivalent to a period of = F2 (5) = 1.12 (5) or 5.6 hours 

when the diffusivity is the lower value. Then T = 11.3 + 5.6 or 16.9 hours. 

= The corresponding value of T for a timber 10 inches in diameter 

6.21 hours. The value of Um for this period is found from figure 2 

R1609 -14-
to be about 139° F. Similarly, the value of Un, for or 2.06 hours, 

= 69° F. , approximately. Substituting equation (A) , in 

approximately, which is the temperature to be found. 

The following example will illustrate how to find Um and the 

corresponding values of T1 and Ux when Uc, U2, Ub, Ua, the cooling period 

(T - T1), and are assumed. 

Example 3 

Assume the following conditions: Uc = 160° F.; Ub = 240° F.; 

Ua = 75° F.; T - T1 = 6 hours; diameter of timber = 14.5 inches; U2 = 10° F.; 

and = 0.00028. 

Find T1 and the temperature Ux to which the center must be heated 

before cooling starts, 

The first step is to find the time Th from equation (E) corresponding 

to a 6-hour heating period when = 0.00028. In this case, 

6(0,00028) = Th(0.00025) or Th = F2 (6) = 6,72 hours. For a 10-inch diameter 

timber the corresponding period would be From figure 2 

the temperature Un for this heating period is found to be about 89° F. 

Substituting equation (B), appendix, in of the 

From figure 2 it is found that a temperature of 172.5° F. is obtained in a 

10-inch diameter timber in about 10.1 hours when the diffusivity is (=T)

0.00025. This = or 9 hours when 

the diffusivity is 0.00028. This time T must be multiplied by the factor 

"f" (table 1) which gives T = 2.1(9) or 18.9 hours for a timber 14.5 inches 

in diameter. Since T - T1 = 6 hours, T1 = 12.9 hours. The corresponding 

time T1 for a 10-inch diameter timber = = 6.15 hours. This corresponds 

to a heating period of 6.15 or 6.9 hours when the 

diffusivity is 0.00025, The temperature for this heating period is found 

from figure 2 to be about 146° F. This is the center temperature U, 

obtained in time T1, which is 6.9 hours for a 10-inch diameter or -inch 

(6.9) (2.1) = 14.49 hours for a 14.5/diameter timber when the surface ternperature is taken as 200° F. and the initial wood temperature as 60° F. 

R1609 -15-
For the heating conditions assumed, the temperature Ux is computed from 

equation (C) which gives, Ux = 240 -

From these computations the required value of T for the 14.5-inch 

diameter timber is therefore 18.9 - 6 or 12.9 hours, and the temperature that 

must be obtained at the center before cooling starts is 176° F. 

Since this temperature is higher than the temperature of 160° F. 

required at the center after cooling for 6 hours, it is evident that the 

center temperature is falling rather than rising after cooling for this 

period. An examination of figure 10 shows that the maximum temperature rise 

is reached in a 10-inch diameter timber in about 2 hours when the diffusivity is 0.00025 or or 1.79 hours when the 

diffusivity is 0.00028. For the 14.5-inch diameter timber the maximum temperature would then be reached after cooling for about (1.79)(2.1) or 

approximately 3.76 hours, Computations based on a cooling period of 2 hours 

for a 10-inch diameter timber (when the diffusivity = 0.00025) gives 

Um = 144° F. when Uc = 160° F. The corresponding value of T = 6.65 hours 

and T1 = 4.65 hours. For T1 = 4.65 hours the temperature U = 115.5° F. and 

Ux = 140° F. when Ub = 240° F., the temperature assumed. For a diffusivity 

of 0.00028,T1 = 0.893(4.65) or 4.15 hours. When the timber is 14.5 inches 

in diameter T1 = (4.15)2.1 or 8.72 hours. 

Example 4 

This example will illustrate the method of computing the temperature 

after various vacuum periods, when the steaming and vacuum treatment is 

employed. The following conditions will be assumed: steam temperature 

260° F. = Steaming period 8 hours = T1. Average temperature during 

vacuum period 150° F. = U2 . Length of vacuum period 2 hours = T-T1. 

Diameter of timber 10 inches. Initial wood temperature = 60° F. Diffusivity factor = 0.00030. 

Find the temperature Uc at a distance of 2-1/2 inches from the surface (which for this diameter is midway between the center and the 

circumference) at the end of the vacuum period. 

The first step is to find the temperature obtained at 2-1/2 inches 

from the surface, at the end of the steaming period, Since the diffusivity 

= 0.00030, the equivalent steaming period T1 will be 

= F2(8) or 9.6 hours when the diffusivity is 0.00025, the 

R1609 -16-
value assumed in computing the temperature curves. From figure 3 it may be 

found that a temperature of about 180° F. would be obtained in 9.6 hours 

with the temperature conditions assumed in computing the plotted data. From 

equation (C) the corresponding temperature Ux is found to be about 231° F. 

when the surface temperature is 260° F. 

The corresponding vacuum period T-T1 is = 

1.2(2) or 2.4 hours and the equivalent period T will be 9.6 + 2.4 = 12 hours. 

From figure 3 the temperature Um, for T = 12 hours, is found to be about 

188° F, and Un, for = 2.4 hours, is 107° F. Substituting in equation (A)

which is the temperature desired. points the surface will, of nearer course, 

lie between the surface temperature of 150° F, and the temperature of 206° F. 

The computed drop in temperature at a point midway between the center and 

surface at the end of the 2-hour vacuum period would then be 231° - 206° or 

25° F. 

Temperature Changes in Sawed Timbers 

Figures 12 to 14, inclusive, show the computed rates of temperature 

change at the center of round timbers 8, 10, 12, 14, 16, and 18 inches in 

diameter when heated at 200° F. for various periods of time and then cooled 

at 80° F. Similar curves are shown in figures 15 to 18 for sawed timbers 

with cross-sectional dimensions of 7 by 9, 8 by 10, 10 by 10, 10 by 12, 12 by 12, 

12 by 14, and 14 by 14 inches. 

Figure 19 shows the effect of different diffusivity values on the 

rate of cooling. An 8 -x 10-inch timber has been taken as an illustration 

when heating temperatures of 200°, 220°, 240°, and 260° F. are used. The 

center is assumed to be heated to 135° F. when cooling starts with the surface temperature maintainod at 80° F. Although the rise in temperature is 

the same, for the same heating conditions, it may be noted that the rate of 

temperature change is more rapid as the diffusivity is increased. 

Figures 4 and 5 show the rate of temperature change at the center and 

midway between the center and surface of rectangular timbers of various 

cross-sectional dimensions when the temperature of the heating medium is 

200° F. As previously mentioned, temperature curves for various other distances from the surface to the center of sawed timbers are given in an 

earlier paper (6) and can be used in the same manner as illustrated for 

computations obtained at the center. While examples 1 to 4 illustrate the 

method of computing temperature changes in round timbers, the same procedure 

is to be used for rectangular timbers except that figures 4 and 5 are to be 

used for finding values of Um, Un, and the time T or T1. 

R1609 -17-
Since rectangular timbers vary in two dimensions, namely width and 

thickness, a proportional relation between the dimensions and the required 

heating period can be obtained only for square dimension timbers. In the 

case of square timbers the required heating period varies directly as the 

squares of the cross-sectional dimensions. If, for example, a timber "W" 

inches in width and thickness requires a heating period of Tw hours to reach 

a given temperature at any given point p inches from the surface, to obtain 

the same temperature art the same proportional distance from the surface of a 

timber "x" inches in width and thickness will require a heating period of 

In some cases, as for example in gluing laminated timbers, the entire 

timber is heated to the temperature of the heating medium and is then 

gradually cooled over a period of time to allow the glue sufficient time to 

set properly at a temperature at or above the minimum required. Under such 

conditions the rate of cooling determines the time that the wood will be 

held at a temperature favorable for setting the glue. 

When the entire timber is heated to the same temperature Ub throughout, the value of Um that is to be substituted in equation (A) is the 

heating-medium temperature of 200° F. used in computing figures 2 to 5, 

inclusive. Equation (A) then becomes, 

This form will apply when a uniform temperature has been obtained at all 

points within the timber and is designated as equation (A1) in the appendix. 

The following conditions will be assumed for an example illustrating the 

method of applying equation (A1). 

Example 5 

Timber dimensions 8 by 10 inches. Wood temperature (entire timber) = 

210° F. = Ub. Minimum temperature required for gluing 190° F. Diffusivity 

= 0.00020. Average temperature during cooling period = 150° F. = U2. 

Find Uc after cooling for 2-1/2 hours. The 

the cooling period of 2-1/2 hours is equivalent to 

or 2 hours when the temperature charts are used. 

diffusivity is 0.00020, hence 

Since the center of the timber is at the lowest temperature during 

the heating period, the rate of cooling at this point is of principal 

interest. The rate of cooling at the center, however, will necessarily be 

the slowest, since this point is at the maximum distance from the surface. 

R1609 -18-
From figure 4, Un, for a 2 hour period, is found to be about 72° F. 

Substituting values in equation (A) which in this case takes the form 

shown in equation (A1), 

205° F. which is 15 degrees higher than the minimum temperature of 190° F. 

necessary for setting the glue, 

If, in examples such as the foregoing, it is desired to find the time 

that Uc will be any given temperature, it is merely necessary to solve for 

Un in equation (A,) and find T-T1 from the proper chart among figures 2 to 5 

for the timber under consideration. This gives 

For example, assume it is desired to find the cooling period needed 

to reach a temperature of 190° F. (= Uc) when U2 = 150° F. and Ub = 210° F. 

Substituting in the foregoing expression, 

128° F., approximately. 

From figure 4 it is found that a temperature of 128° F. is reached at the 

center of an 8- by 10-inch timber in about 5.0 hours when the diffusivity 

is 0.00025. In example 5 the diffusivity was assumed as 0.00020, 

Substituting in equation (E) of the appendix, 

Tx (0.00020) = 5.0 (0.00025) = 5 (F1) or Tx = 5(1.25) = 6.25 hours, 

which is the time to be determined. Since it was assumed that a temperature 

Of 190° F. was necessary to set the glue, nothing would be gained by further 

cooling at 150° F. 

Example 6 

This example will illustrate an application of the data for computing 

the approximate temperature at any particular point in a timber when the 

temperature is gradually raised until the maximum is reached. 

The following conditions will be assumed: Green Southern yellow 

pine timbers 10 by 12 inches in cross-section are steamed at a uniform 

temperature of 260° F. for 10 hours after the maximum temperature of 260°F. 

is reached. Two hours are taken to reach the maximum temperature; hence, 

the total heating period, T, is 12 hours. The initial wood temperature will 

be assumed as 75° F. = Ua. If a temperature recording instrument is used, 

the average temperature can be determined from the recording chart, but for 

convenience it will be assumed that the temperature is uniformly increased. 

to the maximum. The average temperature over the 2 hour period will be 

taken as or about 168° F. 

R1609 -19-
Since the wood is first assumed to be heated at 168° F. for 2 hours 

and then heated at 260° F. for 10 hours, Ub = 168° F., U2 = 260° F., 

T1 = 2 hours, T = 10 + 2 or 12 hours and T-T1 = 10 hours. 

The center will be taken as the point at which the temperature is to 

be determined at the end of the 12-hour period, and the diffusivity of the 

wood will be taken as 0.00030. 

Since the curves in figures 2 to 5, inclusive are based on a diffusivity of 0.00025, the temperature Um obtained at the end of 12 hours would be 

determined as that obtained in or 12(1.2) = 14.4 hours 

when the diffusivity is 0.00025 (Equation (F) , appendix). Similarly, the 

temperature obtained in 10 hours would be the same as that shown by the 

temperature curves for a heating period of = 10(F2) or 12 hours. 

Prom figure 5, Um for a heating period of 14.4 hours is found to be 

about 174° F. for a 10- by 12-inch timber, and the temperature Un for a 

heating period of 12 hours is found to be about 163° F. Substituting in 

equation (A) of the appendix and solving for Uc gives 

which is the temperature to be determined. 

If the temperature of 260° F. had been applied for the full period 

of 12 hours (corresponding to 14.4 hours when the diffusivity is 0.00025), 

the temperature Ux would be computed from equation. (c) of the appendix. 

In this case, Ub = 260, Ua = 75, and U = 174. Substituting these values in 

equation 

Ux = 260 ... 

C, 

= 226 or 8 degrees higher than when 

2 hours are taken to reach the maximum temperature. 

R1609 -20-
APPENDIX 

Method of Computing Temperature Changes in Round and 

Sawed Timbers When the Surface Temperature is Changed 

After Any Given Heating Period 

Round Timbers 

In deriving an equation for computing the temperature Uc at any 

point r inches from the axis of round timbers it is necessary to solve the 

following partial differential equation: 

(1) 

In this equation h2 is the diffusivity factor for heating in tho transverse 

direction and t in the time in seconds. 

The following notation will be used: 

t1 = time (in seconds) of first heating period when surface 

temperature is U1. 

t is the total time (in seconds) under consideration and includes 

both the time that the surface temperature U1 is applied and the time that 

the second surface temperature U2 is maintained. In this case t-t1 will 

represent the second heating period when the surface temperature U2, which 

may be either higher or lover than the first heating temperature U1, is 

applied. 

Uo = initial wood temperature 

Uc = temperature obtained at any given point p in a timber after 

time t. 

a = radius of timber. 

r = the distance from the center to point p. 

Equation (1) must be solved to meet the following boundary conditions: 

For first heating period when, t t, 

Let (Uc - U1) 

Uc = Uo when t = 0, then (Uo - U1) when Uc Uo. 

R1609 -21-
< Uc = U1 when r = a and t = t1, then 0 when r = a. 

< when T = T 

For second heating period 

= (Uc - U2) when t > t1 

Uc = U2 when r = a and t > t1, then = 0 when r = a. When t > t1 

(2) 

By substituting values of An and Bn in (2), and (Uc - U2) for 

the first few terms of the general equation for computing the temperature 

Uc at a given point r at any time t becomes, 

(3) 

In the foregoing equations and are Bessel's 

functions of the zeroth and first order respectively. is a root of 

= 0, and e is the base of the Naperian logarithms. 

R1609 -22-
Sawed Timbers 

In the case of sawed timbers the following differential equation 

must be solved for computing the temperature change Uc at any point (x,y). 

This is solved to meet the following boundary conditions: 

< For the first heating period when t = t1, 

For second heating period 

R1609 -23-
Substituting values of Am,n and Sm,n in (5), and (Uc - U2) for Z, the first 

few terms of the general equation for computing the temperature Uc at a 

given point (x,y) in a transverse section, at any time t becomes, 

(6) 

In equations 4 to 6, inclusive, t , t1, Uo , U1, Uc, U2, and h2 are 

defined the same as for round timbers, while a and b are the width and 

thickness of a transverse section. 

R1609 -24-
SYMBOLS USED IN FORMULAS FOR COMPUTING TEMPERATURES 

IN ROUND AND SAWED TIMBERS 

Uo = Initial wood temperature taken as 60° F. in computing figures 2 to 5. 

U1 = Heating medium temperature taken as 200° F. in computing figures 

2 to 5. 

U = Computed temperatures found from figures 2 to 5 after heating for 

time T1 where T1 is in hours. 

Ua = Any assumed initial wood temperature, 

Ub = Any assumed heating medium temperature applied for time T1. 

Ux = Computed temperature when the initial wood temperature Ua, the heating 

medium temperature Ub, or both are different from 60° and 200° F., 

the temperatures assumed in computing curves in figures 2 to 5. 

Um = Temperature found from figures 2 to 5 corresponding to a heating 

period of T hours. 

Un = Temperature from figures 2 to 5 corresponding to a heating period 

of T-T1 hours. 

Uc = Temperature at any point p in a timber after heating for T1 hours at 

any surface temperature Ub and then cooling or heating at surface 

temperature U2 for time T-T1. In other words, Uc is temperature of 

the wood at point p, at end of time T. 

U2 = Surface temperature applied for T-T1 hours. 

T = Total period (hours) for which surface temperature Ub and U2 are 

applied. 

T1 = Time (hours) surface temperature Ub is applied. 

T-T1 = Time (hours) surface temperature U2 is applied. 

Tx 

= Time (hours) required to obtain a given temperature at point P in a 

timber when the diffusivity = 

Th = Time (hours) requred to obtain the same temperature at point p, as 

that obtained in time Tx, when the diffusivity - 0.00025 

R1609 -25-
t and t1 = Time in seconds. 

h2 = Diffusivity factor (square inch per second) taken as 0.00025 in 

computing data for figures 2 to 5 inclusive. 

= Any diffusivity different from h2 = 0.00025. 

R1609 -26-
METHOD OF USING FIGURES WHEN BOTH DIFFUSIVITY AND HEATING 

CONDITIONS ARE DIFFERENT FROM THOSE USED IN COMPUTING 

DATA FOR TIME - TEMPERATURE CURVES 

The following equations (A) to (G) are relations derived from the 

basic equations (3) and (6). These equations show the relation of time and 

diffusivity and methods of finding the corresponding wood temperature when 

the heating conditions are different from those assumed in computing the 

data for temperature curves. (For definition of symbols see list.) 

(A) 

When the entire timber is heated to the temperature of the heating medium 

(A1) 

(B) 

When Ua, Ub, and U are known it is necessary to determine Ux, the 

wood temperature obtained when Ua, Ub, or both are different from Uo and U1. 

Solving for Ux in terms of Ub, Ua, U1, Uo, and U (when Uo = 60° and 

U1 = 200° F.) gives, 

(C) 

When Ux, Ua, and Ub are known it is necessary to solve for U to find 

the heating period T or T1 from the proper figure. Solving for U in terms 

of Ua, Ub, Ux, Uo, and U1 (when Uo = 60° and U1 = 200° F.) gives, 

(D) 

(E) 

R1609 -27-
In the case of round timbers, if Td is the heating period (hours) 

required to obtain a temperature Ud at a point r inches from the center of 

a tinber d inches in diameter (or r) inches from the surface) when the 

diffusivity is 0.00025, and TD is the heating period (hours) required to 

obtain the same temperature at the same proportional distance from the surface of a timber D inches in diameter, 

Let X1 represent the distance from the surface of the timber of 

diameter d inches and X2 the same proportional distance from the surface of 

the timber of diameter D inches. Then X2 is evidently and 

If for convenience d is taken as 10 inches, 

where T10 is the time (hours) required to reach the temperature Ud at the 

point under consideration in a timber 10 inches in diameter. The time T10, 

may be determined from the temperature curve for the 10-inch diameter timber 

if Ud is assumed. 

R1609 -28-
References 

(1) MACLEAN, J. D. 

1930. "Studies of heat conduction in wood.-- Results of steaming 

green round southern pine timbers." Proc. A.W.P.A. 

pp. 197-217. 

(2) 

1932. "Studies of heat conduction in wood.-Part II.--Results of 

steaming green sawed southern pine timber." Proc. A.W.P.A. 

pp. 303-329. 

(3) 

1934. "Temperatures in green southern pine timbers after various 

steaming periods." Proc, A.W.P.A. pp. 355-373. 

(4) 

1935. "Temperature and moisture changes in coast Douglas-fir." 

Proc. A.W.P.A. pp. 77-103, 

(5) 

1936, "Average temperature and moisture reduction calculations for 

steamed round southern pine timbers." Proc. A.W.P.A. 

pp. 256-279. 

(6) 

1940. "Relation of wood density to rate of temperature change in 

wood in different heating mediums." Proc. A.W.P.A. 

pp. 220-248. 

(7) 

1941. "Thermal conductivity of Wood." Heating, Piping, and Air Conditioning, 13(6):380-391. Same in Amer. Soc. Heating and 

Ventilating Engineers. 1942 Transactions Vol. 47, 

pp. 323-354. Abstract in Mechanical Eng. 63(10) 734-736, 

Oct. 1941. 

(8) 

1942. "The rate of temperature change in wood panels heated between 

hot plates." Forest Products Laboratory Report No. R1299. 

(9) 

1943. "Method of computing the rate of temperature change in wood 

and plywood panels when the two opposite faces are maintained at different temperatures." Forest Products 

Laboratory Report No, R1406. 

R1609 -29-
(10) MACLEAN, J. D. 

1943. "Rate of temperature change in laminated timbers heated in 

air under controlled relative humidity conditions." 

Forest Products Laboratory Report No. R1434. 

(11) 

1946. "Rate of temperature change in short-length round timbers.'' 

Transactions of the American Society of Mechanical 

Engineers, Jan. 1946, Vol. 68, No. 1, pp. 1-16. 

(12) CHIDESTER M. S. 

1939. "Further studies on temperatures necessary to kill fungi 

in wood." Proc. A.W.P.A. pp. 319-324. 

R1609 -30-
Table 1.--Multiplying factors for timbers of different diameters 1 

1The time required to reach a given temperature in a timber 10 inches 

in diameter multiplied by factor "f" gives the time required to 

obtain the same temperature for the diameter D, at the same proportional distances from the surface. 

R1609 
Table 

0.00015 to 0.00035 (ratios to nearest 0.01) 

2.--Multiplyingfactors for various diffusivity values of from 

1The factor will be found convenient to use in finding Tx equation (E) 

of the appendix where Tx = 

2The factor F2 can be used in finding Th, when Tx is assumed, where 

Tx = F2TX. In equation (G) TD = 

R1609 
Figure 1.--relation of diffusity and specific gravity of wood. 


figure 4.--Temperature at center or axis of sawed timbers of various 

cross-sectional dimensions heated at 200° F. for different periods of 

time. (Diffusivity = 0.00025' initial wood temperature = 60° F.) 


Figure 7. --Temperature change at center of round timbers when 

cooled with the temperature of the surface at 80° F. after 

the center is heated to temperatures that will result in a 

Z M 67860 F maximm center temperature of 151° F. 





Figure 19.--Effect of different diffusivities on rate of tem

change at center of 8- by 10-inch sawed timber after center 

raised to 135° F. with different heating-medium temperatur

Z M 67346 F face temperature while cooling = 80° F.