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1 156 J. Physiol. (I958) I4V, I56-I63 THE HEAT EXCHANGES OF WET SKIN By D. McK. KERSLAKE AND J. L. WADDELL From the R.A.F. Institute of Aviation Medicine, Farnborough, Hants (Received 29 October 1957) Machle & Hatch (1947) have examined theoretically the effect of skin temperature and skin wetness (Gagge, 1937) on the heat exchange in warm environments. Their equation giving the steady state skin temperature in terms of the metabolic rate and the relevant parameters of the environment was designed to cover the full range of warm environments, but proved unusable in most circumstances because the skin wetness could not be determined. Skin wetness can be calculated from skin temperature on the basis of the equations, but can be independently stated only in the case of complete wetness, that is, when the skin is covered with a film of sweat. In this condition the term for skin wetness becomes unity, and the steady state skin temperature can be predicted from a knowledge of the metabolic rate and the environment (Woodcock, Pratt & Breckenridge, 1952). The work to be described was an attempt to provide a direct check of this theoretical approach. In practice it was found that the steady state could not be reached in the severe environments required to ensure full wetness of the skin, and recourse was had to the prediction previously made by Machle & Hatch of the rate at which the skin temperature should approach its equilibrium value. Their formulae include certain secondary statements or assumptions which are incidental to the main thesis. These have been examined directly, and the equations have been modified to avoid the inclusion of those statements which were found inapplicable to the situation used in the present work. Derivation of the formulae for the prediction of the temperature of the wet skin The approach used by Machle & Hatch to the expression of the temperature of wet skin either in the steady state or before this has been reached is here restated, so that the context of the alterations which have been found necessary may be made clear. The rate of heat gain by unit area of skin from the environment by convection and radiation may be expressed by Her = kcr (Ta - T.), where the constant kc, is the sum of the constants kc, for heat exchange by convection, and kr, for heat exchange by radiation, Ta is the temperature of the air and walls, and T. that of the skin.

HEAT EXCHANGES OF WET SKIN Where the skin and wall temperatures do not vary greatly and wall temperature equals air temperature, there is little error in assuming this linear relationship for heat

2 HEAT EXCHANGES OF WET SKIN Where the skin and wall temperatures do not vary greatly and wall temperature equals air temperature, there is little error in assuming this linear relationship for heat exchange by radiation and convection. The rate of heat loss by evaporation from unit area of wet skin is given by He =ke (E.-Ea), where ke is the constant for heat loss by evaporation (expressed in heat units) and E, and Ea are the vapour pressures at the skin surface and in the ambient air. The vapour pressure at the skin surface is taken as 0*2 mm Hg less than that of pure water at skin temperature, to allow for the dissolved substances in the sweat. It is supposed that the sweat rate considerably exceeds the rate of evaporation so that there is no significant concentration as a result of the evaporation. Over the small skin temperature range covered by the experiments to be described, the water vapour pressure at the skin surface may be expressed as a linear function of temperature; Es =2-6 x T , (error 0-06 mm Hg at 35 C and 0-14 mm Hg at 390 C). The above expression differs from that used by Machle & Hatch, who were considering a range of skin temperature greater than that which was covered by the present experiments and having a lower mean value. These formulae may be combined to give an expression of the skin temperature at which the metabolic heat production, im (per unit area) would be exactly dissipated. T*= kcr Ta + k,e(ea ) + M S (1) (2-6 xlkce±kcr) The expression has the general form of equation (4) of Machle & Hatch (1947), but differs from it in the following ways. The numerical constants are slightly different because of the different range of skin temperatures considered (see above). All area terms have been omitted by expressing the metabolic heat production per unit area and assuming that the skin is wet, so that the areas for heat exchange by convection and evaporation are equal. The term for wall temperature has been omitted, since in the present work air and wall temperatures were equal. It might appear that there is here an implicit assumption that the areas available for heat loss by radiation and convection are equal. Allowance is in fact made for this in the value assigned to kcr. In the present work this was experimentally determined, and the contribution of the true radiation constant to the whole coefficient is automatically weighted by the ratios of these two areas. Heat exchange in the respiratory tract has been neglected, since this must have been small in the environments used here (McCutchan & Taylor, 1951). Machle & Hatch (1947) have expressed the relation between skin temperature and time for constant skin wetness in the following way: (T* - T.) = (T* - T.) exp (- AC _t) 157 Here T?'-final skin temperature in the steady state; T, =skin temperature at time t; T0 =skin temperature at time 0; A =body surface area; C'= 2-5 ke + kcr; S =specific heat of body; W weight of body; t =time. (an + b) represents the ratio of the change in mean body temperature to the change in skin temperature. Change in mean body temperature is defined as the weighted mean of skin and deep temperature changes (aat, + bat,). It is supposed that the two temperatures will be linearly related over the relevant range so that ATr= nat.. Since a and b are weighting factors, their sum is unity. It was found in the present experiments that, over the range examined, n was near to unity (see results), so that (an + b) also has this value, and the difficulty of allocating values to a and b does not have to be faced. The value of 2-5 in the expression for C' given by Machle & Hatch is derived from the linear relation used by them for saturated water-vapour pressure in terms of temperature. For the present case 2-6 represents a closer approximation.

3 158 D. McK. KERSLAKE AND J. L. WADDELL For the circumstances used here, therefore, the following expression should represent the relation between skin temperature and time when the skin is completely wet. (7T -T.)=(T* -TO) exp ( S(2W+ke+ t). (2) The linear approximation for the relation between temperature and water-vapour pressure is accurate to within 0*1 mm Hg over the range of observed skin temperatures. When the final skin temperatures are above 390 C the assumed relation introduces some error into their calculation, but this does not affect the calculation of the rates of change of skin temperature within the range of the observations. METHODS All experiments were conducted in the same position in an air-conditioned room. During any one experiment air temperature was constant to ±0'25 C and relative humidity to +0.5% r.h. The air circulated from ceiling distributors to extraction orifices at the floor level runningalongopposite sides of the room. Air movement in the region occupied by the subject was between 45 and 55 ft./ min (katathermometer), and great care was taken to avoid varying this by rapid movement of the observer or subject. The aspiratingpsychrometer usedfor measuring theenvironmental temperature was run continuously for the same reason. The subject reclined on a deck chair with a leg rest, the canvas being replaced by a wide-mesh nylon net. His posture was one of semirecumbency with the buttocks low and the lower legs horizontal and at about the level of the xiphisternum. The chair was arranged on the platform of a recording balance, since this was required for the determination of the heat exchange constants. Skin temperatures were measured by an end-to-end thermocouple, lightly tensed, which was applied to each point in turn with sufficient pressure to produce slight deformation of the skin. This was calibrated during each experiment. Mouth temperature was measured with the same couple, detached from its mount and placed under the tongue. Mouth breathing was prohibited. Skin temperature was measured at the following points: 1, dorsum of foot; 2, anteromedial aspect of leg midway between knee and ankle; 3, posterolateral aspect of leg midway between knee and ankle; 4, medial aspect of thigh midway between perineum and knee; 5, anterolateral aspect of thigh midway between perineum and knee; 6, posterolateral aspect of thigh midway between perineum and knee; 7, abdomen over rectus at the level of the umbilicus; 8, abdomen in mid-axillary line between costal margin and ilium; 9, back, at margin of erectores spinae at the same level as 8; 10, chest 1-5 in. medial to nipple; 11, back over supraspinatus; 12, anterolateral aspect of upper arm midway between shoulder and elbow; 13, posterior aspect of forearm midway between elbow and wrist; 14, dorsum of hand; 15, forehead. These points were chosen so that different regions of the body were represented by numbers of points approximately proportional to their areas, and an unweighted mean of the readings could be used for the expression of mean skin temperature. When metabolic rate was measured, mouth temperatures were not taken. The subject breathed from a mask covering the mouth and nose, the expired air passing through a gas-meter. A sample was drawn slowly from the expired air line during each estimation. Owing to the likelihood that some overbreathing was taking place as a result of the thermal stress, metabolic rate was calculated from the oxygen consumption, assuming a value of 0-85 for the respiratory quotient. Before entering the hot room, the subject rested, nude, for a period of half an hour in a room at

HEAT EXCHANGES OF WET SKIN 159 280 C, 40% r.h. and 50 ft./min air movement.

4 HEAT EXCHANGES OF WET SKIN C, 40% r.h. and 50 ft./min air movement. The hot exposure lasted about an hour, but in some cases was terminated rather sooner than this on account of distress of the subject or observer. The duration in each case may be read from Fig. 2. Determination of heat exchange constants In order to provide values for the constants, ke and kc,, appearing in the equations being tested. a series of experiments was performed using a dummy instead of a living subject. The dummy was jointed at the neck, shoulders, elbows, wrists, back, hips, knees and ankles, and could be arranged in the chair in a posture similar to that adopted by the subject. It was clothed all over in closely woven cotton under-wear, which was soaked in water. It was found that dripping continued from the buttocks and heels for so long that there was risk of some areas drying out before it had stopped. The drips were therefore allowed to fall into dishes containing liquid paraffin, which were placed on the balance pan. Evaporation could thus be measured although dripping was still occurring. An experiment was first carried out in order to discover for how long the dummy could be regarded as completely wet. It was set up in a fixed environment of low humidity and the weight recorded continuously. The rate of weight loss soon settled down to a steady level, which was maintained for about 40 min. After this time the rate of weight loss decreased, suggesting that some parts of the dummy were no longer completely wet. The duration of subsequent experiments was limited so that the total weight loss did not exceed half that which had occurred in this first experiment by the time the weight record began to deviate. The wetted dummy was placed on the chair and the weight record started. When this had been straight for about 10 min, the surface temperature of the dummy was measured in the same regions and by the same technique as was used for the living subjects. The ambient humidity was then raised and weighing continued. The rising humidity produced a decrease in the rate of evaporation, which later partly recovered as the surface temperature rose. A second series of skin temperature observations was made when the weight loss had been steady for a further period of 10 min. The sequence of operations was continued until it became necessary to rewet the surface of the dummy. Ambient temperatures of 32, 36, and 40 C were used, and no effect of ambient temperature on the heat exchange constants was detectable. Humidities ranged from 10 mm Hg partial pressure to near saturation. The evaporative constant, he, was found from the relation of water vapour pressure difference to the rate of water loss. The regression line for this relation had an insignificant intercept and a slope of 24-40±0-55 (s.e.) g/hr. mm Hg. This is equivalent to (s.e.) kcalfm2.hr. mm Hg, assuming a value of kcal/g for the latent heat of evaporation of water and a surface area of 1-8 M2. The constant for heat loss by radiation and convection combined, kcr, was found from the relation between the weight loss and the temperature difference between the dummy's surface and the air (and walls). Again the intercept was insignificant, the regression coefficient being 27*72±2-44 g/hr. C. This is equivalent to 8*87±0-78 kcal/m2.hr. C. Metabolic rate Metabolic rate has been assumed to be constant for each subject and is taken as the mean of the measurements made on him during these experiments. The metabolic rate showed little change with time although there was a progressive increase in body temperature. It is probable that under steady body temperature conditions a fall in metabolic rate would have been observed because of the inactivity of the subject, and the absence of a significant change in practice may represent the fortuitous combination of these two opposing trends. It provides some justification for the assumption of a constant metabolic rate which is required in order to enter the equations. The rate used is not that found by dividing the total heat production by the Dubois surface area, since not all this area was available for heat loss. The arms were rested on some parts of the trunk, and allowance should be made for the area of scalp covered by hair. The heat-exchange constants determined using the dummy are related to the entire surface area and are expressed per unit

5 160 D. McK. KERSLAKE AND J. L. WADDELL area. As the effective area of the subject was less, and temperatures were not measured on apposed skin areas or on the scalp, appropriate adjustment may be made by expressing the metabolic rate as the heat production per unit skin area available for heat exchange. This neglects the probable difference between the relative proportions of the radiation and convection areas of the subject and dummy respectively. It has been assumed that both areas were reduced by 15%. It is probable that the error of neglecting this difference is small compared with that implicit in the guess of a 15% reduction in the convection-evaporation area. Its magnitude depends on the environment, and can be found for any given circumstances from equation (1). RESULTS The relation between mouth and mean skin temperatures is shown in Fig. 1, from which it will be seen that the slope appears to be unaffected by the severity of the environment within the limits used. The regression line through all points for D. B. has the slope (S.E.), and that for D. K These coefficients do not differ significantly from unity, and provide justification for the omission from equation (2) of the weighting factors for skin and deep temperatures a b Subject D.B. * 0 Subject D.K _ 0 _ E~~~ 0~~~~~~~~~~~~~~~~~~~~~~0 teprtr hne r prpitl esrbdb qain()i spoal dripp1.sing rey (T8)admuh(emperatures bfrthscudurnot bexpusuedto testete evrnequatinssicelathedfnecessary criteriatrs( wer not satisfied.97,( 4 ordk.o377 For eahe expersimlentohc the final skin temperaturewsfirstcacultedownfrom euthseeion (1) thifgueisndrequisreduinrderto enterecopequtio (2),eso. That sifnh tempeature changehsaigre approreqiately inodesriebyene equation (2), iotht isproabe

6 HEAT EXCHANGES OF WET SKIN 161 that the final skin temperature for that environment was properly predicted by equation (1). The natural logarithm of the difference between the observed skin temperature and its calculated final value, i.e. (T*- TJ) was next plotted against time. This is shown in Fig. 2. If equations (1) and (2) are correct descriptions of the situation, this plot should produce a straight line with a slope of - X x osu. WX. (2 6 x ke + klcr). Thus the slope should be independent of the ambient temperature and humidity, which will affect only the intercept. This intercept is of no significance in the present case since at time zero the skin 30 <) a 30 b 25 0 Subject D.B Subject D.K so 0 0~~~ ~~~~~~ , o O Time since entering (min) 04 I i Time since entering (min) Fig. 2. The relation between time of exposure and difference between observed skin temperature and its calculated final value. Ordinates, temperature differences (log. scale); abscissae, time since entering hot environment. Final skin temperatures (0C) for D.B. C 38'3, ( 39-3, , , 40'1; for D.K , * was not completely wet. The test of equations (1) and (2) depends on the straightness of the lines and on whether their slopes have the predicted value. Linearity appears to be established in Fig. 2, and the lines are nearly parallel. Their slopes are presented in Table 1, as the time constants (negative inverse of slope). They have also been multiplied by SA, to eliminate those quantities - which depend on the characteristics of the subject. The expected value is therefore (2 6 x ke + kcr), or 29-2, and the observations provide values near to this. The mean is 29' (s.e.), which does not differ significantly from 'PIlWVSTl (VTJ

162 D. McK. KERSLAKE AND J. L. WADDELL TABLE 1. Ambient conditions, calculated final skin temperatures, observed time constants for skin temperature and estimates of (2.

7 162 D. McK. KERSLAKE AND J. L. WADDELL TABLE 1. Ambient conditions, calculated final skin temperatures, observed time constants for skin temperature and estimates of (2.6 x ke + kcr) derived from the time constants. T,2 ambient dry-bulb temperature, E. ambient water vapour pressure, T* final skin temperature calculated from equation (1) in the text. The time constant, K, is derived from the slope of the line plotted in Fig. 2. The last column shows the inverse of the time constant multiplied by A for the subject concerned. The expected value in this column is 29-2 Ta Ea T* _W Subject (O C) (mm Hg) (0 C) K AK D. B D.K DISCUSSION Over the limited range of environments used, equations having the general form of those of Machle & Hatch (1947), but adjusted to suit the circumstances more closely, have been found satisfactorily to describe the changes in temperature of wet skin in very severe environments before equilibrium is reached. One stage in the prediction (equation (2)) involves the calculation of the final skin temperature at which equilibrium at the metabolic rate cqnsidered would be reached (from equation (1)) and it seems probable that this estimate is reliable. The steady states in the circumstances examined would demand deep temperatures of C, and even if the subjects were able to stand this at rest, it is probable that their metabolic rates would be increased, so that the actual final skin temperatures would be higher than those appropriate to the initial part of the exposure. In only two cases did the observed skin temperature reach within 1 C of the calculated final value. For the calculation of final skin temperature it is necessary to know the constants for heat exchange by convection and radiation and by evaporation. If wall temperature had differed from air temperature, the radiation and convection constants would have been required separately. In the present work the constants were determined experimentally using a dummy in the posture and location of the subject. Use of the same technique for skin-temperature measurements for the subject and dummy probably reduced the effect of such systematic errors as are inherent in the method used. The only differences between the dummy and the subject (for the present purpose) were in the metabolic heat production, heat capacity, skin texture, respiratory movements and details of topography and posture. The resulting vindication of the equations is thus limited to a demonstration of the differences due to metabolic rate and heat capacity and of the insignificance of other differences which were not allowed for in the formulae.

HEAT EXCHANGES ON WET SKIN 163 From a practical point of view the conclusions which may be drawn are that the fundamental theory on which the equations of Machle & Hatch are based is apparently

8 HEAT EXCHANGES ON WET SKIN 163 From a practical point of view the conclusions which may be drawn are that the fundamental theory on which the equations of Machle & Hatch are based is apparently sound, and the final skin temperatures predicted by their method are probably correct in the case of wet skin. The application of the formulae is dependent upon ability to convert measurements of air movement into heat exchange constants, and to express heat exchange by radiation accurately. For the description of the changes in skin temperature before equilibrium is reached it is also necessary to have knowledge of the distribution of stored heat. This appears to depend on the severity of the stress, since the distribution proposed by Machle & Hatch, based on observations at that time available, and representing smaller stresses than have been used here, was different from that found in the present investigation. A further factor limiting the application of the equations is that in order to predict the skin temperature after a given time it is necessary to know the skin temperature at some other time when the skin is completely wet. It is concluded that the equations of Machle & Hatch are supported by the results described in this paper, but that little practical use can be made of them at present. SUMMARY 1. Skin temperature has been measured in resting men in circumstances where the skin was completely wet with sweat. 2. The steady state was not reached, and the analysis was limited to a consideration of the approach to it. 3. The equations of Machle & Hatch, with modifications of detail to suit the particular circumstances, were found to provide a satisfactory description of the changes in skin temperature. Their prediction of the final steady state skin temperature is indirectly supported by the findings. We are grateful to the Director-General of Medical Services, Royal Air Force, for permission to submit this work for publication. REFERENCES GAGGE, A. P. (1937). A new physiological variable association with sensible and insensible perspiration. Amer. J. Phy8iol. 120, MaCUTCHAN, J. W. & TAYLOR, C. L. (1951). Respiratory heat exchange with varying temperature and humidity of inspired air. J. appl. Phy8iol. 4, MACHiLE, W. & HATCH, T. F. (1947). Heat: Man's exchanges and physiological responses. Physiol. Rev. 27, WOODcocK, A. H., PRATT, R. L. & BRECKENRIDGE, J. R. (1952). Heat exchange in hot environment. U.S. Quarterma8ter Clmatic RBe. Lab. Rep. No

Section 3.5 Thermal Comfort and Heat Stress

Section 3.5 Thermal Comfort and Heat Stress Table 3.6 Metabolic rate as a function of physical activity for a 70 kg adult man (abstracted from ASHRAE, 1997). activity metabolic rate (W) metabolic rate