Meaningful wind chill indicators derived from heat transfer principles

The wind chill index (WCI) and the more widely used wind chill equivalent temperature represent an attempt to combine several weather-related variables (temperature, wind velocity and solar radiation) into a single index which can indicate human comfort. Since its introduction in 1945, the WCI has been criticized mainly on the ground that the underlying model does not comply with modern heat transfer theory. In spite of that, the WCI, calibrated to human comfort, has proven to be successful in predicting discomfort and tolerance of man to the cold. Nevertheless, neither the WCI nor the wind chill equivalent temperature can be actually measured and, therefore, without the additional calibration they are meaningless. In this study we have shown that the WCI represents the instantaneous rate of heat loss from bare skin at the moment of exposure to the cold, and as such, it correlates reasonably well with measurable variables that represent a feeling of cold. Two new wind chill indicators have been introduced: exposed skin temperature and maximum exposure time. These indicators yield more information than the WCI provides, are measurable, have physical meaning and are based on established heat transfer principles.     

Paradox: increased blood perfusion to the face <Emphasis Type="BoldItalic">enhances</Emphasis> protection against frostbite while it <Emphasis Type="BoldItalic">lowers</Emphasis> wind chill equivalent temperatures

A model of facial heat exchange in cold and windy environments is presented. The tissue is depicted as a hollow cylinder and the model includes heat conduction and heat transport by blood circulation from the warmer core. A steady-state solution facilitating the estimation of wind chill equivalent temperature (WCET) as a function of the effective wind velocity, air temperature and blood perfusion rate was obtained. The results quantify and demonstrate the elevation of skin temperatures caused by increased flow of warmer blood from the inner core to the face. Elevated facial temperatures, while enhancing protection against frostbite and other cold-related injuries, also increase heat loss to the colder environment. Paradoxically, such elevated facial temperatures cause WCETs, as estimated by the prevailing definition, to attain lower rather than higher values, indicating, in fact, increased risk of frostbite. The results of this study should be useful in understanding and quantifying the effects of blood perfusion in protection against cold-related injuries. They should also be considered in the re-evaluation and re-formulation of the concept of wind chill, which has been a useful cold weather indicator for decades.     

Convective and radiative components of wind chill in sheep: Estimation from meteorological records

Wind chill is defined as the excess of sensible heat loss over what would occur at zero wind speed with other conditions unchanged. Wind chill can be broken down into a part that is determined by air temperature and a radiative part that comprises wind-dependent effects on additional long-wave radiative exchange and on solar radiation (by reducing solar warming). Radiative exchange and gain from solar radiation are affected by changes that are produced by wind in both surface and fleece insulations. Coefficients are derived for (a) converting the components of sensible heat exchange (air-temperature-dependent including both convective and associated long-wave radiative, additional long-wave radiative and solar) into the components of the total heat loss that are associated with wind and (b) for calculating equivalent air temperature changes. The coefficients contain terms only in wind speed, wetting of the fleece and fleece depth; these determine the external insulation.Calculation from standard meteorological records, using Plymouth and Aberdeen in 1973 as examples, indicate that in April–September 1973 at Plymouth reduction in effective solar warming constituted 28% of the 24-h total wind chill, and 7% in the other months of the year combined; at Aberdeen the corresponding percentages were 25% and 6%. Mean hour-of-day estimates for the months of April and October showed that at midday reduction in solar warming due to wind rose to the order of half the air-temperature-dependent component of wind chill, with a much smaller effect in January. For about six hours at midday in July reduction in solar warming due to wind was similar in magnitude to the air-temperature-dependent component.It is concluded that realistic estimates of wind chill cannot be obtained unless the effect of solar radiation is taken into account. Failure to include solar radiation results not only in omitting solar warming but also in omitting the effects of wind in reducing that warming.The exchange of sensible (non-evaporative) heat loss between a homeothermic animal and its environment can be divided into two parts: one part is due to the temperature difference between the animal and the surrounding air, and the other part is due to additional long-wave radiative exchange between animal and environment and to solar radiation. Both parts of the heat exchange are determined in magnitude by the animal's thermal insulation, which is itself affected by windspeed and wetting. Wind diminishes as animal's external insulation, so increasing heat loss under all conditions when the air temperature is lower than the animal's surface temperature: this effect is termed wind chill. Wind chill has previously been investigated more commonly in relation to man (Burton an Edholm, 1955; Smithson and Baldwin, 1978; Mumford, 1979; Baldwin and Smithson, 1979). This paper is concerned with the separate contributions to wind chill calculated for sheep that can be associated with convective and radiative heat exchanges.     

The calculation from weather records of the requirement for clothing insulation

Standard meteorological measurements of dry bulb temperature, wind speed, sunshine, cloud cover and rainfall are used to calculate the clothing insulation required by man for thermal comfort under given weather conditions. The calculation is based on earlier work on the effect of weather on sensible (non-evaporative) heat loss from sheep, which used the relation between heat flow, thermal insulation and the difference between body and environmental temperatures.Clothing insulation for man is estimated in two ways: as clothing (I_c) that is impervious to the effects of wind and rain; and as the equivalent depth of sheep fleece (f_m), which is not impervious. This allows the assessment of wind chill for a range of clothing of varied penetration by wind instead of for only one type of garment.Results are given as daily means calculated from hourly measurements throughout 1973 for Plymouth (on the south coast of Britain) and Aberdeen (on the far northeast coast of Britain). Wind chill is estimated both by its effect on f_m requirement and by the fall in air temperature that would be needed to produce under still-air conditions the same demand for f_m that occurs in the actual environment. The monthly mean f_m requirement is reduced by about 40% when the effect of wind is removed. When wind chill is estimated as an equivalent fall in air temperature it approximates to 1 K per knot wind speed measured at the standard meteorological height of 10 m.     

Face cooling by cold wind in walking subjects

The effects of low to moderate wind speeds on face temperature, thermal and pain sensations while subjects walked on a treadmill during cold exposure were studied in eight healthy men. The purpose of the study was to evaluate further the risk of frostbite at different activity levels. The walking speed was 2.8 km h(-1) and two inclination levels were used, 0 degrees and 6 degrees. The subjects were exposed to -10 degrees C and 0, 1 or 5 m s(-1) wind for 60 min dressed in cold-protective clothing with only the face unprotected. Results from previous experiments with the same subjects standing for 30 min were included in the analysis of the data. Each individual was exposed to all combinations of air velocity and activity level. The exposure to -10 degrees C and the highest wind speed used would carry no risk of frostbite according to the wind chill index. Cold lowered the skin temperature of the face significantly and wind further increased skin cooling. The activity level did not affect forehead and cheek temperatures, but the average nose skin temperature was higher and pain sensations were reduced at a higher work rate. The predicted risk of frostbite in the nose, based on average responses, would thus be less at a higher work rate. However, the results indicate that exercise does not necessarily protect all individuals from frostbite at moderate air speeds, since the nose skin temperature of 25% of the subjects dropped to 0 degrees C at 5 m s(-1) during both standing and walking. Thus the potential individual risk of frostbite in the nose is similar during light exercise and standing. Moreover, the risk of frostbite seems to be underestimated by the wind chill index under the conditions tested in this study.     

A parametric study of wind chill equivalent temperatures by a dimensionless steady-state analysis

A first order analytical approximation of steady-state heat conduction in a hollow cylinder exchanging heat at its external surface by convection with a cold and windy environment is presented. The model depicts the thermal behavior of certain body elements, e.g., head/face, when exposed to such environments. The results are presented by dimensionless parameters and facilitate the estimation of wind chill equivalent temperatures (WCETs). The effects of several variables on determining WCETs were studied using specific examples, leading to the following generalizations: (1) the conditions assumed for "calm" wind speed appear to be a dominant factor in determining WCET; (2) the effects, on both (skin) surface temperature and on WCET, of a 1°C change in environmental temperature appear to be more pronounced than those of a 1 m/s change in wind speed; (3) similarly, predicted WCETs are more sensitive to the geometrical dimensions assumed for the modeled entity than they are to wind speeds; and (4) tissue thermal conductivity, the angle at which the convective heat transfer coefficient is measured relative to wind direction, and the factor used to establish "effective" wind speeds in the domain occupied by humans relative to reported values, all seem to have relatively small effects on the determination of WCET. These conclusions strongly suggest, among other things, that for any given combination of environmental conditions, wind chill indices may best be presented as ranges rather than as single values. This seems to apply even when worst-case scenarios are considered. Also emphasized is the need for careful and realistic selection of all the parameter values used in the determination of WCETs.     

Modeling conductive cooling for thermally stressed dairy cows

Conductive cooling, which is based on direct contact between a cow lying down and a cooled surface (water mattress, or any other heat exchanger embedded under the bedding), allows heat transfer from the cow to the cooled surface, and thus alleviate heat stress of the cow. Conductive cooling is a novel technology that has the potential to reduce the consumption of energy and water in cooling dairy cows compared to some current practices. A three-dimensional conduction model that simulates cooling thermally-stressed dairy cows was developed. The model used a computational fluid dynamics (CFD) method to characterize the air-flow field surrounding the animal model. The flow field was obtained by solving the continuity and the momentum equations. The heat exchange between the animal and the cooled water mattress as well as between the animal and ambient air was determined by solving the energy equation. The relative humidity was characterized using the species transport equation. The conduction 3-D model was validated against experimental temperature data and the agreement was very good (average error is 4.4% and the range is 1.9–8.3%) for a mesh size of 1117202. Sensitivity analyses were conducted between heat losses (sensible and latent) with respect to air temperature, relative humidity, air velocity, and level of wetness of skin surface to determine which of the parameters affect heat flux more than others. Heat flux was more sensitive to air temperature and level of wetness of the skin surface and less sensitive to relative humidity.     

Prediction of temperature profiles in the human skin and subcutaneous tissues

Exact mathematical solutions in terms of confluent hypergeometric and Airy's functions are obtained to study the steady state temperature distributions in human skin and subcutaneous tissues (SST). It is assumed that the skin is exposed to an air environment and heat transfer from the skin occurs by convection, radiation and evaporation. A mathematical model of the SST, accounting for heat conduction, perfusion of the capillary beds and metabolic heat productions of the dermis and subcutaneous tissues, has been solved to obtain interface temperatures for a wide range of environmental temperatures, rates of evaporation of sweat, wind speeds and relative humidities. The solutions provide inter-relationships between interface temperatures, thermal conductivities, metabolic heat production, blood perfusion, thicknesses of various layers of SST and ambient temperature.     

The perceived temperature – a versatile index for the assessment of the human thermal environment. Part A: scientific basics

The Perceived Temperature (PT) is an equivalent temperature based on a complete heat budget model of the human body. It has proved its suitability for numerous applications across a wide variety of scales from micro to global and is successfully used both in daily forecasts and climatological studies. PT is designed for staying outdoors and is defined as the air temperature of a reference environment in which the thermal perception would be the same as in the actual environment. The calculation is performed for a reference subject with an internal heat production of 135 W m⁻² (who is walking at 4 km h⁻¹ on flat ground). In the reference environment, the mean radiant temperature equals the air temperature and wind velocity is reduced to a slight draught. The water vapour pressure remains unchanged. Under warm/humid conditions, however, it is implicitly related to a relative humidity of 50%. Clothing is adapted in order to achieve thermal comfort. If this is impossible, cold or heat stress will occur, respectively. The assessment of thermal perception by means of PT is based on Fanger’s Predicted Mean Vote (PMV) together with additional model extensions taking account of stronger deviations from thermal neutrality. This is performed using a parameterisation based on a two-node model. In the cold, it allows the mean skin temperature to drop below the comfort value. In the heat, it assesses additionally the enthalpy of sweat-moistened skin and of wet clothes. PT has the advantages of being self-explanatory due to its deviation from air temperature and being—via PMV—directly linked to a thermo-physiologically-based scale of thermal perception that is widely used and has stood the test of time. This paper explains in detail the basic equations of the human heat budget and the coefficients of the parameterisations.     

哺乳动物毛被传热性能及其影响因素

毛被能够加强或减弱动物向周围环境的热量散失,毛被的形态结构和颜色是传热性能的决定因素,其传热过程往往是传导、对流和辐射3个过程的耦合。以往研究发现环境因子中,风可增加机体向环境中的散热速率,且散失量与风速正相关,且动物通过调节在风场中的姿态来适应不同风向。动物体与环境间的温差是影响散热速率的另一因素,不同环境中的动物通过改变毛被结构来适应温差变化。毛被含水率上升会引起导热和蒸发冷却作用加强,动物通过行为或毛被结构变化来调节毛被含水率。毛色决定毛被吸收和反射热辐射的能力。毛被传热性能直接把动物的生理特点与环境因子关联起来,这对揭示动物的适应、进化都具有重要意义。同时提出,毛被结构和传热性能的研究还有助于仿生学意义的挖掘。因此,今后应重点在毛被结构和物理性能、研究技术与方法以及毛被生物学和仿生学意义等方面开展研究。     

Simulation of sensible and latent heat losses from wet-skin surface and fur layer

A simulation model that simultaneously calculates heat and mass transfer from a wetted skin surface and fur layer of a cow is presented. The model predicts evaporative, convective and radiant heat losses for different levels of skin and fur wetness, air velocity, air temperature and relative humidity. In the model, fur layer (hair coat) properties such as fur thickness and hair density assumed are that of summer conditions. Evaporative cooling from wet-skin surface and hair coat is the dominant mode of heat mitigation mechanism in stressful hot environments and is further enhanced by increased air velocity. Evaporative cooling is, however, depressed by increased relative humidity because of deficit of water-vapor concentration between the skin surface and ambient air.     

Effects of metabolic rate on thermal responses at different air velocities in -10 degrees C

The effects of exercise intensity on thermoregulatory responses in cold (-10 degrees C) in a 0.2 (still air, NoWi), 1.0 (Wi1), and 5.0 (Wi5) m x s(-1) wind were studied. Eight young and healthy men, preconditioned in thermoneutral (+20 degrees C) environment for 60 min, walked for 60 min on the treadmill at 2.8 km/h with different combinations of wind and exercise intensity. Exercise level was adjusted by changing the inclination of the treadmill between 0 degrees (lower exercise intensity, metabolic rate 124 W x m(-2), LE) and 6 degrees (higher exercise intensity, metabolic rate 195 W x m(-2), HE). Due to exercise increased heat production and circulatory adjustments, the rectal temperature (T(re)), mean skin temperature (Tsk) and mean body temperature (Tb) were significantly higher at the end of HE in comparison to LE in NoWi and Wi1, and T(re) and Tb also in Wi5. Tsk and Tb were significantly decreased by 5.0 m x s(-1) wind in comparison to NoWi and Wi1. The higher exercise intensity was intense enough to diminish peripheral vasoconstriction and consequently the finger skin temperature was significantly higher at the end of HE in comparison to LE in NoWi and Wi1. Mean heat flux from the skin was unaffected by the exercise intensity. At LE oxygen consumption (VO2) was significantly higher in Wi5 than NoWi and Wi1. Heart rate was unaffected by the wind speed. The results suggest that, with studied exercise intensities, produced without changes in walking speed, the metabolic rate is not so important that it should be taken into consideration in the calculation of wind chill index.     

A model of evaporative cooling of wet skin surface and fur layer

(1) A theoretical model that simultaneously solves heat and mass transfer in a wet skin surface and fur layer that occurs when an animal is cooled by blowing air over its wetted skin surface and hair coat is presented. (2) The model predicts evaporative and convective heat losses for different levels of wetness, air velocity, ambient temperature, relative humidity and fur properties. (3) Model predictions provide insight about evaporative and convective cooling processes of cows in stressful hot environments.     

Modified wind chill temperatures determined by a whole body thermoregulation model and human-based facial convective coefficients

Wind chill equivalent temperatures (WCETs) were estimated by a modified Fiala’s whole body thermoregulation model of a clothed person. Facial convective heat exchange coefficients applied in the computations concurrently with environmental radiation effects were taken from a recently derived human-based correlation. Apart from these, the analysis followed the methodology used in the derivation of the currently used wind chill charts. WCET values are summarized by the following equation: $$ \mathrm{WCET}=12.87+0.5334\ast {T}_o-\left(12.66-0.4414\ast {T}_o\right)\ast {U}_{reported}{}^{0.1228} $$ Results indicate consistently lower estimated facial skin temperatures and consequently higher WCETs than those listed in the literature and used by the North American weather services. Calculated dynamic facial skin temperatures were additionally applied in the estimation of probabilities for the occurrence of risks of frostbite. Predicted weather combinations for probabilities of “Practically no risk of frostbite for most people,” for less than 5 % risk at wind speeds above 40 km h^?1, were shown to occur at air temperatures above ?10 °C compared to the currently published air temperature of ?15 °C. At air temperatures below ?35 °C, the presently calculated weather combination of 40 km h^?1/?35 °C, at which the transition for risks to incur a frostbite in less than 2 min, is less conservative than that published: 60 km h^?1/?40 °C. The present results introduce a fundamentally improved scientific basis for estimating facial skin temperatures, wind chill temperatures and risk probabilities for frostbites over those currently practiced.     

Convective heat transfer measured directly with a heat flux sensor

A heat flux disk has been developed that directly measures the convective heat transfer in W/m2. When the sensor is calibrated on an aluminum cylinder, the calibration constant obtained is greatest in still air. As air movement increases, the calibration constant is reduced with increasing convective heat transfer coefficient, 0.5%.W-1.m2.K. The influence of wind on the calibration value is greatly reduced when the sensor is attached to a surface with lower thermal conductivity. The local convective heat transfer coefficient (hc) of the human body was measured. The leg acts in a manner similar to that of a cylinder, with the highest hc value at the front facing the wind and the lowest approximately 90 degrees from the wind, and in the wake a value is obtained that is close to the average hc value of the leg. When hc is measured at several angles and positions all over the body, the results indicate that the body acts approximately as a cylinder with a hc value related to the wind speed as hc = 8.6.v0.6 W.m-2.K-1, where v is velocity.     

TLV in cold environments

1. 1. The risks encountered during cold exposure are general body cooling or local cooling of parts of th body.

2. 2. Measures of cold stress must account for the effects of climate, clothing and metabolic heat production on heat balance.

3. 3. The combinaed effect of air temperature, mean radiant temperature, humidity and air velocity determines the cooling power of the environment.

4. 4. The cooling power can be easily converted into a required insulation value (IREQ) for whole body heat balance.

5. 5. Extensive cooling of hands and feet may be a limiting factor, even when sufficient total insulation is provided. In addition the cooling effect of wind on unprotected skin must be considered.

6. 6. Recommendation regarding acceptable exposures can be expressed as lowest ambient temperatures and time limits as function of available protection and activity level, with due attention to both general and local effects.

A canine thermal model for simulating temperature responses of military working dogs

Military working dogs (MWDs) are often required to operate in dangerous or extreme environments, to include hot and humid climate conditions. These scenarios can put MWD at significant risk of heat injury. To address this concern, a two-compartment (core, skin) rational thermophysiological model was developed to predict the temperature of a MWD during rest, exercise, and recovery. The Canine Thermal Model (CTM) uses inputs of MWD mass and length to determine a basal metabolic rate and body surface area. These calculations are used along with time series inputs of environmental conditions (air temperature, relative humidity, solar radiation and wind velocity) and level of metabolic intensity (MET) to predict MWD thermoregulatory responses. Default initial values of core and skin temperatures are set at neutral values representative of an average MWD; however, these can be adjusted to match known or expected individual temperatures. The rational principles of the CTM describe the heat exchange from the metabolic energy of the core compartment to the skin compartment by passive conduction as well as the application of an active control for skin blood flow and to tongue and lingual tissues. The CTM also mathematically describes heat loss directly to the environment via respiration, including panting. Thermal insulation properties of MWD fur are also used to influence heat loss from skin and gain from the environment. This paper describes the CTM in detail, outlining the equations used to calculate avenues of heat transfer (convective, conductive, radiative and evaporative), overall heat storage, and predicted responses of the MWD. Additionally, this paper outlines examples of how the CTM can be used to predict recovery from exertional heat strain, plan work/rest cycles, and estimate work duration to avoid overheating.     

Computer-based analysis of steady-state and transient heat transfer of small-sized leaves by free and mixed convection

In order to study convective heat transfer of small leaves, the steady‐state and transient heat flux of small leaf‐shaped model structures (area of one side = 1730 mm²) were studied under zero and low (= 100 mm s^?1) wind velocities by using a computer simulation method. The results show that: (1) distinct temperature gradients of several degrees develop over the surface of the model objects during free and mixed convection; and (2) the shape of the objects and onset of low wind velocities has a considerable effect on the resulting temperature pattern and on the time constant τ. Small leaves can thus show a temperature distribution which is far from uniform under zero and low wind conditions. The approach leads, however, to higher leaf temperatures than would be attained by ‘real’ leaves under identical conditions, because heat transfer by transpiration is neglected. The results demonstrate the fundamental importance of a completely controlled environment when measuring heat dissipation by free convection. As slight air breezes alter the temperature of leaves significantly, the existence of purely free convection appears to be questionable in the case of outdoor conditions. Contrary to the prognoses yielded by standard approximations, no quantitative effect of buoyancy on heat transfer under the considered conditions could be detected for small‐sized leaf shapes.     

Advances,shortcomings, and recommendations for wind chill estimation

This article discusses briefly the advances made and the remaining short-comings in the "new" wind chill charts adopted in the US and Canada in 2001. A number of indicated refinements are proposed, including the use of whole body models in the computations, verification of heat exchange coefficients by human experiments, reconsideration of "calm" wind conditions, reconsideration of frostbite threshold levels, the inclusion of cold-related pain and numbness in the charts, etc. A dynamic numerical model is applied to compare the effects of wind speeds, on the one hand, and air temperatures, on the other, on the steady-state exposed facial and bare finger temperatures. An apparent asymmetry is demonstrated, favoring the effects of wind speeds over those of air temperatures for an identical final facial temperature. This asymmetry is reversed, however, when SI unit changes in these quantities are considered.     

An evaluation of heat exchange in small birds

Summary Equations are derived that quantify the component thermal resistances to heat transfer in small birds and account explicity for the effects of variation in these resistances. Heat transfer theory is used to quantify external resistances, and an experiment was conducted to estimate body resistance (r _b, plumage plus tissues) as a function of external temperature and wind speed. The value ofr _b decreased with wind speed, and decreased as air temperature approached 0°C. Heat transfer from small birds is shown to be relatively independent of external resistances and mainly dependent onr _b. The predictions of the new theoretical equations are shown to agree well with existing empirical data.