Mechanisms for heat transfer

This chapter is theoretically relevant to Section R1(ii) of the 2023 CICM Primary Syllabus, which expects the trainees to "outline the mechanisms for heat transfer between the body and its environment". Question 20 from the second paper of 2016 asked about this in a way which was made more practical and clinically relevant by allocating 60% of the marks to a discussion of the relative importance of each mechanism in a sedated intubated adult patient.

  • The total heat transfer of a human is the same as the metabolic heat production, and is approximately 100 watts, or 400 kJ/hr, or 60-70 kcal/hr at rest.
  • It occurs by:
    • Radiation (50%)
    • Convection (30%)
    • Evaporation (20%)
    • Conduction (usually 0%)
  • Radiation is heat transfer by emission of IR-spectrum electromagnetic radiation,
    • Contributes about 50% of the total 
    • Relatively fixed and predictable
    • Dependent on
      • Emissivity of the skin (0.98, close to ideal black body)
      • Surface area of the skin
      • Temperature gradiant between the skin and the environment
  • Convection is heat transfer by conduction to a moving gas or liquid
    • Determined by:
      • Surface area of contact
      • Temperature gradient
      • Rate of flow for the gas or liquid
      • Temperature gradient between the body and the gas/liquid
      • Specific heat capacity and thermal conductivity of the gas or liquid (i.e. more heat transferred to water than to air)
  • Evaporation is loss of heat energy to the latent heat of vapourisation of water
    • Respiratory heat transfer usually contributes about 10%
    • (2% heating of inspired air, and 8% latent heat of vapourised lung water)
    • Determined by:
      • Rate of sweating
      • Ambient temperature pressure and humidity
      • Respiratory rate
      • Cardiac output
  • Conduction is the transfer of heat energy to a lower-temperature object by direct surface contact, and usually plays a minor role as humans are well insulated.
    • Determined by:
      • Surface area of contact
      • Temperature gradient
      • Thermal conductivity and specific heat capacity of the other object:
        •  0% of total heat transfer in a clothed individual (conduction to textiles and air is minimal)
        • 10-15% of total heat transfer in somebody collapsed on a cold concrete surface
        • 50% of total heat transfer in somebody immersed in cold water

Of the peer-reviewed resources available, there are multitudes, and many would be more than adequate for the purposes of the CICM exam candidate, which means to identify outstanding works as recommendations is even more important.  Santee & Gonzalez (1988) or Gagge & Gonzalez (2010) are by far the best, in terms of the level of detail available, the structure of the work, and the quality of the information synthesis presented by the authors. This should be surprising, as Adolf Pharo Gagge (1908-1993) was not around to write this 2010 article, but he did write the first version of that article in 1977, and contributed so extensively to the field that Richard R Gonzalez  only reworked the older paper and kept Gagge as the first author. The original 1977 paper was co-authored with Ysaunobu Nishi, who also wrote this excellent 1981 book chapter for Studies in Environmental Science. It's not at the top of the list purely because it would be hard to find.  

Heat transfer

Heat transfer, mass transfer and mechanical work are the three main ways in which energy can be exchanged between systems. Heat is defined as the change in thermal energy because of a temperature difference between systems, and mechanical work is defined as the change in kinetic or potential energy (which is just a larger better organised version of thermal energy). Heat is exchanged between systems when there is a temperature difference between them, until each system reaches an equilibrium with the others. The ways in which this happens are discussed below (conduction, convection, etc) but the net effect is that thermal energy is exchanged in some predictable way, and the following terms refer to this exchange:

  • Heat flux is energy per unit area per unit time, which represents the transfer of heat through a surface quantitatively, in watts per square metre, and is mostly determined by the thermal conductivity of the surface material. The heat flux of human skin, around the sternum (where this variable is most stable), is around 35-42 mW/cm2 according to experiments by de Rivera et al (2019). As a comparison, the heat flux of the sun, on a sunny day, is about 1 kW/m2, and anything in excess of 10 kW/m2 would be interpreted as unbearable scorching heat. 
  • Thermal conductivity is the measure of a material's ability to act as a medium for conductive heat transfer, and measured in watts per meter-kelvin., i.e. it describes how much heat is conducted for a given size of temperature gradient and material thickness. Materials with low thermal conductivity (eg. air) are poor media for heat transport. For human skin, the thermal conductivity is 0.187  W/mK, according to Xu et al (2008), which appears to be approximately the same as that of acrylic glass. For a bit of a comparison, diamond is generally viewed as the most thermally conductive material (2000 – 2200 W/mK). The lowest thermal conductivity, i.e. zero W/mk, would be something expected from a perfect vacuum.
  • Heat transfer coefficient is a "proportionality coefficient" between heat flux and the temperature difference, i.e. how much heat energy is exchanged when the difference is x and the heat flux is y.  It is calculated in watts per square metre per kelvin, and can be calculated for each type of heat exchange mechanism. For example, de Dear et al (1997) were able to calculate the radiative and convective heat transfer coefficients for adult humans, which were 4.5 W/m2/K and W/m2/K, respectively.

It is probably also useful to refer to another chapter for definitions of heat in general, as well as latent heat and specific heat, as these become important here. Latent heat is the thermal energy required to produce a phase change in a substance, which has special relevance to the sweaty human cooling by evaporation, as will be discussed below. Heat, wherever possible, will be presented here in joules, which is the official SI measurement unit for it, but because Deranged Physiology proudly wallows in antique references, anachronistic measurements are occasionally mentioned (eg. calories per kilogram per ten minutes, as used by Burch in 1945), and conversions are attempted with potential errors. Human metabolic activity is occasionally expressed in watts as this is convenient for engineering reasons, and one hour of one watt equates to approximately 3600 J (as 1W = 1J/s), or in kilocalories (kcal), where 1 kcal = 4186J (the energy required to raise the temperature of 1L of water by 1°C).

Definitions of convection conduction and radiation

In their comments to  Question 20 from the second paper of 2016, the examiners specifically remarked that they expected these terms to be used  "in the manner defined in the texts, rather than the layman’s use of the terms", presumably in response to those trainees who answered this SAQ using Joss Wheadon dialogue. This comment has made it difficult to move on without exploring exactly what kind of elevated dignified language each official text has used for the topic. Thus:

Middleton (2021, ch.4):

 

"Conduction: the flow of heat by conduction occurs via direct collisions between the atoms and molecules of warmer and cooler regions and the resultant transfer of kinetic energy."

"Convection: the transfer of heat from a body by the liquid or gas which surrounds it. The fluid has a tendency to rise if it is hotter because it is less dense; colder, denser material sinks under the influence of gravity."

"Radiation: hot bodies emit thermal energy in the form of electromagnetic radiation; this radiation is absorbed by the surroundings, resulting in heat transfer"

Boron & Boulpaep (2017, p.1195):

"Heat transfer by conduction occurs when the body touches a solid material of different temperature"

"Heat transfer by convection occurs when a medium such as air or water carries the heat between
the body and the environment."

"Heat transfer by radiation occurs between the skin and solid bodies in the environment. The infrared portion of the electromagnetic energy spectrum carries this energy"

Ganong (23rd ed., p.284):

"Conduction is heat exchange between objects or substances at different temperatures that are in contact with one another."

"Convection ... the movement of molecules away from the area of contact" [between objects or substances at different temperatures that are in contact with one another]

"Radiation is the transfer of heat by infrared electromagnetic radiation from one object to another at a different temperature with which it is not in contact"

Guyton & Hall, 13th ed, around p. 912-913 use H3-level chapter subheadings to give these definitions before explaining with examples. Incidentally, examining that pdf has revealed that the official Guyton & Hall font is Frutiger

"Conductive Heat Loss Occurs by Direct Contact With an Object."

"Convective Heat Loss Results From Air Movement"

"Radiation Causes Heat Loss in the Form of Infrared Rays."

Davis and Kenny (5th ed, p. 122), only give examples for everything other than conduction:

"Conduction is the process whereby heat energy is transmitted through a substance by the transfer of the energy of motion of the molecules to adjacent molecules"

There was no definition of these terms in Kam (2015), nor in Stoelting (2015), nor in The Physiology Viva of the vintage that happens to be in the author's possession, but perhaps that is for the best, as the reader will agree that these are all sufficiently similar that the individual wording becomes unimportant. In the general terms of physics, eg. from a textbook like Thermodynamics by Cengel (9th ed, 2019) 

"Conduction is the transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles.

Convection is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion, and it involves the combined effects of conduction and fluid motion.

Radiation is the energy emitted by matter in the form of electromagnetic waves"

Advection is often mentioned in various places, as an alternative mechanism, but on closer inspection advection and convection are really the same mechanism. Convection is the movement of a fluid or gas, whereas advection is the movement of some material dissolved or suspended in that fluid or gas, and so for the intents and purposes of human heat exchange it is entirely unimportant, being more useful for describing ocean currents.

The magnitude of total heat transfer in humans

One will have observed that humans do not spontaneously overcook by accumulating thermal energy from their metabolic processes, which means the total heat transfer out of the human must usually be roughly equal to the rate of heat production by the metabolism, as described by this classical equation:

S = (M + Wk) - (R + C + E + K)

where

  • S is total rate of storage of body heat
  • M is the metabolic energy production rate,
  • Wk is the rate of work
  • R is the rate of radiative heat transfer
  • C is the rate of convective heat transfer
  • E is the rate of evaporative heat transfer
  • K is the rate of conductive heat transfer)

Therefore, in order for S to be zero, the net rate of heat transfer (R + C + E) should be something like 60-70 kcal/hr at rest, which equates to around 400 kJ/hr or 10,500 kJ per day. Considering that 1W = 1J/s, 10,500 kJ per day equates to about 120 watts, and a round figure of 100 W per person is usually plugged into calculations for the heating and cooling design of public buildings. The assumptions made here are of course that this person is normal and is not squandering their metabolic energy on fruitless activities like running or cycling; because exercise can increase the total amount of heat being generated by a substantial amount (albeit for short periods). A table from Bansal et al (1994) gives a good set of ballpark figures to help the reader appreciate the sort of range of normal values one might expect to have to account for when building a large structure to shelter a group of humans:

Activity  Rate of heat production (W) (kJ/hr)
Sleeping 60 216
Resting quietly  80 288
Normal office work  100 360
Typing  150 540
Slow walking (3km/hr)  200 720
Fast walking (6km/hr)  250 900
Hard labour Over 300 Over 1080

How much "over 1080" can you get? When some kind of sustained energy output is being produced (a marathon run, extremely laboured breathing, or just relentless seizures), the upper limit of the energy production appears to be something like five times the normal basal metabolic rate, or around 50,000 kJ (a crude approximation from a whole series of exercise physiology studies involving abnormally athletic people). The relevance of this is that under various circumstances it is impossible for the heat transfer to perfectly match heat production, as there is obviously going to be some kind of maximum rate at which heat can be transferred out of the human body, and so the human body will increase in temperature. That maximum rate of heat transfer is strongly dependent on the range of factors that affect the efficiency of heat transfer mechanisms, which brings us to:

Proportion of heat transfer according to mechanisms

Textbooks generally like to offer ballpark figures for the proportions of heat transfer which occurs by the different mechanisms, and because these are presented as percentages, readers have a tendency to record and memorise them, attributing an increased meaning to something because it appears to have been measured. This is not an entirely misguided practice, and in fact will remain effective for as long as examiners continue to make the same error by attributing importance to these numbers in their marking rubrics. The exact numbers will obviously differ somewhat from resource to resource, as the question "how much heat does a person lose by each mechanism of heat transfer" can only be answered precisely if one specifies the conditions involved, and none of the textbooks do this. The following table was collected from a representative sample of official sources to demonstrate the range of reported values:

Textbook  Convection  Conduction  Radiation  Evaporation
Kam (2015) 15% 40-50% 30%*
Middleton (2021, ch.4): 30% 0% 40% 30%
Davis and Kenny (5th ed, p. 122): 30% 0% 40% 30%**
Ganong (23rd ed., p.284): 3%*** 70% 27%
Guyton & Hall, 13th ed 15% 3% 60% 22%

* plus 5% as respiratory loss, which is basically evaporation

** 20% evaporation + 8% respiratory evaporation and 2% heating of air

*** for Ganong, there is no convection, only respiration, urination and defecation

Obviously these mechanisms will make quite different contributions depending on the circumstances. One's evaporative and respiratory heat losses are going to be contributing more if one is sweating and panting like a dog, whereas if one is simply laying quietly on the bottom of a still pond, direct surface-to-surface heat conduction may play a dominant role instead. Each mechanism will also differ in their capacity to scale up or down as needed; for example it would usually not be possible to intentionally increase the conductive heat loss by maximising the contact between skin and conductor, because the skin is sensitive and the conductor is cold (i.e. this heat exchange solution would not be accepted for long). 

Conductive heat transfer in humans

Conduction, the transfer of heat energy between two systems which are in direct contact, usually plays very little role in the total thermal energy accounting of the normal healthy resting human, as normal healthy resting humans usually surround themselves with things that are especially unsuited for conduction. The thermal conductivity of most objects one would find oneself in persistent contact with is usually very low, if one thinks carefully about this; as one is usually clothed in some kind of  fabric, laying on some other kinds of fabric, suspended above a wooden bed on a mattress which is essentially 99% air. In fact generally textiles have an extremely high air content (92-77% according to Baxter, 1946), and because air has extrely poor thermal conductivity, the trapped air in the fabric becomes a dominant barrier to heat loss, making the conductive transfer of heat directly into these structures minimal. In case one is wondering, the thermal conductivities of some common materials  involved in preventing conductive heat loss are listed below:

  • Air: usually given as about 0.03 W/mK
  • Animal fur: 0.035 W/mK
  • Beard hair: 0.20 W/mK
  • Knitted hemp: 0.022 W/mK
  • Viscose: 0.031 W/mK
  • Linen: 0.043 W/mK
  • Cotton: 0.026–0.065 W/mK
  • Bamboo: 0.039–0.045 W/mK
  • Wool: 0.043–0.046 W/mK
  • Silk: 0.083 W/mK

In short, the thermal conductivity of most things a human being comes into contact with is relatively poor, which makes conductive heat loss among the least important mechanisms of heat transfer, at least under normal circumstances.  It is therefore usually either omitted entirely, or relegated to some position of comical unimportance, as for example in this hilarious image from Guyton & Hall, where a naked man is depicted conducting heat into his chair via his arse. The situation changes dramatically when the human in question is placed in a position where they are forced to remain in contact with a good thermal conductor. The thermal conductivity of concrete, for example, is 1.2 W/mK. Most human experience of being prostrate and exchanging heat with concrete is in the realm of accidental hypothermia, and so we do not have specific calorimetry figures for our species, but cruel animal experiments have revealed the effects of cold concrete floors on the bellies of cute newborn piglets, and the conductive heat loss from these was estimated as something like 15% of the total heat transfer, which would be probably representative for other similarly bellied mammals.

The reason this value is not greater is mainly related to surface area. Only a small fraction of a piglet is in contact with the floor; whereas an normal adult male has a surface area of something like 1.9 m2, and if all of this were in contact with a good thermal conductor, the rate of heat loss by conduction would be massive. This is what happens when a person is immersed in a body of water, which has a thermal conductivity of 0.6 W/mK. The specific heat capacity of water is also massive, which makes it an excellent sink for heat, i.e. as the immersed human continues to heat the surrounding water, the surrounding water does not increase in temperature very much, which maintains the temperature gradient and therefore facilitates heat transfer. Wu et al (2023) estimated that the loss of heat into water would be four times faster than into air of the same temperature. There does not appear to be any literature giving the value as a neat percentage figure, but plugging things into a calculator,  to cool a 70kg free diver from a core temperature of 37 to 35°C over one hour by immersion in  15°C water, one would have to be conducting away about 884 kJ of heat per hour (given a specific heat capacity for the diver's body is 2.98 kJ·kg−1·°C). If all the other mechanisms of heat transfer remain unchanged in their capacity, that would mean that 50% of the heat transfer for the immersed human would be occurring by conduction.

Irrespective of what surface you are in contact with, conductive heat transfer into and out of the human body is also limited by the thermodynamic properties of the human tissues. The body can be fairly neatly separated into a warm core and a cooler outer shell, which has known thermal conductivity properties. From Tarlochan et al (2005), these are:

  • Muscle: 0.5 W/mK
  • Subcutaneous fat: 0.19 W/mK
  • Dermis: 0.45 W/mK
  • Epidermis: 0.24 W/mK

This plays less of a role then one might think. When the US Army Research Institute of Environmental Medicine immersed twenty males in water baths of different temperatures, they found that the presence of a fat layer was a significant influence on the heat transfer, but that the vasoconstriction accounted for more of the difference, i.e. "under vasoconstriction the core mass can account for greater insulation than the fat mass". To rephrase again, the changes in convective heat exchange between the core and the skin are more important than the thermodynamic properties of the fat tissue itself. Which is a neat segue into:

Convective heat transfer in humans

Convection is merely conduction with extra steps. The specific added effect is the movement of the heated mass away from the skin surface, to be replaced by unheated mass. In this fashion the temperature gradient is preserved and the transfer of heat can continue. In some theoretical world, where air is fixed in place and remains still against the skin, the effect of heating it would have no additional properties beyond normal conductive heat exchange, so because air has such poor specific heat capacity and thermal conductivity, the only way a breeze can be said to cool you is by moving. 

Fortunately, air does not usually sit still, and even in the absence of large scale movement the warmed air will rise and circulation will occur. The complexity of the movements is mindboggling and to try to model them mathematically is to go mad. Clark (1981), for example, describes how a naked standing person has laminar flow of warmed air ascendig from their toes up until the centre of their abdomen, beyond which point it transitions into turbulent flow around the arms and head.

In short convective heat transfer is not easy to predict, and we mostly have empirical measurements to inform our appreciation of how much this contributes. For example, Colin & Houdas (1967) performed hot experiments involving gently blowing 15° C air directly onto nude subjects (with a wind speed of 1.2m/sec) and found that the rate of convective heat loss was something like 192-284 kJ/hr per m2 of naked surface area, or 60-70% of the total heat transfer. But this air was being moved by the investigators, whereas if it was still, the only movement would be due to the rise of warmed air and the sinking of cooling air, a phenomenon usually referred to as "natural convection", and occurring at a much lower air flow velocity, perhaps as low as 0.05m/s (Rapp, 1973). That would probably contribute a lot less. In the modern era, when it is much more socially acceptable to use a warmed mannequin instead of a naked volunteer, Kurazumi et al (2008) determined that the highest convective heat transfer coefficient was is something like 1.271 W/m2 K, as compared to the radiative heat transfer coefficient of 2.958 W/m2 K for the same posture (sitting cross-legged), which means that in still air, convection probably contributes 30% of the total heat transfer at most, and possibly even less if the subject is sweating and breathing (unlike the thermal mannequin in the study). Which is a helpful way to transition to a discussion of:

Heat transfer by evaporation

The attentive reader may point out that, if convection is just conduction with extra steps, then surely so is evaporation, as the thermal energy of the body is conducted to the droplets of sweat which are then carried away by air current. However, there is an important distinction between evaporation and convection. The thermal energy transferred to sweat is latent heat, i.e. the thermal energy is used to produce a phase change in the water, which turns to vapour without becoming any hotter. That is the definition of latent heat - it is the heat absorbed by a system which does not produce a change in temperature; and most reasonable people will agree that an unchanging temperature should be the objective of a thermoregulatory mechanism. As such, this is an essential part of the human thermoregulatory toolkit, and contributes considerably to the scalability of thermoregulatory responses, because we can choose how much sweat we produce. 

Heat transfer by sweat evaporation

Skin is not 100% dry, and threatens to lose moisture constantly, as we are sometimes reminded by an entirely parasitic industry. How much evaporation occurs from the skin under normal circumstances? Gagge & Gonzalez give the combined rate of water loss from the body, occasionally referred to as an "insensate" loss because we usually have no way of measuring it precisely, as 0.5ml per minute, though apparently your sweat glands can ramp this up to 25-30ml/min for short bursts of intensely sweaty activity.  As the latent heat vapourisation of water is 40.8 kJ/mol and one mole of water is 18.014g, and sweat is sufficiently similar to water that they can be considered the same substance,  this slow boil can be expected to produce a loss of 1.132 kJ per minute, or about 68 kJ per hour. This figure is of course so highly dependent on other factors as to be entirely meaningless. Body surface temperature, rate of metabolic heat production, ambient temperature pressure and humidity, air flow, exchange of heat in the cutaneous circulation, and the presence of clothing - all of these would adjust this figure. 

As is the custom for Deranged Physiology, the presence of such an abundance of variables leads down the path towards finding extreme examples at the edges of a range of values. At one end, we can find the minimal heat transfer through sweat vapour, which would obviously be 0 kJ/hr, and which would occur if the ambient conditions did not allow any evaporation to take place. That would occur at 100% relative humidity, where the water vapour in the air is in equilibrium with the liquid phase of water on the skin. In this scenario no evaporation is possible, and therefore the latent heat of vapoursation cannot be exploited to achieve heat loss. If this were occurring at a temperature higher than the human body surface temperature, which is around 35 °C, the effect would be an exchange of heat into  the human, which would result in hyperthermia and unpleasantness. This  35°C threshold for "wet bulb temperature" was modelled and popularised as the limit of human survival by Sherwood & Huber (2010), who went on to point out that we have (had?) about a 5% chance of achieving this level of warming (7-10 °C globally) over the course of the twenty-first century. 

On the other extreme edge of this range, the maximum amount of sweat that can be produced to cool a hard-working human seems to be truly stupendous. Of the experimental models, the sweatiest seems to have been the study subjects of the Rochester Desert Unit, documented by Adolf (1947), unavailable to the casual internet user but quoted by Torii (1995) as reporting something like 3700 ml/hr from soldiers working in the Californian sun. Assuming perfectly dry airflow (0% humidity) and assuming that all of that sweat had evaporated politely instead of just dripping everywhere, the latent heat of vapourisation disposed of through 3.7L of sweat would be something like 8380 kJ. That might sound like a completely unrealistic figure, but real official textbook chapters (eg. Gafnon & Crandall, 2018) also quote theoretical heat loss rates of 1000-1700 watts, or 3600-6120 kJ/hr. The qualifying factor here is that the conditions required to produce such efficiency are unlikely to ever occur in nature (the abovementioned authors continue that,. "for humans to lose a similar amount of heat through dry exchange would require standing outside, naked, in a 2 mph wind during the coldest day ever recorded in the United States").

Respiratory heat transfer

Sweat is not the only body fluid that can evaporate. Lungs and the respiratory tract offer a large evaporative surface area, and contribute to the loss of water and heat, which produces the need to incorporate specialised equipment that would defend their heat and moisture from the mechanical ventilator.  Most resources separate the heat loss by evaporation of sweat from the heat loss by evaporation of respiratory gases, even though they are probably very similar from a physics perspective. The heat and moisture exchange that occurs via the nasopharynx humidifies and then again dehumidifiers the inhaled air, which results in heat loss by convection (the air itself is heated and then exhaled) as well as evaporation (the loss of alveolar and respiratory tract water). The exact amount of heat lost will again depend on numerous ambient factors as well as whether or not you are breathing through your mouth, what the minute volume is, and the cardiac output (as this is what

delivers the water to the lungs for evaporation).

How much does the heating of the air itself contribute? Probably very little, the attentive reader would readily answer, as air has an extremely poor specific heat capacity. To raise the temperature of a single gram of air requires around 1.0035 joules per every kelvin of temperature increase, which means to go from 21 to 37 °C for a normal 500ml tidal volume (which weighs about 0.6465g) requires 10.38J. Assuming a respiratory rate of twelve breaths per minute, and assuming that all of this air ends up heated to body temperature and none of the heat is reclaimed, this would give a total heat transfer rate of 7.47 kJ/hr, or less than 2% of the total heat energy output of a sleeping person. This would obviously scale according to minute volume, but the overall contribution would remain minimal, as the higher minute volume would require a higher metabolic activity and therefore more heat production.

How about the contribution of the latent heat of vapourisation of lung water? Making some of the same assumptions as above, a normal 500ml tidal volume ends up with 0.0235g (1.3 mmol) of water evaporated into it, which has a latent heat of 53.04 joules. The rate of heat transfer by this mechanism is therefore something like 38.188 kJ/hr, or about  8% for a quietly resting person. 

These are of course calculations based on a series of assumptions, but they seem to correspond to the values quoted in an official CICM textbook (Davis & Kenny), and there seems to be some experimental data to support them. Burch (1945), a widely quoted study of "subjects ... normal and experienced around laboratories and included both sexes and the white and Negro races", gave a value of 10-15 W for the total heat transfer by resting tidal respiration, or 36 kJ/hr which ends up being about 10-15% of the total resting heat transfer. On the other hand, Cain et al (1990) ended up with values closer to 25-30%. 

Radiative heat transfer in humans

Thermal energy can be emitted directly out of any matter which is not at the temperature of absolute zero. These emissions are in the form of electromagnetic radiation, released when a charged particle in the matter decelerates. Most textbooks give a handwave to this mechanism before moving on, which produces a great sadness in anybody fascinated by the internal workings of the universe. Without driving the reader insane with half-remembered highschool physics, the short explanation is that the generation of electromagnetic radiation requires the presence of an oscillating dipole (a pair of opposing electric charges that vary sinusoidally with time, such that at any given moment the two charges have equal magnitude but an opposite sign). Molecules and atoms, with their unevenly distributed surface charge, produce these kinds of dipoles when they vibrate chaotically (i.e have thermal energy). In this case the instantaneous and transient local concentrations of electron charges are the origins of the momentary and fleeting dipole emitter. This is the case for gases,  liquids and amorphous matter like protein, whereas in a lot of crystalline solid matter the source of these dipoles are often  "lattice vibrations" which can be conceptualised as waves in a sea of swarming electrons that surrounds the orderly array of atoms in a crystal lattice.

A charged particle at rest, eg. an electron], creates an electric field, and a moving electron is a current, which creates a magnetic field; which means an accelerating electron  (eg. rotating or changing velocity) produces changes in the electric and magnetic field that surround it. Thus, the movement of charge produces electromagnetic waves where electric and magnetic field vectors all are vibrating perpendicular to one another. This is the emitted photon.  Without getting into the wild woods of radiation physics, the wavelength of the emitted photon is determined by Planck's Law, which states that the higher the energy of the dipole (i.e the temperature), the higher the energy of the emitted photon, i.e the shorter the frequency of that photon. An object would have to be extremely hot to emit radiation with a frequency high enough to be in the human-visible spectrum, and for the non-burning human body most molecular and atomic dipoles end up emitting photons of a frequency in the mid-infrared region, mainly at the wavelength of around 10-12 microns. Incidentally, considering all the action potentials and other ionic activity around the human body, it is unsurprising that it is a rich source of other electromagnetic waves, emitting even visible light (albeit at a very low intensity). 

Without any further digression, the human body radiates heat in the form of IR-spectrum electromagnetic waves, and it does this completely involuntarily, nor can it stop, nor can it make any major adjustments to the rate, as the variables in the equation that describes this radiation are generally not under our control. The factors that determine the rate of heat transfer by radiation from the human body are described by the Stefan-Boltzmann law, as follows:

QR = σ × ε × (Te4 - Ts4) × A

where

  • QR is the radiated heat in joules per second per m2 , or watts per m2
  • σ is the Stefan-Boltzmann constant
  • ε is the emissivity of the surface,
  • Te is the temperature of the environment
  • Ts is the temperature of the skin,
  • A is the surface area

As one may note, none of these are readily modifiable in any meaningful way. The human body surface area remains fairly stable, the emissivity of the human skin is fixed (0.98) and varies very little even in people of different skin colour, and the Stefan-Boltzmann constant is an immutable property of the cosmos. Thus, the radiative heat transfer in humans can only really be regulated by changing the temperature of the skin, which is controlled by skin perfusion. Increasing the perfusion of the skin can increase the amount of heat it radiates, but only trivially, as all skin perfusion can do is bring the temperature of the skin closer to the temperature of the core, i.e up by about 2 °C. Even though the  temperature variable in the equation is elevated to the fourth power, which means small temperature differences could still have substantial effects on the total heat transfer, the range of human temperatures is so narrow that most authors can confidently give a figure (4.7 W/m2K) and be reasonably correct irrespective of how febrile the patient. 

Obviously people are not usually surrounded by objects which are at a temperature of absolute zero, which means that the environment is also constantly irradiating back, transferring heat in the opposite direction, and the net balance of the back-and-forth heat trading is generally a loss of heat in the direction of the temperature gradient. This was the basis of the genius experiment by Colin & Houdas (1967), who could not measure the radiation directly, and who chose to eliminate them from the calculations by making the walls of their climate chamber the same temperature as the subject's skin. The values they measured for radiative heat loss, when the surrounding temperature was a comfortable 20 degrees or so,  was something like 125 kJ/m2/hr, or around 240 kJ/hr for a person with a normal body surface area of around 1.9m2. This means that the heat transfer by radiation contributed approximately 50% of the total heat transfer in that particular experiment, which seems like a representative value, and matches what is seen in the college textbooks.

Emissivity of the human skin

Emissivity, the property of surfaces which describes their ability to emit radiation (usually specific to a waveform or type of radiation), is a dimensionless number between 0 and 1, where 0 is a perfect reflector and 1 is a perfect emitter. The high emissivity of human skin (usually given as 0.98) is often touted as its great advantage, a triumph of thermoregulatory ability which allows the skin to be a near-perfect blackbody radiator.  This is in fact not a unique property, and most materials other than pure metals have an extremely high emissivity in the infra-red spectrum, including ice (0.99), paper (0.98), concrete (0.95), glass (0.95) and wood (0.9). It is in fact difficult to find examples of poor infra-red emissivity in the natural world. 

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