OTTO-VON-GUERICKE-UNIVERSITY MAGDEBURG
Departement of Process and System Engineering
Institute of Fluid Dynamics and Thermodynamics
Prof. Dr.-Ing. E. Specht
Humans as heat technical reactor
Contents
1.
2.
3.
4.
5.
6.
7.
8.
Introduction
Operating temperature of humans
Measuring system
Mechanism of the heat emission
Amount of heat release
Energy balance of humans
Individual energy consumption
Warmth comfort of humans
Magdeburg, July 2004
1.
Introduction
Humans are from a technical view a biological reactor with an operating temperature of 37
°C. Since the environmental temperature of humans is lower, they constantly deliver heat.
Therefore energy must be produced constantly by internal oxidation (combustion). As for
each combustion process humans also produce waste materials. These are solid, liquid and
gaseous, whereby for each of these three types of refuse a separate exit exists. The gaseous
emissions distribute themselves however occasionally in two exits. In the following the
energy balance is the feature not the waste problem. The energy balance and thus the human
weight as well as the figure are subject to physical laws and can be explained with the first
law of thermodynamics. Humans react extremely sensitively to changes of its operating
temperature. Therefore it possesses a complex measuring and control system. This is
explained first.
2.
Operating temperature of humans
The reactions in the human body are adjusted to a core temperature of 37 °C with a tolerance
of approximately ± 0.5 Kelvin (degrees). It is warmest in the liver and in the kidney, where
the most intensive chemical reactions take place, the colded is the skin, which is colder about
4 to 7 Kelvin (degrees). Humans are very sensitive to internal variations in temperature. For
example, the most sensitive organ, the brain, breaks down at temperatures above 40,5 °C and
below 35 °C. Starting from a temperature of 41 °C the protein structures begin to deform and
destroy the tissue. At a temperature of 34 °C the logic diminishes and one loses speech.
Below 33 °C the metabolism is reduced and the ability of the thermal regularization is lost.
Then there is mortal danger. At 27 °C one becomes inmobile and at 25 °C as consequence of
insufficient respiration death occurs.
3.
Measuring system
For the perception of the body’s temperature humans possesses two special senses, i.e. a
cooling and a heating sense. Therefore humans have more than the otherwise well-known
"five" senses. In the skin are warming and cooling points, each one is about a square
millimeter large. Below them are nerve cells, whose internal chemistry changes depending on
temperature. Thus signals are released and sent to the brain.
The sensors lie most dense in the lips. Here the density is about 25 sensors per square
centimeter. The lips sensors supervise that the food we eat is not too hot or too cold. On the
fingers are still 5 sensors per square centimeter. One can check with fingers therefore
temperatures well through touch. On the torso is approximately only 1 sensor per square
centimeter. The legs are most temperature insensitive. Therefore the heat loss is hardly
noticed there and isn’t so unpleasant. There are more cooling than heating points. Their
measuring accuracy is very high, the measuring range is however relatively small. The
cooling sensors possess a measuring range of approximately 8 °C to 37 °C and the heat
sensors of approximately 37 °C to 50 °C. Below 8 °C and above 50 °C humans possess no
more sense of temperature but feel pain. The cooling sensors have at approximately 25 °C and
the heat sensors at approximately 45 °C their highest sensitivity, with which temperature
differences can be felt by a hundredth of Kelvin.
4.
Mechanism of the heat emission
The body constantly produces heat. Therefore the food we eat, becomes oxidized and thereby
burned. For the movement of muscles, and thus for the production of mechanical energy, food
must be burned. The efficiency of muscles is however relatively low. As with an automotive
engine only 20 % of the combustion energy is used for movement. The remaining
80 % is converted into heat and must be emitted as calorific loss to the environment. Due to
our movement waste heat thus always results.
How is this heat released into the environment? First the heat from the inside must be
transported to the surface of the body. This transportation is carried out by blood circulation.
Between skin and hypodermis is a close network of veins and arterry, which serve only for
heat release. If more heat has to be transported than normally the main blood circulation rises
around the eight to twelvefold ones. Then nearly a third of the blood is pumped to the surface.
The veins and arterry expand themselves. Thus the surface is increased to the heat emission.
One recognizes this condition by a strong red coloration of the skin. With cold weather on the
other side the blood circulation of the skin is reduced to a fifth of the normal value. The skin
looks therefore chalk-bleaches. With Sauna visitis the extreme widening of the skin and
following sudden shrinking by dipping in the basin are trained by the way.
From the skin the heat is transferred by radiation and by convection to the environment.
Radiation are electromagnetic waves, which are air permeable and are absorbed at solid walls.
The mechanism of the heat transfer by radiation is well-known from the radiation of the sun.
Convection one names the heat emission to the surrounding medium, usually air and water
when bathing. If the heat emission is not sufficient by radiation and by convection, because
for example the ambient temperature is too high or because by strong sporty movement much
heat is generated by the muscles, then the body uses sweating as further means to the heat
emission. By the evaporation of the sweat (water) the extremely high transition enthalpy is
extracted from the body.
For sweating humans possess about two million sweat glands. The highest density of glands is
at the head, since the brain is most worth to protect, the lowest density is at the member
masses. The sweat glands at the palms and soles do not serve however for cooling. These
glands become active with unrest, anxiety and fear and cause so-called "psychological
sweating". The sweat glands in the shoulder caves have likewise another sense than cool.
They produce odoriferous substances with originally sexual meaning. The allocation of the
different mechanism of heat release amounts to resting humans in an environment of 20 °C:
-
46 % radiation
33 % convection
19 % sweating
2 % respiration.
In the case of a change of the environmental conditions the portions shift. If a strong wind
prevails, then the portion of convection increases. Thus it seems to us more coldly during this
weather condition. With sporty activation the portion of sweating rises.
5.
Amount of heat release
The amount of the biologically necessary heat loss essentially depends
- on the heaviness of the activity and
- on the size of the surface and thus of the body size of humans.
In fig. 1 the heat flow of humans with standard size (75 kg) is represented as a function of the
ambient temperature with the heaviness of activity as parameter. The standard human gives a
heat flow of 120 W (normal line) as minimum value during calm sitting with ambient
temperatures above 16 °C. This value is independent of the ambient temperature. Below 16
°C the heat flow increases something with reducing ambient temperature. The lower broken
line of the hatched area shows the heat release by radiation and convection. This kind of heat
release decreases with the ambient temperature to the value zero with 36 °C. If the
environment reached the body core temperature, no more heat can be dissipated by radiation
and convection. With such high ambient temperatures the heat is dissipated exclusively by
sweating. The hatched range indicates the amount of this kind of the heat emission. In an
environment with temperatures above 37 °C thus the heat can be only dissipated by sweating.
With moderately severe work the heat emission of humans approximately doubles in relation
to calm sitting, since the muscles produce 80 % waste heat as previously mentioned. With
hard work the heat emission can rise to approx. 300 W. Trained sportsmen can produce still
& of the human body can be described mathematically
higher values. The emitted heat flow Q
by the Newton's approach:
.
Q = k · A · (ΤSkin - T∞.) .
(1)
Here k is the overall heat transfer coefficient, A the body surface the temperature of the skin
and T∞ the temperature of the environment. The heat emission of humans depends
proportionally on its surface and thus on the body size. The surface of standard humans
amounts to approximately 2 m2. Therefore large humans release more heat and have to insert
more energy with food, small humans according less energy. From the above equation it is
further evident that humans would release the more heat the colder the environment is.
Humans adjust this effect by reducing the heat transfer coefficient accordingly. This so-called
k-value is a measure for the lagging. Naked humans have for example a k-value of
approximately 10 W/(m2 K). Thus a heat flow of 120 W for an ambient temperature of 26 °C
results from the above equation. At this temperature humans feel well on the average. With
increasing temperatures sweating begins. Below 26 °C humans have to reduce its k-value to
compensate the increased heat emission. One reduces the k-value as well known by the kind
of clothes. With normal clothes for example the k-value is halved, by warm clothes lowered
around 2/3.
6.
Energy balance of humans
Daily energy requirement
As shown in fig. 1, on the average large humans release with easily activity a heat flow of
approximately 120 W. Thus one results during the day (24 hours) a released amount of heat
(by multiplication with 24 h) of approximately 2.9 kWh per day. This is a relatively small
energy quantity. The same quantity of energy is used for example, if a bulb of 120 W lightens
all day long. The value of this energy is using an electricity tariff of 17 Cent per kWh of about
50 Cent. The above emitted energy quantity amounts in another unit to 2500 kcal per day.
This energy quantity has to be replaced by average humans with food each day.
Decreased energy supply (weight reducing)
Which happens now, if less than these 2500 kcal per day are supplied to the body with the
food? Since the body absolutely needs the 2500 kcal for the combustion to keep its
temperature, it has to cover the difference between necessary and supplied energy from its
stored energy quantity. This corresponds to the energy conservation, the law of nature. The
body stores energy in form of fat padding. Fat is a material with extremely high energy
content and possesses a heating value of approximately 8000 kcal per kilogram. If one
supplies no energy for one day, the body diminishes 300 gram fat. This is the maximum
weight reduction which is possible per day. One cannot remove more for physical reasons
(energy conservation).
From above remarks it becomes clear that the body (inevitable!) diminishes fat and thus
weight if no energy is supplied with food. Food means meal and drinks. In particular with
sugar and alcoholic beverages much energy is often supplied to the body. Humans with for
example 30 kg predominance have to fast 100 days long to reach standard weight. They could
hold a winter sleep from energetic view, without to die. This is not possible however, since
humans lose water, salts and mineral materials by sweating. Animals, which hold a winter
sleep, cannot sweat therefore. If sufficient water, minerals, and also vitamine are supplied to
the body, fasting is not dangerous for healthy humans. Only if all fat reserves are used, fasting
becomes dangerously: The body diminishes then muscles for energy generation. Humans can
for a very long time fast, if sufficiently liquid is supplied. This was often proven in practice:
In makabre way in catching and concentration camps, and in radical cures to defatting, with
fasting one year long. Slimness means promise often higher weight reducing per day than 300
gram. These means contain materials, publing water from the fabric, which is then emitted
over the urinary passage. Since the body consists about 60 % of water, a fast weight reduction
can be pretended by dehydration. A healthy body deposits the water after joggle of the
preparations again. A real weight reducing can thus only by to be reached by lowering food
and drinking energy. Other slimness means contain therefore appetite losing materials and/or
materials, which swell in the stomach and cause thus a full feeling.
High energy supply (weight increasing)
Which happens now, if one supplies more than the 2500 kcal per day with food for the
calorific losses of the body? According to the energy conservation (1st main law of
thermodynamics) the difference between the supplied and generated energy is then stored, in
form of fat. If one supplies permanently more energy than 2500 kcal per day, fat is produced
until a new equilibrium is reached. This condition is given when according to equation (1) the
surface of the human body become larger in such a way that the supplied energy can be
released again to the environment. If one insert for example on the average 3000 kcal per day
the new equilibrium adjusts at around 20 % increased body surface.
Since with predominance more heat has to be released, a higher blood circulation is needed, in
order to transport the heat from the inside of the body to the skin surface. Therefore the heart
is loaded more strongly than under normal conditions. This is also a substantial reason, why
over-weighty person are particularly strongly affacted by cardiovascular diseases, blood high
pressure, cholesterine, diabetis, arteriosclerosis, etc. and thus possesses a shorter life
expectancy.
Influence of the metabolism
As shown by the past remarks, average large humans have to loss weight, if less than 2500
kcal per day with food is inserted. If more kilocalories inserted, humans become inevitably
over weighty. Frequently it is said that cannot be true, since humans would have a different
"metabolism". The efficiency of food combustion should be different with humans. We regard
the human history of the development. Humans had always to suffer from lack nutrition
during the last 10 000 years. In the Middle Ages more humans died for hunger than by
diseases. The human organism therefore has developed itself to be able to convert food
completely. Therefore food surplus can immediately converted into fat and stored. A
permanent offer in excess at food is available to humans, and only for those in the industrial
nations, since approximately 40 years - a tiny period of people history. Humans do not have
any possibility of separating surplus food and give it away.
7.
Individual energy consumption
The individual energy consumption of humans can be very different, as was shown in the past
remarks. The most important results are summarized in the following:
- the energy consumption of humans is essentially determined by its calorific losses to the
environment.
- the released heat flow depends on the size of humans. Humans of average size with a
weight of 75 kg release a heat flow of approximately 120 W.
- a daily energy requirement (for a standard) human of 2500 kcal results for easily activity.
For each kilogram deviation from these 75 kg the energy consumption changes
approximately 30 kcal. Humans of 60 kg weight e.g. need daily only 2050 kcal, humans of
90 kg however 2950 kcal.
- this basic consumption increases somewhat, if e.g. heavier activities on sport.
- the basic consumption can change slightly due to the individual heat feeling of humans.
Humans, who heat their flat highly or dress regularly warmly have smaller calorific losses
and need therefore less energy input. Humans, who prefer a colder environment need more
energy.
- human who eats and drinks more than its individual basic consumption of energy,
increases weight inevitably. The increase lasts so long, until the surface enlargement is
sufficient to release the energy to the environment.
- the individual metabolism of humans have not significan influence. Due to the
predominant lack nutrition during the evolution of humans the organism developed all
abilities to convert food completely in phases of an offer in excess food, and to store the
surplus energy in form of fat.
8.
Warmth comfort of humans
The warmth comfort of humans depends on the right "warm-physiologically temperature".
This temperature is no standard value, but a subjective feeling. For example at a room air
temperature of 20 °C about 45 % of the men and 40 % of the women feel thermal
comfortable. This temperature however 15 % of the men and 20 % of the women feel as too
cool and in each case 40 % as too warm.
The felt temperature of humans depends on theire heat emission. This temperature is
determined by radiation to the enclosure walls with the average temperature Tu and by
convection to the air with the temperature TL. The felt temperature can be approximated by
the equation
Te =
α K ⋅ TL + α S ⋅ Tu
α K + αS
(2)
whereby αK and αS are the heat transfer coefficients for convection and radiation respectivly.
In some cases the two heat transfer coefficients are similar. Then the felt temperature can be
regarded as arithmetic means of wall and air temperature.
Humans often are in radiation exchange with several surfaces of different temperatures. Thus
humans radiate to windows, to enclosed walls and to floor, which have usually different
temperatures. The lower the temperature of the surface is, the higher is the radiated heat flow.
From heaters humans receive radiation. As mean wall temperature for the radiation exchange
the so-called enclosure temperature is introduced. This temperature can be approximated by
ϑU =
A ⋅ ϑ1 + A 2 ⋅ ϑ2 + ...A n ⋅ ϑn
.
A1 + A 2 + ...A n
(3)
Comfortably felt temperatures are represented in fig. 2 (hatched range) for different air and
wall temperatures. Thus for example one feels it as too cold despite a relatively high air
temperature of 25 °C, if the confinement temperature of the walls lies below 12 °C. On the
other hand one feels still comfortable with air temperatures of 15 °C, if the wall temperatures
with 22 °C to 28 °C are relatively warm. A similar temperature feeling results also in the free
atmosphere. There one radiates heat to the space and receives radiation from the sun. Heat is
convectively dissipated, too. If strong wind prevails, the convective heat transfer is multiple
higher than with resting air. Then it seems more coldly. In the weather forecasts often the
temperature is called current air temperature and the temperature with zero wind with
comparable heat emission as "felt" air temperature. One feels a higher outside temperature
with clear sky with cloudy weather.
Fig. 1: Heat release of humans with standard size (75 kg)
Fig. 2: Range of comfortable warmth feeling