06.02 Thermal Comfort

Categories: Building Comfort

Introduction
Thermal comfort criteria define the degree of thermal equilibrium between an individual's body and the surrounding environment.  Thermal comfort is primarily dependent on factors such as temperature differences , both air and radiant, between the human body and its surroundings, the humidity of the air, the air speed around the body, the degree of activity, the body's metabolism and the degree of clothing.

Various thermal comfort indices have been developed that reflect the combined effect of various environmental variables. For example Fanger's Predicted Mean Vote (PMV) [ISO 7730 ] and Gagge's Standard Effective Temperature (SET).  By using these methods of comfort evaluation, a designer can obtain a range of environmental temperatures that are considered comfortable for a particular application. This thermal comfort band can then be utilised within a vent control system by developing a numerical model to modulate the vent position to provide a floating temperature within calculated comfort zone limits.

Although comfort indices represent good engineering models for the human physiology, they are somewhat restricted when used to simulate an individual’s perception of thermal comfort within a real world situation. In fact, research that has compared field data with predicted values obtained from comfort standards, show that there are discrepancies in results. For example, ISO 7730 states that internal design temperature should be around 20-24° C for winter, 23-26° C for summer, whereas field studies have found that the neutral temperatures preferred by people ranged from 17 to 30° C.  For this reason it is often advisable to provide individual over-rides for automated systems rather that relying on comfort theory simulation results.

All animals respond to their surroundings and are sensitive to the state of the thermal micro-climate. Many cold-blooded animals (poikilotherms) keep their body temperature within a preferred range by behavioural methods, such as moving into sunlight or shade. In contrast, warm-blooded animals (homeotherms) can maintain a constant body temperature by physiological responses to changes of microclimate, although these adjustments are often supplemented by ingenious stratagems of behaviour. Man uses both physiological and behavioural methods of temperature regulation, but he has also developed the skill to control his own microclimate by the use of heating and air conditioning, or less extravagantly by selecting appropriate clothing.

Whatever process is involved, thermal equilibrium between a man and his environment depends on the physical mechanisms which govern heat transfer from the body core to the skin surface and from the skin through clothing to the environment.

There are many models for thermal comfort, these include Fanger’s work in ISO 7730, comfort temperature, and heat stress index. The majority of them relate thermal comfort to a thermal balance equation based on the first law of thermodynamics. The equation is written as follows;

S  =  M - W - ( R + C + K ) - E - RES   ........ (1)

S       heat storage in body [W]
M      metabolic rate [W]
W      mechanical work or activity level [W]
R       heat exchange by radiation [W]
C       heat exchange by convection [W]
K       heat exchange by conduction [W]
E       evaporative heat loss [W]
RES heat loss by respiration [W]

When S is positive the body temperature is rising, and when S = 0 the body is in thermal equilibrium. Under normal conditions the body core temperature is approximately 37°C and remains almost constant over a wide range of ambient conditions, while the skin temperature fluctuates in response to any variations.

The terms in the equation above can also be expressed in Watts per square metre [W/m²] based on the skin area of the human body. The outer skin area may be evaluated using Dubois’ equation

A_D  =  0.202 m^0.425 H^0.725

A_D    the Dubois Area, total surface area of human body [m²]
m     body mass [kg]
H     body height [m]

The human body continuously generates heat so that the body temperature can be maintained within a narrow temperature range. Heat is not generated uniformly throughout the body, nor is it dissipated uniformly. However, for most engineering applications, it is sufficient to consider the human body as two concentric cylinders when describing heat dissipation to the environment. The inner cylinder represents the body core (skeleton, muscle, internal organs), and the outer cylinder represents the skin layer. The model assumes that:

the temperature in each compartment is uniform;

metabolic heat production, external work and respiration losses are associated with the core compartment;

the core and skin compartments exchange energy passively through direct contact and through the thermoregulatory controlled peripheral blood flow.

Equation (1) can be rewritten in terms of the heat balance of the two compartments:

S_cr  =  M - W - RES - Q_cr,sk

S_sk  =  Q_cr,sk - ( C + R + K ) - E

S_cr      rate of heat storage in the core compartment [W/m²]
S_sk      rate of heat storage in the skin compartment [W/m²]
Q_cr,sk  rate of heat transport from core to skin (includes both conduction through body tissue and convection through blood flow) [W/m²]

Heat exchange exists in relation to zones of different physiological and behavioural response. Within an individual’s band of comfort lies a neutral temperature where the environment is neither hot nor cold, and where no action from the physiological control system is required to maintain normal body temperature.

Conditions either side of the neutral midpoint can be classified into six basic zones:

Zone of vasomotor regulation against the cold, if the rate of heat loss from the skin to the environment increases, the body decreases the blood flow to the skin;

Zone of behavioural regulation against cold, an alternative control reaction which involves increasing clothing and activity levels;

Zone of body cooling, if all control reactions prove inadequate, the body enters this zone. When the core temperature falls below 35° C, people suffer major losses in efficiency, core temperatures below 31° C can be lethal;

Zone of vasomotor regulation against heat, a narrow zone which increases the blood flow to the skin;

Zone of evaporative regulation, the release of water from sweat glands for evaporative cooling.

Zone of body heating, where the core temperature starts to rise. When the core temperature rises above 39° C, people suffer major losses in efficiency. Deep body temperatures above 43° C may prove fatal.

When the body is able to maintain a state of equilibrium, its average core and skin temperatures are at their neutral values:

t_sk,n  =  33.7^oC

t_cr,n  =  36.8^oC

t_sk,n  neutral skin temperature
t_cr,n  neutral core temperature

Empirical relationships derived from laboratory experiments describe how the thermoregulatory control processes (vasomotor regulation, sweating and shivering) are probably stimulated and governed by temperature signals from the skin and the core (derivations from their respective neutral setpoints). Five signals trigger these processes:

warm signal from the core (WSIG_cr);

cold signal from the core (CSIG_cr);

warm signal from the skin (WSIG_sk);

cold signal from the skin (CSIG_sk);

warm signal from the body (WSIG_b).

The signals are written in terms of actual temperature (t) and neutral temperature (t_n) such that they can only take positive values:
 

The average temperature of the human body t_b can be predicted by the weighted average of the skin and core temperatures:

t_b  =  a t_sk + ( 1 - a ) t_cr

a     = fraction of body mass concentrated in skin compartment  (see vasomotor regulation)

The neutral body temperature is calculated from the neutral skin and core temperature in the same manner.
 

Behavioural Thermoregulation
Typically the body generates heat through muscular tension, shivering, or spontaneous activity. If the heat generated balances the increased heat loss to the environment, deep body temperature is maintained. An alternative control reaction is that of behavioural regulation against cold, which involves increasing clothing and activity levels.
 

Clothing
The clothing people wear depends upon on the external weather conditions. Clothing levels worn to work may vary on a day to day basis, but only slightly. The large variations are seasonal and have some correlation to external air temperature and solar irradiance.

A variation in clothing level is a personal adjustment that an occupant can make if they are uncomfortable. By taking off or putting on a jumper our personal band of comfort is widened (good for rooms with more than one occupant). In cold weather, an occupant can either wear more layers or wear thicker layers; more layers gives the occupant finer control over a specific comfort band. Whether people make clothing adjustments before resorting to the facade control system varies from person to person and from control system to control system. Typical clothing levels are usually taken into account at the design stage when deciding temperature bands as there is a limit to the amount of clothes a person can take off and put on while performing certain tasks.

Many of the physiological adjustments mentioned in the next section are dependent on clothing level and ratio.
 

Physical Movement
Within the internal environment an occupants’ level of comfort is sometimes dependent on their proximity to the external facade. Glazed areas of a facade are associated with air infiltration, cold down-drafts and sunlight penetration and in some situations occupants can choose whether they wish to be subjected to such conditions or whether they should move to an area that is unaffected. In the office environment such decisions are not regularly available to the occupant who usually has an allotted work area. Therefore there are often variations in comfort levels between occupants seated near to and away from a facade.

The utilisation of an intelligent facade and a state of the art building services system can go some way towards alleviating this problem, however a better initial building design should or might be a basic requirement. Designing narrow plan office buildings rather than deep plan buildings ensures that the number of square metres of facade per person is high enough to enable the facade control strategy to have a greater effect on each individual’s comfort. These control strategies should take into account that the facade will affect some areas of the building less than others, therefore a sufficient number of sensors should be located in the central zones.
 

Activity of Work
A person’s activity level is related to the tasks they perform. In an office environment the variety of tasks tend to involve similar activity levels. Exceptions will occur where people perform rare tasks, for example moving office furniture. The comfort band of the occupant performing such a task can usually cope with this change of activity with no change of ambient conditions, for example by removing an item of clothing. Another method of coping with a high workload is to control the rate of work, for example, rather than an individual running up a set of stairs they could walk (or even take the lift). A high rate of activity is useful in cold weather were the body is trying to produce more heat to counter any heat losses. For example if we are cold we may move around to keep warm.

Activity cannot be measured effectively within a control strategy, therefore it is simply taken into account within the initial design calculations.
 

Physiological Regulation

Metabolism
Metabolism is the body heat production resulting from the oxidation of food. Its value for each person depends upon their diet and level of activity (respiration rate) and may be estimated using the equation below:

M  =  2.06x10^-4 V'_res ( F_oi - F_oe )

V_res    air breathing rate [l/s]
F_oi     fraction of oxygen in the inhaled air
F_oe     fraction of oxygen in the exhaled air

As the human level of activity increases the energy required to maintain that activity level will also increase. In order to allow the body's metabolism to maintain an equilibrium there must be a rise in respiration rate. Thus the factors vary depending on an individual’s activity and fitness levels and in addition to individual psychological preferences, accounts for the diversified levels of thermal comfort perceived by people in the same environment. Fortunately, the human comfort band is wide, thus in a multi-occupant zone the majority of individual comfort bands will overlap, allowing us to form a narrow consensus band of comfort.

In cold weather our metabolic rate increases so as to produce extra heat. The liver plays an important part in this. Shivering which is caused by an involuntary contraction of our muscles can raise our metabolic rate to as much as three times its sedentary value. Metabolic rate production due to shivering requires simultaneous cold signal from both the skin and the body core.

M_skin  =  19.4 CSIG_sk CSIG_cr

A measurement of metabolism is difficult to achieve without having the occupant attached to cumbersome experimental equipment. In the office environment, where activity levels are fairly uniform, assumptions are normally made during the design process as to an average value of metabolism. An adaptive control system would cater for a single occupant by learning their preferences, whereas better overall design and control diversity is required for spaces with more than one occupant in order to achieve a suitable consensus band of comfort.
 

Respiration Heat Loss
Inspired air is usually warmed and humidified by its passage through the respiratory system. The sensible and latent heat losses are proportional to the volume flow rate of air to the lungs which in turn is proportional to metabolic rate.

RES  =  C_res + E_res

C_res  =  m'_res C_p,a ( t_ex - t_a ) / A_D

E_res  =  m'_res h_js ( W_ex - W_a ) /A_D

C_res     convective respiratory heat loss [W/m²]
E_res     evaporative respiratory heat loss [W/m²]
m'_res    pulmonary ventilation rate [kg/s]
t_ex         temperature of exhaled air [°C]
W_ex      humidity ratio of exhaled air
W_a     humidity ratio of inhaled (ambient) air
c_p,a     specific heat of air [KJ/kgK]

Respiration heat loss is only significant at high levels of activity and under normal office conditions can be usually be neglected.
 

Vasomotor Regulation
If the rate of heat loss from the body to the environment increases, the body decreases the blood flow to the skin. The blood is diverted from the blood capillaries just under the epidermis to blood vessels deeper down. This cools the skin and subjacent tissues and maintains the temperature of deep tissues. This response is brought about by the contraction of surface blood vessels and this mechanism is called vasomotor regulation.

Blood flow to the skin increases when desirable heat loss to the environment is restricted. The physiological control mechanisms for this condition correspond to those used against the cold condition. The increase in blood flow can double or even triple the conductance of heat to superficial tissues over the characteristic neutral point, causing skin surface temperature to come closer to the temperature of the body core.

In our concentric cylinder model vasomotor regulation causes the fractions of body mass taken by the core and skin compartments to vary as we have assumed that each compartment’s temperature is uniform. This is represented in the equation below:

a  = 0.0418 + 0.745 / ( 3600 m'_bl + 0.585 )

a      fraction of body mass concentrated in skin compartment
m'_bl     mass flow rate of blood [kg/sm²]

The effects of core and skin temperature deviations on blood flow can be expressed mathematically as:

m'_bl  =  [ ( 5.3 + 200 WSIG_cr ) / ( 1 + 0.5 CSIG_sk ) ] / 3600

Blood flow is limited to a range between 1.4 x 10^-4 and 2.5 x 10^-2 kg/sm².

We can now derive an equation for the heat transfer between the core and the skin compartments:

Q_cr,sk  =  ( k + C_p,bl  m'_bl ) ( t_cr - t_sk )

k   effective conductance between the core and the skin (5.28 W/m²K)
C_p,bl     specific heat of blood (4187 J/kgK)
 

Radiation (body-environment)
Two types of radiant energy are important when considering the exchange between the surface of the human skin or clothing and its environment:

thermal radiation of terrestrial origin;

solar radiation.

The two bands of electromagnetic radiation are effectively separate, solar or short wave radiation (R_S) lying largely in a band of wavelengths from 0.3 to 3mm, while longer wavelength thermal radiation (R_S) from local sources lies mainly between 3 and 40mm.
 

Thermal long-wave radiation
Thermal radiation transfer is the result of an exchange involving both emission and absorption. All surfaces emit thermal radiation at a rate depending on their surface temperature and emissivity. The emitted long-wave flux R_L [W/m^-2] is given by the Stefan-Boltzmann equation:

R_L  =  es t₅⁴

s   the Stefan-Boltzmann constant (s = 56.7 x 10^-9 W/m²K⁴ )
t_s    the surface temperature [K]
e    emissivity

This can be rewritten for a clothed person to give:

R_L  =  f_eff f_cle s ( t_cl⁴ - _meant_r⁴ )

f_eff         factor of effective radiation area, i.e. ratio of the effective radiation area to the total surface area of clothed body
f_cl          factor of clothing area, i.e. ratio of surface area of clothed body to surface area of naked body
t_cl          surface temperature of clothing [K]
_meant_r    mean radiant temperature, i.e. effective temperature of the room [K].

As the range of temperatures in the internal environment is usually small (typically 10 - 30°C), the equation above can be adequately replaced by a linear equation:

R_L  =  f_cl h_r ( t_cl - _meant_r )

where the radiant heat transfer coefficient, h_r, can be approximated by:

h_r  =  4.6 ( 1 + 0.01 _meant_r )

If a natural ventilation strategy is implemented within the facade design it is possible to control the majority of the surface temperatures of a space and thus the mean radiant temperature.
 

Short-wave Radiation (human body - air)
The exchange of short-wave radiation is variable and complex, since it depends on both surface colour and the geometry of interception. External short-wave radiation, e.g. solar radiation, often exceeds metabolic heat production even in cold climates, indoors other high temperature sources of radiation such as lighting etc, may also provide highly asymmetric sources of radiant energy. The net short-wave radiation flux, R_S, [W/m²] is given by the equation:

R_s  =  a R_si

R_si   incident energy flux [W/m²]
a   the average absorptivity of the skin and clothing

The spectral absorptivity and reflectivity of an occupant’s skin and clothing varies from person to person depending on skin colour and type of clothing worn. In the office environment each individual’s value tends to remain constant. An intelligent facade strategy is able to control the large variable R_si.

The net radiation exchange is given by the equation:

R  =  R_S + R_L
 

Convection (human body - air)
The heat transfer between a body and the surrounding air is primarily by convection which can either be free (natural) caused by buoyancy or forced (mechanical) caused by relative movement between body and air. Both types of convection are dependent on the following parameters:

the skin’s thermal characteristics (fraction of skin exposed, the insulation value of the clothing worn)

the skin temperature

the air temperature

Forced convection which accounts for the largest proportion of convection heat transfer is also dependent on air velocity, v. Air movement can be created by a mechanical system (such as a fan), the wind through a ventilation opening (such as a window) or simply the thermodynamic and convective properties of the room (such as a down draft from a window).

The general heat convection equation is :

C  =  f_d h_c ( t_cl - t_a )

h_c      convective heat transfer coefficient [Wm^-2K^-1]
t_a       air temperature [°C]
t_cl      clothing temperature [°C]

The convective heat transfer coefficient, h_c, depends on the mode of heat transfer. For free convection it is typically given by:

h_c  = 2.38 ( t_cl - t_a )^0.25

For forced convection it is typically:

h_c  =  12.1 v^0.5
 

Conduction (human body - solid surfaces)
Heat transfer by conduction occurs between the human body and solid surfaces such as chairs, beds and floors with which it is in contact. However, it is usually a small component of the total heat balance, for two reasons:

the contact area is small;

the thermal diffusivity of the materials are usually low.

It is for this reason that conductivity is usually overlooked when carrying out comfort analysis within an office environment.
 

Evaporative heat loss of a human body
Heat loss by evaporation is partly due to

diffusion of water vapour through the skin tissues.

evaporation of sweat from the skin surface (regulatory sweating).

In both cases the heat is absorbed from the skin and this process controls the rise in body temperature. The water diffusion is a continuous process which occurs even in a cool environment. The sweat evaporation only occurs in a hot environment and when the body activity is higher than normal.

E  =  E_diff + E_rsw

E_diff     evaporation heat loss through natural diffusion of water through the skin [W/m²]
E_rsw    evaporative heat loss through regulatory sweating [W/m²]

Both types of evaporative heat loss depend on the difference between the saturated vapour pressure at skin temperature, the vapour pressure of the surrounding air and air velocity. The equation below shows how the evaporative heat loss of a human body is dependent on the amount of moisture on the skin (skin wettedness):

E  =  w ( p_sk,s - p_a ) / [ R_e,cl + 1 / ( f_cl h_e )]

p_a         water vapour pressure in ambient air [Pa]
p_sk,s    water vapour pressure at skin, normally assumed to be that of saturated water vapour at t_sk [Pa]
R_e,cl     evaporative heat transfer resistance of clothing [m²Pa/W]
h_e         evaporative heat transfer coefficient [W/m²Pa]
w          skin wettedness

If w= 1 is applied to this equation then we can find the maximum possible evaporative heat loss (E_max).

The proportions of diffusion and regulatory sweating can be found using the following equations:

E_rsw  =  m'_rsw h_fg

m'_rsw  =  4.7x10^-5 WSIG_b exp (WSIG_sk / 10.7)

h_fg        heat of vapourization of water [KJ/kg]
m'_rsw    rate at which regulatory sweat is generated [kg/sm²]

The proportion of the body wetted to evaporate regulatory sweat w_rswis:

W_rsw  =  E_rsw / E_max

E_diff  =  ( 1 - w_rsw ) 0.06 E_max

Research has been undertaken to find the change of wetness under constant average skin temperatures. This has shown that there is:

a positive correlation between wettedness and environmental humidity and a negative correlation between wettedness and air temperature.

a positive correlation between the evaporative heat loss from the skin surface and air temperature and a negative correlation between the evaporative heat loss and the environmental humidity.

a negative correlation between wettedness and evaporative heat loss.

As air temperature rises the body relies on evaporative heat loss to release excess heat, as other mechanisms are less effective. The relative humidity ideally should be fairly low in order to gain the best conditions for sweating. In the office environment, latent loads which will cause the relative humidity to rise, will originate from the occupants, cups of coffee and the external air. In the UK the relative humidity of the external air tends to be fairly low enabling a natural ventilation strategy to use a constant supply of fresh air to combat the minimal internal latent loads of an office space.
 

Artificial thermoregulations
Various systems can be used for artificial thermoregulation: heating systems, cooling systems, opening windows, use of blinds, night time ventilation,... For a diagram outlining man's physiological, behavioural and artificial mechanisms for thermal discomfort click here. The artificial thermoregulations are shown in blue in the thermal comfort diagram.