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Thermal Exchange of Body with Environment
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Heat balance equation for a human being

The temperature of human body depends upon the energy balance between itself and the surrounding thermal environment. Taking the human body as the control volume, one can write the thermal energy (heat) balance equation for the human body as:

Qgen =Qsk +Qres +Qst

where Qgen = Rate at which heat is generated inside the body

Qsk = Total heat transfer rate from the skin

Qres = Heat transfer rate due to respiration, and

Qst = Rate at which heat is stored inside the body

The heat generation rate Qgen is given by:

Qgen = M(1− η)≈M

where M = Metabolic rate, and η = Thermal efficiency ≈ 0 for most of the activities

The metabolic rate depends on the activity. It is normally measured in the unit “met”. A met is defined as the metabolic rate per unit area of a sedentary person and is found to be equal to about 58.2 W/m2. This is also known as “basal metabolic rate”. Table below shows typical metabolic rates for different activities:

Studies show that the metabolic rate can be correlated to the rate of respiratory oxygen consumption and carbon dioxide production. Based on this empirical equations have been developed which relate metabolic rate to O2 consumption and CO2 production.

Since the metabolic rate is specified per unit area of the human body (naked body), it is essential to estimate this area to calculate the total metabolic rate. Even though the metabolic rate and heat dissipation are not uniform throughout the body, for calculation purposes they are assumed to be uniform.

The human body is considered to be a cylinder with uniform heat generation and dissipation. The surface area over which the heat dissipation takes place is given by an empirical equation, called as Du Bois Equation. This equation expresses the surface area as a function of the mass and height of the human being. It is given by:

where ADu = Surface area of the naked body, m2 m = Mass of the human being, kg h = Height of the human being, m

Since the area given by Du Bois equation refers to a naked body, a correction factor must be applied to take the clothing into account. This correction factor, defined as the “ratio of surface area with clothes to surface area without clothes” has been determined for different types of clothing. These values are available in ASHRAE handbooks. Thus from the metabolic rate and the surface area, one can calculate the amount of heat generation, Qgen.

The total heat transfer rate from the skin Qsk is given by:

Qsk = ± Qconv ± Qrad + Qevp

where Qconv = Heat transfer rate due to convection (sensible heat)

Qevp = Heat transfer rate due to evaporation (latent heat)

The convective and radiative heat transfers can be positive or negative, i.e., a body may lose or gain heat by convection and radiation, while the evaporation heat transfer is always positive, i.e., a body always looses heat by evaporation. Using the principles of heat and mass transfer, expressions have been derived for estimating the convective, radiative and evaporative heat transfer rates from a human body. As it can be expected, these heat transfer rates depend on several factors that influence each of the heat transfer mechanism.

According to Belding and Hatch, the convective, radiative and evaporative heat transfer rates from the naked body of an average adult , Qc, Qr and Qe, respectively, are given by:

In the above equation all the heat transfer rates are in watts, temperatures are in °C and velocity is in m/s; Ps,b and Pv are the saturated pressure of water vapour at surface temperature of the body and partial pressure of water vapour in air, respectively, in kPa. From the above equations it is clear that the convective heat transfer from the skin can be increased either by increasing the surrounding air velocity (V) and/or by reducing the surrounding air DBT (t). The radiative heat transfer rate can be increased by reducing the temperature of the surrounding surfaces with which the body exchanges radiation. The evaporative heat transfer rate can be increased by increasing the surrounding air velocity and/or by reducing the moisture content of surrounding air.

The heat transfer rate due to respiration Qres is given by: Qres = Cres +Eres

where Cres = Dry heat loss from respiration (sensible, positive or negative)

Eres = Evaporative heat loss from respiration (latent, always positive)

The air inspired by a human being is at ambient conditions, while air expired is considered to be saturated and at a temperature equal to the core temperature. Significant heat transfer can occur due to respiration. Correlations have been obtained for dry and evaporative heat losses due to respiration in terms of metabolic rate, ambient conditions etc.

For comfort, the rate of heat stored in the body Qst should be zero, i.e.,

Qst = 0 at neutral condition

However, it is observed that a human body is rarely at steady state, as a result the rate of heat stored in the body is non-zero most of the time. Depending upon the surroundings and factors such as activity level etc., the heat stored is either positive or negative. However, the body cannot sustain long periods of heat storage with a consequent change in body temperatures as discussed before.

Since the body temperature depends on the heat balance, which in turn depends on the conditions in the surroundings, it is important that the surrounding conditions should be such that the body is able to maintain the thermal equilibrium with minimum regulatory effort. All living beings have in-built body regulatory processes against cold and heat, which to some extent maintains the body temperatures when the external conditions are not favourable. For example, human beings consist of a thermoregulatory system, which tries to maintain the body temperature by initiating certain body regulatory processes against cold and heat.

Indices for thermal comfort

It is seen that important factors which affect thermal comfort are the activity, clothing, air DBT, RH, air velocity and surrounding temperature. It should be noted that since so many factors are involved, many combinations of the above conditions provide comfort. Hence to evaluate the effectiveness of the conditioned space, several comfort indices have been suggested. These indices can be divided into direct and derived indices. The direct indices are the dry bulb temperature, humidity ratio, air velocity and the mean radiant temperature (Tmrt).

The mean radiant temperature Tmrt affects the radiative heat transfer and is defined (in K) as:

where:

Tg = Globe temperature measured at steady state by a thermocouple placed at the center of a black painted, hollow cylinder (6” dia) kept in the conditioned space, K. The reading of thermocouple results from a balance of convective and radiative heat exchanges between the surroundings and the globe

Ta = Ambient DBT, K

V = Air velocity in m/s, and

C = A constant, 0.247 X 10^9

The derived indices combine two or more direct indices into a single factor. Important derived indices are the effective temperature, operative temperature, heat stress index etc.

Effective temperature (ET): This factor combines the effects of dry bulb temperature and air humidity into a single factor. It is defined as the temperature of the environment at 50% RH which results in the same total loss from the skin as in the actual environment. Since this value depends on other factors such as activity, clothing, air velocity and Tmrt, a Standard Effective Temperature (SET) is defined for the following conditions:

Clothing = 0.6 clo, Activity = 1.0 met, Air velocity = 0.1 m/s, Tmrt = DBT (in K)

Operative temperature (Top): This factor is a weighted average of air DBT and Tmrt into a single factor. It is given by:

where hr and hc are the radiative and convective heat transfer coefficients and Tamb is the DBT of air.

ASHRAE has defined a comfort chart based on the effective and operative temperatures. Figure below shows the ASHRAE comfort chart with comfort zones for summer and winter conditions. It can be seen from the chart that the comfort zones are bounded by effective temperature lines, a constant RH line of 60% and dew point temperature of 2°C.

The upper and lower limits of humidity (i.e. 60 % RH and 2°C DPT, respectively) are based on the moisture content related considerations of dry skin, eye irritation, respiratory health and microbial growth. The comfort chart is based on statistical sampling of a large number of occupants with activity levels less than 1.2 met. On the chart, the region where summer and winter comfort zones overlap, people in winter clothing feel slightly warm and people in summer clothing feel slightly cool. Based on the chart ASHRAE makes the following recommendations:

Inside design conditions for Winter:

Top between 20.0 to 23.5°C at a RH of 60% Top between 20.5 to 24.5°C at a DPT of 2°C

Inside design conditions for Summer:

Top between 22.5 to 26.0°C at a RH of 60%

Top between 23.5 to 27.0°C at a DPT of 2°C

Table below shows the recommended comfort conditions for different seasons and clothing suitable at 50 % RH, air velocity of 0.15 m/s and an activity level of ≤ 1.2 met.

The above values may be considered as recommended inside design conditions for comfort air conditioning. It will be shown later that the cost of air conditioning (initial plus running) increases as the required inside temperature increases in case of winter and as the required inside condition decreases in case of summer. Hence, air conditioning systems should be operated at as low a temperature as acceptable in winter and as high a temperature as acceptable in summer. Use of suitable clothing and maintaining suitable air velocities in the conditioned space can lead to reduced cost of air conditioning. For example, in summer the clothing should be minimal at a socially acceptable level, so that the occupied space can be maintained at higher temperatures. Similarly, by increasing air velocity without causing draft, one can maintain the occupied space at a higher temperature in summer. Similarly, the inside temperatures can be higher for places closer to the equator (1°C rise in ET is allowed for each 5° reduction in latitude). Of course, the above recommendations are for normal activities. The required conditions change if the activity levels are different. For example, when the activity level is high (e.g. in gymnasium), then the required indoor temperatures will be lower. These special considerations must be kept in mind while fixing the inside design conditions.

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