Gagge's Two-Node Model

G agge's tw o-node m odel represents the body as tw o concentric cylinders : th e in n er cylinder rep resen tin g b ody core (skeleton, m uscle, in tern al organs) an d the o u ter one rep resen tin g the skin surface. The m odel assu m es the follow ing : conductive h eat exchange is negligible; the tem p eratu re of each com partm ent is uniform ; m etabolic heat production, ex te rn al w ork, a n d resp ira to ry losses are associated w ith th e core com p artm en t; an d the core and skin com partm ents exchange energy p a ssiv e ly th ro u g h d irec t contact a n d th ro u g h th e rm o -re g u la to ry - controlled blood flow. The energy balance is such that the rate of heat storage is equal to the net rate of heat gain m inus the heat loss. The m odel is described by tw o coupled heat balance equations, one applied to each com partm ent :

Core : Scr = M - W - ( Cres + Eres ) - Qcrsk

Skin : Ssk = Qcrsk - ( C + R + Esk )

w h ere,

Scr = rate of heat storage in the core, W /sq.m Ssk = rate of heat storage in the skin , W /sq . m Q crsk = rate of heat transport from the core to the

skin, W /sq. m

Fanger's Steady-State m odel is the basis for the determ ination of therm al c o m fo rt in m o d e ra te th erm al e n v iro n m e n ts as e m b o d ie d in an international standard know n as ISO 7730-1984 [11]. The m odel is also the basis for Fanger's Com fort Equation w hich is w idely used by ASHRAE in d eveloping the Com fort C harts for various com binations of tem perature an d hum idity [7].

In the p resent study, therm al comfort is studied by the direct analysis of the therm al sensation and therm al com fort scales. N o m easurem ents of physiological variables like skin tem perature and sw eat rate w ere carried out, an d so, the present study will not be able to contribute tow ards any validation of the two models.

2.3.3 H um phreys' Simplified Model for Field Studies

H u m p h rey s [12] has conveniently deriv ed therm al com fort conditions especially for applications in field surveys. The equations can be used w here a range of activities occur at the same time and a range of clothing is w o rn by different individuals over the period of the studies. The heat tran sfer from the body core to the environm ent has been d iv id ed into three stages, nam ely, from the body core to the skin, from the skin to the outer surfaces of the clothing and from the outer surfaces of the clothing to th e en v iro n m en t. C om bining the th ree stages of h eat flow s, the follow ing equation emerges :

M ( Rb + k R c + k R e ) = Tb - T g

w h ere,

M = rate of metabolic heat production, W /sq . m

k = proportion of metabolic heat dissipated by means other than evaporation

R b = therm al resistance of peripheral tissues, sq. m °C /W R c = therm al resistance of the clothing (in term s of

Du Bois area), sq. m °C /W

R e = therm al resistance betw een clothing surface and the surroundings, sq. m °C /W

Tb = body core tem perature, °C T g = globe tem perature, °C

The equation is relatively sim ple and with a know ledge of the constant, k, and the therm al resistance, a set of lines for various clothing levels m ay be d raw n on a graph w ith metabolic rate and globe tem perature as axes. The w id th of the comfort zone at different metabolic rates and clothing levels m ay then be determ ined.

2.3.4 Conditions for Thermal N eutrality

The conditions required for therm al neutrality can be categorised u n der tw o m a in fa c to rs , n a m e ly , e n v ir o n m e n ta l a n d h u m a n . The e n v iro n m e n ta l fa c to rs in c lu d e a ir te m p e r a tu re , m ea n r a d ia n t tem p eratu re, relative hum idity and air m ovem ent. Except for the m ean rad ian t tem perature, the other three factors are fam iliar terms.

M ean ra d ia n t tem p eratu re can be defined as the u niform blackbody tem perature of an im aginary enclosure w ith which a person exchanges the sam e heat by radiation as he w ould in the actual complex environm ent. It can be m easured indirectly w ith a globe therm om eter after correcting for air velocity and air tem perature. A globe therm om eter is an o rd in ary m ercu ry -in -g lass th erm o m eter in serted into the m id d le of a 100mm copper globe w hich is painted m att black. Once the air tem perature. T a , globe tem p eratu re ,T g , and air velocity, V , are know n, the m ean rad ian t tem perature, Tmrt, can be calculated as follows :

Tm rt = ( 1 + 0 .2 2 Vv ) ( Tg - Ta ) + Ta

N ote that w hen no radiative effect exists, i.e. T g = T a, Tmrt is equal to Ta.

The air tem p eratu re and the m ean rad ian t tem p eratu re affect the heat exchange of the body by convection and radiation. The rate of the heat exchange d epends on the air m ovem ent. H u m id ity becom es significant w hen the body attem pts to lose heat by evaporative cooling.

The h u m an factors that affect therm al neutrality are clothing and bodily activity levels. The am ount of clothing on the body insulates against heat losses or gains while the bodily activity, as m easured by the metabolic rate, will determ ine the am ount of heat generated internally in the process of w orking and to m aintain w arm th.

The conditions for therm al com fort includes subjective or psychological factors in addition to the conditions listed for therm al neutrality. Rohles [13], one of the prom inent psychologists w ho review ed 5 previous studies that discussed the psychological aspect of therm al comfort, recom m ended a 3 d im en sio n al re p re se n ta tio n of the h u m a n b ein g in a th erm al environm ent. The m odel consists of a cuboid w ith each axis representing organism ic factors (age-sex, psyche, drive, body type, sensory process and genetics), physical factors (sound, light, volum e, radiation, inspired air, atm o sp h eric p ressu re , force fields, air m o v em en t, te m p e ra tu re an d relative hum idity) and reciprocative factors ( diet, clothing, exposure, social incentive and activity). The m odel has attributed the condition of m in d ' to n u m e ro u s facto rs, as above. W hile th e s tu d y is n o t com prehensive due to the small sam ple used, it should m ake an im pact on researchers w ho hold simplistic m odels of hum an com fort based on a set of physical factors only.

2.4. T herm al Com fort and Therm al Sensation

In this section, the term s therm al sensation, therm al com fort, therm al acceptance and preferred tem perature are explained. Therm al sensation an d th erm al com fort are different term s w hich are som etim es used interchangeably and therefore require sufficient discussion to show their difference.

2.4.1 Therm al Sensation

Therm al sensation is an expression of the sensation of w arm th or its lack. This is related to a rational experience th at is probably not influenced by an y factors other than physiological an d environm ental, in clu d in g the activity and clothing levels of the person. The ASHRAE [7] Scale, also k now n as the Therm al Sensation Scale as show n in Table 3.4a (C hapter 3), is one w ay of expressing therm al sensation. The neutral tem perature is the tem p era tu re at w hich people experience a sensation w hich is n either slig h tly w arm nor slightly cool. The neutral sensation is in d icated by v o tin g for the central category, know n as 'n e u tra l' on the th erm al sensation scale.

2.4.2 Therm al Comfort

Therm al comfort is defined by ASHRAE [7] as "that condition of m ind in w h ich satisfaction is expressed w ith the th erm al environm ent". The p h ra s e 'co n d itio n of m in d ' im plies th at psychological as w ell as physiological factors are involved. One w ay of identifying the condition of m in d ' is to develop em pirical eq u atio n s th at can relate com fort p erceptions or feelings to physiological responses [7]. In this w ay, the subjectivity elem ent of the resp o n d en t can be red u ced to quantifiable factors [7]. It is also possible th at em otional factors can affect therm al com fort. Thus, therm al com fort is m ore of a non-objective expression w hen com pared to therm al sensation.

A sim ple w ay of expressing therm al comfort is to ask subjects to indicate th e ir com fort feeling on a scale w hich contains term s refe rrin g to com fortable or uncom fortable conditions. Exam ples of the term s often u s e d are 's lig h tly c o m fo rta b le ', 'w a rm ly c o m fo rta b le ', 's lig h tly uncom fortable', and 'very uncom fortable'. C om fort T em p eratu re is the tem perature at w hich respondents express comfort feelings by voting w ith the m iddle category of the comfort scale. The m iddle category is know n as 'com fortable'.

H ensel [14] acknow ledged the differences betw een therm al sensation and therm al com fort and Gagge et al [15] used separate scales for therm al sensation and therm al comfort. In the present study, both scales are used. Participants w ere asked to vote on both scales an d analyses have been carried out for both sets of results.

2.4.3 Thermal Acceptance and Preferred Tem perature

Two other frequently quoted terms are therm al acceptance' and Preferred T em p eratu re'. ASHRAE [16] specifies T herm al A cceptability as any condition in which " 80% or m ore of the people express satisfaction w ith a given environm ent". A nother m ore w idely used m eth o d considers the votes w ithin the three m iddle categories of the therm al sensation scale, i.e. betw een 3.0 and 5.0 inclusive, as therm al acceptability conditions. This m ethod was proposed by Fanger in developing the concept of Predicted Percent Dissatisfied (PPD).

Preferred Tem perature is the tem perature at which a respondent requests no change in tem perature or at which the greatest percentage of a group of people request no change in tem perature. The Preferred T em perature can be established by using the McIntyre scale [17].

2.4.4 Therm al Com fort Indices

M any therm al indices have been developed over the years in an attem pt to combine some or all of the environm ental variables into a single index th at w ould uniquely define therm al comfort. ASHRAE [7] classifies the indices into three types, namely, direct, rationally derived and em pirically derived.

D irect in d ices are th o se w hich can be m e a su re d d ire c tly in an e n v iro n m en t, such as, d ry -b u lb tem p era tu re , w et-b u lb tem p era tu re , relative hum idity and air velocity. These are the sim plest of the indices.

The rationally derived indices are based on the body's therm al balance eq u atio n , nam ely. M ean R adiant T em p eratu re, P red icted M ean Vote (PMV), Index of Thermal Stress (ITS), etc.

Predicted Mean Vote is an index developed by Fanger [9] w hich predicts the m ean vote (therm al sensation) of a large group of people exposed to the sam e therm al condition. It is based on responses from a large num ber of students from the U.S.A. and D enm ark com bined w ith a steady-state heat balance m odel of the hum an body (see Therm al C om fort Theory Section)

The Index of Therm al Stress is the cooling rate p ro d u ced by sw eating w hich w o u ld m aintain the person's therm al balance u n d e r the given condition. It is useful in overheated conditions as long as the physiological adjustm ents are able to m aintain therm al balance. ITS w as developed by G ivoni [18] from extensive research in desert climates.

The em pirical indices involved experim entation w ith people. Examples of these indices are Effective Tem perature, C orrected Effective T em perature (CET), N ew Effective Tem perature and Predicted Percentage Dissatisfied (PPD).

The Effective T em perature (ET) is the tem perature of the still, satu rated condition w hich w ould, in the absence of rad iatio n , p ro d u ce the sam e effect as the given condition. It integrates three variables, nam ely, air tem p eratu re, hum idity, and air m ovem ent.

The C orrected Effective T em perature (CET) is sim ilar to the Effective T e m p e ra tu re b u t in clu d es the rad ia tiv e effect, w h ere the d ry -b u lb tem perature is replaced by the globe tem perature. This is useful w hen the condition is not uniform , for example, w hen the walls are not at the same tem perature as the air. The CET is obtained using nom ogram s [19].

The N ew Effective T em p eratu re (ET*) is d efin ed as th e d ry -b u lb tem p eratu re of a uniform enclosure at 50% relative h u m id ity in w hich people w ould have the same net heat exchange by radiation, convection, an d ev ap o ratio n as they w ould in the v arying h u m id ities of the test environm ent. The ASHRAE [16] SET* scale assum es clothing at 0.6clo, air m ovem ent at 0.2m /s, time of exposure at 1 hour w ith the activity level as sedentary. This set of specific values is know n as the stan d ard condition. W hen lines of constant ET* are plotted u n d er the stan d ard condition, the isotherm for the n eu trality threshold is at 23.5°C ET* [16]. N eu trality continues to be sensed u p to the 25.0°C ET* iso th erm . The slight discom fort region is represented by the 30°C ET* line. These tem peratures are determ ined based on physiological considerations rath er than direct calculations from therm al scales.

2.5 T herm al Com fort and Perform ance

Before looking in detail at therm al comfort research, this brief section will consider w ork carried out on the effect of comfort on perform ance. As it is an accepted fact that people prefer to be therm ally comfortable, it is to be expected that people will perform better w hen comfortable, w hatever they are doing.

W yon of the N ational Swedish Institute for Building Research has carried o u t a large n u m b er of studies on the effects of the in d o o r th erm al en v iro n m en t on h u m an p ro d u ctiv ity and perform ance. In one of the studies, W yon et al. [20] observed the effect of m oderate therm al stress on the potential w ork perform ance of factory w orkers in South Africa. The a u th o rs o b serv ed the p erform ance of sim ple m an u al tasks, nam ely, picking u p 3 sm all pegs and inserting them one after another in the sam e hole using fingers of the preferred hand. The perform ance of the task is found to fall w ith the reduced finger skin tem perature as show n in Figure 2.2. The stu d y also n o ted th at th ere is no difference b e tw ee n the perform ances of Black and W hite Males.

W yon et al. also studied the relationship betw een air tem perature and the resu lta n t finger tem p eratu re for w orkers of both ethnic g ro u p s. The