Thermal comfort can be defined as “the condition of the mind in which satisfaction is expressed with the thermal environment” [
28]. However, several other definitions for thermal comfort have been pointed out and even debates around how thermal comfort can be defined [
29]. The problem is that the mechanism of being “thermally comfortable” is highly complicated and affected by various factors, such as physiology, psychology, and behaviour [
30]. Hence, several comfort models are used for different environments [
31].
According to Fanger [
32], thermal comfort can be quantitatively measured using six parameters, namely air velocity (Av), mean radiation temperature (MRT), air temperature (dry-bulb temperature—DB), air relative humidity (RH), metabolic rate (met), and clothing insulation (clo). Combining these parameters indicates thermal comfort in a controlled and conditioned environment. The level of thermal comfort (or discomfort) of a group of people is rated via predicted mean vote (PMV) index scaling from −3 (cold) to +3 (hot) [
33]. Along with PMV, the index of the predicted percentage of dissatisfied (PPD) indicates the proportion of thermally dissatisfied people in the group. This principle makes up the classic PMV (Fanger) thermal comfort model shown in
Figure 6.
As the most classical thermal comfort model, the PMV thermal comfort model is commonly used in standards or guidelines such as ISO 7730, ASHRAE 55 (standard of The American Society of Heating, Refrigerating and Air-Conditioning Engineers) [
28], or the REHVA (Federation of European Heating, Ventilation, and Air Conditioning Associations) Guidebook Number 7 [
34]. The PMV thermal comfort model is well-suited and commonly used to assess thermal comfort in conditioned office spaces [
35]. Loveday et al. [
36] conducted an experiment proving that the PMV model accurately assesses thermal comfort in a radiant conditioned environment and concluded that a radiant conditioned space is similar to an air-conditioned space. According to ASHRAE 55, a thermal environment with an acceptable comfort level would have a PMV between −0.5 and +0.5, resulting in a PPD of less than 10% (
Figure 6) [
28]. However, the Fanger PMV comfort model can be considered conservative [
37], and acquiring a PPD of less than 10% is not common [
28]. Hence, the PPD of less than 20% (PMV between −0.8 and +0.8) is also welcomed as an acceptable level of thermal comfort (
Figure 6) [
28,
37].
Mean Radiant Temperature (MRT)
MRT is a crucial parameter determining thermal comfort [
14,
28,
38]. It is defined as “the uniform surface temperature of an imaginary black enclosure in which the radiation from the occupant equals the radiant heat transfer in the actual non-uniform enclosure” [
39]. Stefan Boltzmann defined MRT as “a temperature value to evaluate the total radiation flux over the human body” [
40]. MRT is the relationship between indoor surface temperature, direct and scattering solar radiation power, view factor toward transparent and translucent surfaces, and solar radiation receiving area of the occupant body [
41]. MRT is the most complex parameter of thermal comfort, often difficult to control, calculate, and measure [
41,
42]. Yet, it is important to note that radiant systems function on the principle of MRT, not air temperature (dry-bulb). This is the crucial problem in radiative system control, which functions on the control principle of a thermostatic sensor (air temperature).
MRT was assumed to be equal to the air temperature in many early research papers in space conditioning [
39,
43,
44]. However, this is not the case on many occasions, especially when solar heat gain is introduced [
28,
45]. In residential buildings, access to sunlight is a fundamental requirement. Thus, MRT will not be equal to the air temperature in residential buildings. Instead, MRT is a better index to represent occupants’ thermal sensation than air temperature [
38,
46]. Hence, in retrofitting residential buildings, MRT control should be prioritised.
Sui and Zhang [
10] investigated the relationship between MRT and other thermal comfort parameters, namely air temperature, air velocity, and air humidity. The research proved the significant influence of MRT on thermal comfort. Sui and Zhang [
10] illustrated that thermal comfort can be achieved even at high air temperatures with a low MRT. This allows the concept of high air temperature cooling and low air temperature heating to occur in a room. Air temperature and MRT are the two most critical aspects determining thermal comfort [
34]. Radiant conditioning focuses on changing MRT via the internal surface temperature rather than changing the air temperature. Hence, cooling can be achieved even with high air temperatures, while heating can be provided with low air temperatures [
34]. Additionally, Sui and Zhang [
10] argued that, while a low air velocity means reductions in convection and evaporation, MRT can play a significant role to improve thermal comfort. Their research also indicated that the higher the humidity, the lower the MRT.
Figure 7 charts an investigation in achieving thermal comfort performed by Luther, Tokede, and Lui [
37], applying similar principles as Sui and Zhang [
10]. The circle and the triangle represent thermally unsatisfactory conditions, and there are three options to reach the acceptable level of thermal comfort (PPD = 20%). Option A raises the air temperature by about 3.5 °C, which can increase the conditioning energy cost by 30–45% [
25]. Option B increases the MRT by 4.5–23.5 °C (for the circle) and provides heating while the air temperature remains at 20.5 °C. This can be achieved with the radiant surface’s temperature at 30–35 °C at a minimum cost [
25]. Hence, the radiant system is more energy-efficient. Nevertheless, option C raises the air temperature and MRT, the shortest path, although the energy consumption will be higher than option B.
Figure 7. Air temperature vs. mean radiant temperature concerning PPD [
25]. Source: Redrawn by the second author.
In a uniform air temperature environment, nonuniform MRT can cause thermal discomfort [
36]. In turn, with uniform MRT, local thermal discomfort can be avoided even with high air temperature gradients [
36]. Hence, MRT has more effect on human thermal comfort than the air temperature itself [
47].
MRT can be calculated using the surface’s temperature and view factor (angle factor) between an occupant and internal surfaces. The equation is [
48]:
where
Tr = mean radiant temperature, K;
TN = surface temperature of surface N, K;
Fp−N = view factor (angle factor) between a person and surface N.
The view factor is the proportion of energy radiated from a surface and received by another surface [
49]. The view factor represents the radiant heat exchanges between two surfaces [
50]. The total view factor toward an occupant in a room equals 1 [
34]. The view factor is affected by the surface shapes, angle, and distance between the two surfaces [
49]. Hence, in thermal comfort, the view factor depends on the dimensions of the radiant surfaces and the distance to the occupant. The view factor for a person in a room also depends on the posture and position [
51]. Although determining the view factor is highly complicated, two conventional methods of approximately determining the view factor’s value are the Fanger-Rizzo method and the Nusselt Analog method [
52]. While the Fanger-Rizzo method is used in fundamental documents ASHRAE and the REHVA Handbook [
34,
48], the Nusselt method is not. This is an important factor in designing radiant systems for retrofitting residential buildings, especially where the systems can be mounted for maximum effectiveness.