**1. Introduction**

The energy consumption of space heating and cooling has attracted attention, and thermal transmittance (*U*-value) must be limited to maximum acceptable values for commercial and residential buildings according to construction regulations and related energy efficiency standards [1–3]. Therefore, increasing the normal thermal resistance (*R*-value in steady state) of a building envelope is the main measure used to protect the indoor environment from extreme external conditions and reduce the energy consumption on space heating and cooling. However, these factors are not sufficient to characterize the dynamic thermal behavior. In a transient situation, the thermal mass of a structure can store or release heat depending on the surrounding temperature differences. Balaras [4] reviewed tools for calculating cooling load, accounting for thermal mass, and indicated the effectiveness of thermal mass on an indoor thermal environment and energy conservation, particularly in the places with deep diurnal temperature differences. Regulating the amount of thermal mass can increase the time lag and decrease the temperature fluctuation in a conditioned space. Optimizing the thermal mass has been regarded as an important measure for passive heating/cooling strategies and for designing low-energy buildings [5–7]. Besides, the phase change materials (PCMs) embedded in a building

enclosure are regarded as a useful passive method to increase in heat storage capacity and thermal inertia further [8]. The structures are expected to narrow indoor temperature fluctuations and reduce energy demands [9], and the integration of PCM technologies has been on trial in some net-zero energy buildings recently [10,11].

Many studies have focused on the investigation of thermal behavior for an individual building envelope with the objective to optimize arrangement of insulation and massive layers. Al-Sanea [12] developed a concept of dynamic thermal resistance, accounting for the influences of wall orientation, long wave radiation exchange, thermal energy storage, and nominal thermal resistance. With this concept, Al-Sanea et al. [13,14] investigated the effects of insulation locations and various amounts of thermal mass on thermal performances of building external walls based on the climate of Riyadh. They recommended that building walls should contain a minimum critical amount of thermal mass, and that the insulation be placed on the outside in a case where the air conditioning system runs continuously; otherwise the insulation layer should be placed on the inside. Tsilingiris [15–17] investigated the effects of various insulation configurations and heating systems on the energy loss through a building envelope. The results showed that the position of a massive layer strongly influences the transient heat transfer through the structure, but that it has no effect on the heat flux in the time-average quasi steady-state; and they also confirmed that the thermal insulation performs better when located at the inside in an intermittently conditioned room. Deng et al. [18] suggested that the high thermal mass in an external wall should be directly faced toward the indoor air to avoid overheating in the part-time, part-space cooling conditions. An experimental study by Kumar et al. [19] showed that a high inside mass can help to reduce excess heat discomfort for a significant time; i.e., 40% and 98% of the summer and winter respectively in a naturally ventilated office building in India. Reilly and Kinnane [20] developed new metrics (transient energy ratio and effective U-value) to quantify the effects of thermal mass on the energy use for heating and cooling. They found that a high thermal mass possibly causes reductions in energy use in a hot climate with big diurnal temperature differences, but it could lead to more energy use in cold climates. In addition, with the building energy simulation tools being well-developed, the transient thermal behavior can be investigated, and the effect of thermal mass on energy performance can be evaluated in a building approximating real-life, wherein the occupancy gain, solar gain, and HVAC operation strategies can be involved. Rodriguez et al. [21] stated that human behavior is one of the most important factors when understanding building physics. Eben Saleh [22,23] used a computer program named National Bureau of Standards Load Determination to analyze the energy use of an entire building and showed that placing the insulation on the outside of the building envelope can improve performance. Kossecka and Kosny [24,25] utilized simulation software DOE to investigate the thermal performances of six different configurations used in residential buildings in different USA climates. They recommended that a wall with an internal insulation layer can improve performance in a continuously used residential building, but indicated that a wall with inside insulation can enhance performance for intermittent heating and cooling. Verbeke and Audenaert [26] reviewed the impacts of thermal inertia in buildings across climate and building use, and suggested that assessing the impact of thermal inertia should be based on studies on the scale of whole buildings. According to their conclusion, the impacts of thermal inertia on energy use are relatively small and variable, with both positive and negative performances existing, but the thermal inertia can be used to shift the peak-load of an HVAC system in a proper control strategy.

In the light of the previous studies, additional problems have still not been focused on or clearly addressed:


At present, the radiant system has been widely used in recent years and is regarded to have many advantages in indoor environmental control and energy efficiency [27]. As an alternative cooling method, the radiant system is suggested to make use of the construction thermal mass to shift the peak HVAC system cooling load and power use [26,28]. However, as stated by Niu et al. [29], the radiant effect of a chilled ceiling can decrease the heat storage capacity of a building envelope. Feng et al. [30,31] also indicated the cooling load differences between radiant and air systems through simulation and measurement verification. Several methods of operating the radiant system in practice are available [32,33], and appropriate scheduling techniques can provide some opportunities to reduce the energy consumption with smaller initial investments [34]. The present authors [35] have conducted research on the operating characteristics of two radiant systems using various strategies in a typical office building through simulative and on-site measurements. The thermal mass of a slab can be utilized for cooling storage to shift the peak cooling load, particularly for a thermally active building system (TABS) in which a hydronic system is deeply embedded in the slab. In addition, an experimental study by Tahersima et al. [36] showed that the mass in the radiant floor can also be used for heating conservation during off-peak hours, and the operational costs result in significant savings.

On the basis of those considerations, the present study analyzed the effects of thermal mass in external walls on transmission loads in spaces with radiant cooling systems, and we present the differences from an identical room equipped with only an equivalent convective air system (CAS). In addition, operative temperature was used to evaluate the thermal comfort level in a room with radiant surfaces [37–40]. That parameter combines room air temperature and radiant temperature, weighted by convection and radiation heat transfer coefficients respectively.

#### **2. Methodology**

In a zone with a CAS alone, convection heat gain directly becomes the cooling load of the CAS, whereas instantaneous radiation gain is absorbed and stored in the thermal mass, and then converted to be the cooling load by convection with a time lag (Figure 1a). In a zone with a radiant system (Figure 2), which usually acts as a cooling ceiling or a floor, a CAS as an auxiliary system is necessary to maintain the indoor hygiene level, and is responsible for the zone latent load. Thus, besides the convection gain which is immediately handled by the auxiliary CAS, a part of the radiation heat gain is directly absorbed by the cooling surface (active surface). The remaining radiation heat gain is absorbed by the structure or furniture and then extracted by these two systems simultaneously (Figure 1b).

**Figure 1.** Cooling load generation schemes for (**a**) a convective air system [41] and (**b**) for a combined system (fresh air system + radiant cooling system) [35].

Dynamic simulation is generally a reliable method used to compute heat transfer in a given zone [42]. Feng et al. [30] stated that the heat balance method should be employed to calculate the cooling loads of radiant systems; and used the Energy-Plus simulation software to assess the cooling load. Energy-Plus was developed by U.S. Department of Energy and Lawrence Berkeley National Laboratory. The present algorithm models have been validated according to the standard method of test for the evaluation of building energy analysis computer programs (ANSI/ASHRAE 140) [43]. Thus, the Energy-Plus simulation software was also selected for computing instantaneous heat transfer in a building with cooling surfaces in this study. The algorithm is based on the conduction transfer function.

**Figure 2.** Configurations of radiant system.

In this study, the results of instantaneous heat extracted from a given zone (*qZH*), heat extracted by a cooling surface (*qcs*), and the portion due to radiation (*qZRH*, *qCSRH*) are significant for analysis, but they cannot be directly obtained from the simulation, and the deduction process is as follows.

In a conditioned space, heat balances of an inside face and the indoor air can be expressed as follows:

$$q\_{LN\mathcal{V}\mathcal{X}}^{\*} + q\_{SW}^{\*} + q\_{L\mathcal{V}\mathcal{S}}^{\*} + q\_{ki}^{\*} + q\_{sol}^{\*} + q\_{conv}^{\*} = 0 \tag{1}$$

$$q\_{\rm conv} + q\_{\rm CE} + q\_{IV} + q\_{\rm airsys} = 0\tag{2}$$

Thus, total convection heat transfer from surfaces in an envelope can be expressed as follows:

$$q\_{conv} = \sum\_{i=1}^{surfases} q\_{conv}^{"} = - (\sum\_{i=1}^{surfases} q\_{LWX}^{"} + \sum\_{i=1}^{surfases} q\_{SW}^{"} + \\\sum\_{i=1}^{surfases} q\_{LWS}^{"} + \sum\_{i=1}^{surfases} q\_{li}^{"} + \sum\_{i=1}^{surfases} q\_{sol}^{"}) \\\ \tag{3}$$

and the cooling load of the air-conditioning system can be expressed as follows:

$$\begin{aligned} q\_{\text{air sys}} &= \stackrel{\text{surfaces}}{\sum\limits\_{i=1}^{n} q\_{\text{LWX}}^{\*} + \sum\limits\_{i=1}^{\text{surfaces}} q\_{\text{SW}}^{\*}} \\ &+ \stackrel{\text{surfaces}}{\sum\limits\_{i=1}^{n} q\_{\text{LWS}}^{\*} + \sum\limits\_{i=1}^{\text{surfaces}} q\_{\text{ki}}^{\*} + \sum\limits\_{i=1}^{\text{surfaces}} q\_{\text{sol}}^{\*} - q\_{\text{CE}} - q\_{\text{IV}}} \end{aligned} \tag{4}$$

In a zone where a hydronic system is contained in a concrete floor or ceiling (Figure 2), the heat can be conducted from both sides to the internal source. Thus, the heat extraction at cooling surfaces can be expressed in Equation (5) as follows.

$$q\_{\rm fS} = q\_f + q\_\emptyset = -[(\sum\_{i=\rm ceiling}^{\rm floor} q\_{\rm LWX}^{\circ} + \sum\_{i=\rm ending}^{\rm floor} q\_{\rm SW}^{\circ} + \sum\_{i=\rm ceiling}^{\rm floor} q\_{\rm LWS}^{\circ} + \sum\_{i=\rm scaling}^{\rm floor} q\_{\rm sol}^{\circ}] + \sum\_{i=\rm scaling}^{\rm floor} q\_{\rm conv}^{\circ}] \tag{5}$$

Thus, the heat extraction from the thermal zone ( *qZH*) can be expressed as follows:

*qZH* <sup>=</sup> *qf* <sup>+</sup> *qc* <sup>+</sup> *qair sys* <sup>=</sup> *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *LWX* <sup>+</sup> *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *SW* <sup>+</sup> *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *LWS* <sup>+</sup> *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *ki*+ *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *sol* <sup>−</sup> *qCE* <sup>−</sup> *qIV* <sup>+</sup> *qf* + *qc* = *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *LWX* <sup>+</sup> *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *SW* <sup>+</sup> *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *LWS*+ *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *sol* = − *floor <sup>i</sup>*=*ceiling <sup>q</sup>*" *LWX* <sup>+</sup> *floor <sup>i</sup>*=*ceiling <sup>q</sup>*" *SW* <sup>+</sup> *floor <sup>i</sup>*=*ceiling <sup>q</sup>*" *LWS* <sup>+</sup> *floor <sup>i</sup>*=*ceiling <sup>q</sup>*" *sol* + *sur f aces <sup>i</sup>*=<sup>1</sup> *q*" *ki* − *floor <sup>i</sup>*=*ceiling <sup>q</sup>*" *conv* <sup>+</sup> *qCE* <sup>+</sup> *qIV* (6)

However, the size of a radiant system cannot be directly assessed by the Energy-Plus simulation software, because only CAS is assumed when sizing a calculation. For the consideration of differences in the heat transfer process between the zones with and without a radiant system, hydronic systems are assumed in an initial simulation, and the parameters (pipe dimension, water flow rate, water inlet temperature, etc.) refer to many practical items. Thus, repeat computations must be implemented until the room operative temperature can meet the design criteria.

Instantaneous zone radiation heat gain *qZRH* is distributed to the surfaces according to their surface temperatures and shape factors; it is the sum of short wave and long wave radiation gains:

$$q\_{ZRH} = \sum\_{i=1}^{surfacs} q\_{LINX}^{\circ} + \sum\_{i=1}^{surfacs} q\_{SW}^{\circ} + \sum\_{i=1}^{surfacs} q\_{LWS}^{\circ} + \sum\_{i=1}^{surfacs} q\_{sol}^{\circ} \tag{7}$$

Radiation heat gain at the active surfaces *qCSRH* can be obtained using Equation (8):

$$q\_{\rm CSRH} = \sum\_{i=\rm ceiling}^{flow} q\_{\rm LWX}^{\circ} + \sum\_{i=\rm ceiling}^{flow} q\_{\rm SW}^{\circ} + \sum\_{i=\rm ceiling}^{flow} q\_{\rm LWS}^{\circ} + \sum\_{i=\rm ceiling}^{flow} q\_{\rm sol}^{\circ} \tag{8}$$

When *qZRH* ≥ *qCSRH*, a part or all of the radiation heat gain is absorbed by the active surfaces via direct and indirect radiation transfer; for *qZRH* < *qCSRH*, not only is the zone radiation heat gain absorbed, but also more conductive heat transfer on inactive surfaces is compensated by the active surfaces through radiation heat transfer. (Heat gain on the fenestration surface, excluding short-wave transmitted heat gain, is grouped under conduction heat gain for simplicity in this study.)
