The advantages of great indoor thermal comfort and energy savings are the primary reasons why floor radiant heating has become such a popular heat supply mode [1–3]. In southern China, although building energy saving is very necessary [4–5], room heating demand in winter is one increasingly important issue, as a result of outdoor climatic impact and people’s concerning about indoor comfort. As to avoid the rapid growth of energy consumption and improve indoor thermal environment in winter, discontinuous radiant heating has widespread application in this region. The discontinuous radiant heating is used to meet the need of heating when someone is inside room and has thermal comfort requirement, but stop heating when no one is in the room. Namely, the discontinuous radiant heating can meet the heating demand of part time and part space under reasonable control strategy. At present, the floor radiant heating system is a universal form of discontinuous radiant heating in southern China. For the whole process of discontinuous radiant heating, effective and timely guarantee of indoor thermal environment depends on the features of floor radiant heating system, the control system, the thermal insulation performance of the external walls and outdoor climate.
The performance of floor radiant heating is one basic factor impacting the indoor thermal environment under discontinuous radiant heating, which is affected by multiple parameters. Sattari et al.  studied the effects of design parameters on the performance of typical radiant floor heating system using the finite element method; transient conduction, convection and radiation heat transfer mechanisms were considered. Fontana  examined the thermal performance of floor radiant heating system on a scale model and evaluated the effect of furniture. Zhang et al.  presented a simplified calculation of the heating capacity of radiant heating floor, the uniformity of the surface temperature distribution and the lowest temperature at the surface, found that the thickness and heat conductivity of each layer had important influences on the performance of radiant floor and the influence of the water pipes should not be ignored. Zhang et al.  analysed the operating characteristics of one lightweight radiant floor heating (LRFH) system and investigated a heat transfer model for the evaluation of LRFH. They determined the heat-transfer capability, temperature field distribution and thermal comfort of the LRFH system by using the model. The above research results indicate that there is a complex heat transfer process in floor radiant heating system. The process includes internal heat transfer and surface heat exchange. Accordingly, the thermal boundary condition derived from the radiant heating floor should be reasonably determined in the heat transfer model of building room. In addition, regarding the advantage of radiant heating, Milorad Bojić et al.  investigated the energy, environmental and economic performances of the floor, wall, ceiling and floor-ceiling heating and found that the floor-ceiling heating had the best performances, including the lowest energy and exergy consumption, the lowest exergy destruction, the lowest carbon dioxide emissions (compound, direct, and avoidable), the lowest operation costs, and the use of a boiler of the lowest power. Zheng et al.  found the non-heating surface temperature had a significant impact on the heat output of the radiant floor. Koca and Çetin  found when the wall was integrated to the ceiling, total and radiant heat transfer coefficients decreased in both ceiling and wall, convective heat transfer coefficient also decreased in wall but increased in ceiling cases. Wang et al.  built a dynamic heat transfer model based on thermal-electrical analogy to compare convective and radiative heating systems for intermittent heating. Kuznetsov et al.  revealed the mean convective Nusselt number at the bottom solid-fluid interface was slightly altered in the cavity with the local radiant heater when varying the governing parameters. In addition, Jia et al.  found it is possible to use the air temperature for controlling the radiant systems in lieu of the operative temperature, as a result of reducing both first cost and maintenance costs. It can be seen from above research results that the performance of radiant heating may change with multiple factors.
For another thing, the thermal performance of building external wall is one important factor impacting the achievement of floor radiant heating property, especially under discontinuous operation. At present, according to the form and structure of thermal insulation, there are four types of external wall thermal insulation applied in building room, as shown in Fig. 1. Moreover, according to actual function of each layer, external wall structure and constitution can be divided into three layers, namely, the coating layer, insulating layer and structural layer, although they may be multi-layered. The self-insulating layer has functions of both thermal insulation and structural force bearing. The structural layer is only used for structural force bearing. Their thermal performance index can be adjusted by choosing reasonable materials for each layer and meet requirements of the local situations. As to obtain the differences of diverse external wall thermal performance, the heat transfer models and assessment methods are necessary. Diasty  developed a finite difference model that had advantages in describing the thermal performance of multi-layered wall panels. Saleh  studied and evaluated three different arrangements of building insulation with different thicknesses, considering their thermal performance and impact on indoor temperature in a hot-dry climate context. The utilization of thermal insulation showed a significant improvement when the thermal insulation was located on the outer side of the building envelope. Kossecka et al.  analysed the effect of mass and insulation location on the heating and cooling loads for six characteristic wall configurations and discussed the correlations between the structural and dynamic thermal characteristics of walls. According to the energy analysis of a one-story residential building with various external wall configurations for six different US climate conditions, the best thermal performance was obtained when massive material layers were located at the inner side and directly exposed to the interior space. Praditsmanont et al.  found that the Main Hall's lightweight and highly insulated building envelope outperformed other commonly used heavyweight envelopes in preventing building energy gain in the hot-humid climate of Thailand. Peng et al.  developed a new harmonic method, the thermoelectricity analogy method (TEAM), to compute the periodic heat transfer in external building envelopes (EBEs). Comparisons showed that this method was highly accurate and efficient. Aste et al.  assessed the parameters enhancing or damping the role of thermal inertia and provided a variety of results. Several external wall systems with the same thermal transmittance but different dynamic properties were investigated to calculate the associated achievable energy savings. Tosun et al.  proposed a new approach for determining the thermal insulation layer using the artificial neural network (ANN) technique. Their research results showed that the ANN model can be used as a reliable modelling method. Alterman et al.  developed a novel concept for characterizing the dynamic thermal response of walling systems and assisting in the evaluation of thermal performance of walling systems and possible housing. Kaynakli  provided optimization procedures and economic analysis methods for insulation thickness, implemented a practical application and investigated the effective parameters to achieve the optimum value. Giancola et al.  found the ventilated facade could play an important role in reducing the heating and cooling thermal loads as long as the outdoor temperatures were not extreme in warm climates with high levels of solar radiation. Moreover, Giancol and Soutullo et al. [26–27] evaluated the improvement of indoor environment by upgrading the thermal characteristics of building envelope in a social housing. They found the refurbishment of building envelope was always convenient for better indoor microclimate and thus energy savings. Mirsadeghi et al.  discussed the uncertainty related to the use of external convective heat transfer coefficient models by means of a case study. Zhang et al.  developed a method of determining the ideal thermal conductivity of an external wall with constant volumetric specific heat based on the concept of ideal passive energy-efficient buildings. After the optimization of external wall used in a passive room of Beijing, the integrated discomfort degree was reduced by 64.3%, compared with that of the traditional external wall. Stazi et al.  verified the dynamic performance of three kinds of envelopes characterized by different traditional wall constructions adopted in temperate climates and determined the impact of different retrofit solutions on the buildings. The results indicated that the behaviour of three kinds of envelopes differed greatly because they interacted in different ways according to changes in the climate. Sanchez et al.  focuses on the analysis of open joint ventilated facades with both vertical and horizontal apertures. The mean velocity and the turbulence quantities were enhanced by buoyancy. It had also been observed that the instabilities in the flow increased with the Ra numbers. As confirmed by the above studies, the influence level of the insulation location on the thermal performance of building external wall strongly depends on their exposure conditions to the thermal environment.
It can be seen from existing studies that, as to certain floor radiant heating system and outdoor climate condition, the performance behaviour of building external wall has a close relationship with effective and timely improvement and realization of indoor thermal environment, especially for discontinuous radiant heating. Namely, reasonable assessment of thermal performance of building external wall is very necessary under discontinuous radiant heating condition. However, basic parameters, such as heat transfer coefficient, heat storage coefficient and so on, can’t directly reflect the perfor- mance behaviour of building external wall under discontinuous radiant heating condition and outdoor climate impact. In addition, direct heat exchange is occurring between external wall inner surface and indoor air. Moreover, the inner surface temperature for specific external wall is depending on outdoor and indoor air temperature. Therefore, the direct connections and interactions among the indoor air temperature, external wall inner surface temperature, and outdoor air temperature should be established to reveal the mechanism of coupled heat transfer occurring among
Fig. 1 Four kinds of external wall used in building room
them. For the aforementioned research purpose, this present study involves a proposed method, namely, the first and second impact factors of temperature deviation based on a mathematical model of room heat transfer, which establishes the direct connections of these three kinds of temperature and is used to evaluate the thermal performance of external wall of one experimental room and four types of external walls under discontinuous radiant heating condition.