## 1 Introduction  
The hot-wall heat exchanger (HWHE) has been widely used in thermal engineering fields such as ceiling radiant heating/cooling, refrigerator condenser, solar heat collection, and high-temperature heat recovery. HWHE-based ceiling radiant heating/cooling has attracted much attention in the air conditioning field due to its energy saving and improved thermal comfort. The schematic diagram of a typical radiant heating/cooling HWHE is shown in Figure 1. Another important application of HWHE is in solar heat collectors, which consist of a plate absorber and the pipe (may be another type of channel) directly exposed to air; energy can thus be obtained by the fluid in the pipe from both the air and solar radiation. Besides, HWHE is also widely used in household refrigerator condensers as shown in Figure 2.  
Due to the wide applications of HWHE in the field of building energy conservation and sustainable energy application, several studies have been conducted in thermal property predication and optimization of HWHE. A typical HWHE consists of steel tubing (coated with copper) installed by direct contact with the inner surface of the iron plate of the side walls to realize heat transfer with the external environment. The contact of the tube and plate in HWHE could be regarded as a line in theory, and it may even be a dotted line if the perpendicularity of the tube or the flatness of the plate cannot be guaranteed. In order to ensure close contact and increased heat transfer area between the tube and the plate, several methods including flat tubes, fixing the pipes to the plate using aluminum foil, and increasing the contact angle between the pipe and the plate [1] are normally used, as shown in Figure 1.  
Theoretical models of HWHE have been developed for radiant heating/cooling applications in literature studies. [PERSON] et al. [2] developed an analytical model for the heat transfer of radiation from ceiling cooling and the main factors affecting heat transfer were pointed out according to the theoretical and experimental results. [PERSON] and [PERSON] [3] derived an analytical model for a top insulated metal ceiling radiant cooling panel (CRCP) with parallel tubes, and the analytical model was modified in the studies of [PERSON] and [PERSON] [4; 5]. [PERSON] et al. [6] presented and validated a simplified model for top insulated metal CRCP with serpentine tube arrangement and the influence of pipe spacing, pipe diameter, plate thickness, and plate materials on cooling performance were studied with the model. HWHE is usually used as the condenser in refrigeration applications. The calculation method in the design condition and the key factors influencing heat transfer performance of HWHE as condenser have been given and discussed in several studies. [PERSON] et al. [7] developed a simulation model to calculate heat transfer on the air side of tube plate condenser and the calculation method of heat convection coefficient for the outer nonisothermal plate was determined. [PERSON] and [PERSON] [8] studied the heat transfer of wall plate heat exchanger with thermal resistance method. The heat transfer through the foam insulation into the cooling zone of the refrigerator and the heat transfer enhanced  
Figure 1: Hot-wall heat exchanger (HWHE)-based ceiling radiant heating/cooling for a building. Figure 2: HWHE for a household refrigerator condenser. by aluminum foil used to fix the pipes were neglected as well in their study [8]. [PERSON] and [PERSON] [9] presented a mathematical model of hot-wall condensers in which the condenser tube was divided into elemental units, with each element consisting of adhesive aluminum tape, a refrigerant tube, and outer metal sheet. Their study showed that the aluminum tape used to stick the condensing tube to the outer sheet played a significant role in heat transfer from condenser to environment [9]. [PERSON] and [PERSON] [10] analyzed the heat transfer of hot-wall heat exchangers using the finite element method, neglecting the influence of aluminum foil.