The roles of thermal insulation and heat storage in the energy performance of the wall materials: a simulation study

A high-performance envelope is the prerequisite and foundation to a zero energy building. The thermal conductivity and volumetric heat capacity of a wall are two thermophysical properties that strongly influence the energy performance. Although many case studies have been performed, the results failed to give a big picture of the roles of these properties in the energy performance of an active building. In this work, a traversal study on the energy performance of a standard room with all potential wall materials was performed for the first time. It was revealed that both heat storage materials and insulation materials are suitable for external walls. However, the importances of those materials are distinct in different situations: the heat storage plays a primary role when the thermal conductivity of the material is relatively high, but the effect of the thermal insulation is dominant when the conductivity is relatively low. Regarding internal walls, they are less significant to the energy performance than the external ones, and they need exclusively the heat storage materials with a high thermal conductivity. These requirements for materials are consistent under various climate conditions. This study may provide a roadmap for the material scientists interested in developing high-performance wall materials.


Physical and numerical models
Here we will elaborate the heat transfer processes and corresponding models for the walls. Two primary simulation assumptions are made in BuildingEnergy: (1) the heat transfer across the building envelope is one-dimensional; and (2) the indoor temperature of the room and that of the adjacent rooms is the same, so the center surfaces of the interior walls are adiabatic.
where the superscript p is used to denote the time dependence of T, and the time derivative is expressed in terms of the difference in temperatures associated with the new (p+1) and previous (p) times. From the energy balance perspective, the left-hand side of Equation (1) represents the rate of increase of thermal energy stored in the node-controlled volume. The

Supplementary Information
terms on the right-hand side are, in sequence, the heat flows entering the node from the adjoining node by conduction, that from the other surfaces in the room by the long-wave thermal radiation, and that from the indoor air by convection.
For the node at the outdoor surface of the external wall, i.e., Node n in Figure S 1 where the four terms on the right-hand side are the heat flows entering the node from the adjoining node by conduction, that from the sun by absorption, that from the outdoor surrounding by the long-wave thermal radiation, and that from the outdoor air by convection.
For the node at the indoor surface of the internal wall, i.e., Node 1 in Figure S 1 (d), the energy balance equation is written The energy balance equation for the node on the adiabatic surface of the internal wall, i.e., Node n in Figure S For the internal nodes of both the external and internal walls, the energy balance equations can be written in a single discrete form as which is also known as the discrete heat diffusion equation.
The subscript i denotes the ith node of the external or internal wall.
In these equations, k, ρ and c p are relevant to the thermophysical properties of the wall materials and are the parameters of interest. As already known, k measures the ability of a material to conduct thermal energy. It can be observed that ρ and c p are always multiplied together, so they can be grouped into a single parameter: volumetric heat capacity C V , which measures the heat storage capacity of a material per unit volume.

Experimental validation of BuildingEnergy
The program was validated through a series of experiments in a testing platform located in the campus of University of Science and Technology of China, which is illustrated in Figure

Treatment of the thickness of the walls
In addition to the thermal conductivity and volumetric heat capacity of the material that constitutes a wall, the thickness, δ, also plays an important role in the performance of the walls. However, it is complicated to analyze the performance of walls that identified by three variables. To simplify the analysis by reducing a variable, we will employ a treatment of δ, in which the influence of δ is incorporated into that of k and C V . With the help of this treatment, we can hold the thickness of the walls constant and discuss the effects of k and C V on the performance, and the results may also be adapted to any other thicknesses.
In Equation (1) where Equation (1)~(5) for each type of nodes have been classified into two types of equations: that for the surface nodes (6a) and that for the internal nodes (6b). Another simplification has been made by absenting the terms irrelevant to the thickness. Equation (6) can also be rearranged as Due to the absolute equivalence between Equation (6) and (7), the temperature filed determined from these equations are the same, indicating that each node depicted in Figure S 1 (c) or (d) of one wall is at the same temperature with the corresponding node of the other wall, namely, T 1,i = T 2,i (i = 1, …, n) where the subscript 1 or 2 denotes the wall controlled by Equation (6) or (7). Specifically, the wall with a thickness of Δx 1 ×n or δ 1 and properties of (δ 1 /δ 2 )·k and (δ 2 /δ 1 )·C V , which subjected to Equation (7) and labeled as Wall-1, has an identical temperature distribution of the nodes with that of (δ 2 /δ 1 )·Δx 1 ×n or δ 2 , k and C V , which related to Equation (6) where q is the instantaneous load for space cooling or heating, and T j is the temperature of each surface in a room. The room that contains Wall-1 and the cooling or heating load that needed in the room are separately designated as Room-1 and q 1 to facilitate the presentation. Likewise, the denotations of Room-2 and q 2 are associated with Wall-2. In Equation (8) is the same with the corresponding one in Room-2 containing that of Wall-2, revealing the equivalence between q 1 and q 2 . In other words, the wall with a thickness of δ 2 and a material of k and C V has the same energy performance as the wall with a thickness of δ 1 and a material of (δ 2 /δ 1 )·k and (δ 1 /δ 2 )·C V , meaning that a variation in δ may be incorporated into a change in k and C V . With this useful treatment, the thicknesses of the walls can be normalized into a same value to reduce a variable.
From another aspect, results for a single thickness may also be converted into those for any other thicknesses. From Equation (10), it is evident that U-value is related to the total thermal resistance for the heat transfer between the outdoor air and the indoor air by conduction and convection.

Perspective of engineers
As convection is beyond the scope of this study, U-value depends entirely on the thickness and thermal conductivity.
Equation (10) also implies that the U-value is invalid for an internal wall because no heat transfer occurs across the adiabatic center.
Referring back to the treatment of thickness, the wall with a thickness of δ 1 and a material of k 1 and C V1 was equivalent to the wall with a thickness of δ 2 and a material of (δ 2 /δ 1 )·k 1 and ( 1 1 ) The parameters of each wall are equivalent, implying that the principle of the thickness substitute is to maintain the U-value and total heat capacity constant. The requirements for the wall materials may also be stated as the demand for the wall as a whole component. They can be summarized as: the total heat capacities of both the external and internal walls should be high, and the U-value of the external wall should be low.

General applicability of the results
The  Figure S 3 (c), the roof of the room is also exposed to the external environment, more than one external wall of the basic room. This room can be also perceived as a room with two external walls.

Figure S 3 Results of the rooms with different configurations.
Each subfigure presents one type of configurations based on the basic room, which has a dimension of 4 m ×4 m ×4 m and whose exclusive external wall facing towards the south contains a window of 1.5 m × 1.5 m. The external wall room in (a) faces towards the east. The room in (b) has a dimension of 3 m (height) ×4 m (width) ×5 m (depth). The room in (c) contains two external envelopes, the south wall and the roof. The window of the room in (d) has a size of 2 m × 2 m.

Results under extreme climates
In addition to the cities of Hefei, Beijing and Guangzhou in the main text, two more Chinese cities, Turpan and Mohe, were chosen to represent the cities under the extreme weather.
Turpan locates 42.93° N, 89.2° E, and is of the desert climate. It shares the record of the highest air temperature that once appeared in China. We considered the hottest three months in Turpan, i.e., June, July and August, during which the variations of the dry-bulb temperature are shown in Figure S 4 (a). The corresponding results are displayed in Figure S 4