# Design of the Building Interiors for Efficient Passive and Free Cooling

The amount of cold that can be stored in the building structures is determined by (1) indoor air temperature fluctuation over the day determined by acceptable indoor thermal comfort and (2) the capacity of the building structure to accumulate the cold. This means that the building structure is cooled during the nighttime by one of the passive or free cooling techniques and stores the heat at lower indoor air temperatures during the daytime to prevent overheating and decreasing the energy needs for mechanical cooling.

## With Respect to the Indoor Thermal Comfort

Acceptable range of indoor air temperatures is prescribed by indoor thermal comfort requirements. Standard EN 15251 (2017) defines the quality classes I, II, III, and IV of indoor air temperature 0; for building different categories (use). For example, in office buildings, the summertime indoor air temperature should be in the time of occupancy in the range between 22°C and 27°C (Category III of thermal comfort); meanwhile, Category I of thermal comfort indoor air temperature should be in the range between 23.5°C and 25.5°C. Most often, the indoor thermal comfort Class III is required. It can be concluded that passive and free cooling can be effective without undesirable effect on the indoor thermal comfort. Taken into account indoor thermal comfort requirements, office buildings, kindergartens, schools, and department stores are among most suitable for efficient passive and free cooling.

## With Respect to the Accumulation of the Cold in the Building Structures

In passive or free-cooled buildings, building structures are exposed to the periodic changes of indoor air temperature, which enables a periodic process of storing and releasing the heat in the interior of buildings. The non-stationary indoor air temperature is modeled as a periodic function 0,(0:

where 0j (°C) and 0j (°C) are the daily average and amplitude of indoor air temperature, t_{p} is the period (24 h or 86,400 s), and cp is the time lag of amplitude according to twelve o’clock. It is assumed that there is no thermal resistance to the surface heat transfer between the indoor air; therefore, 0, (t) is equal to the 0_{si} (0,t). Assuming that transient heat transfer is one-dimensional and a homogeneous single-layer building construction, the solution of the differential equation of transient heat transfer in building structure is given by (EN 15251:2017):

where 0(x, t) is the temperature (°C) of building structure at a depth x of the building structure at a time t, 0_{si} (°C) and 0_{si} (°C) are the average surface temperature and the amplitude of the building structure in the period t_{p} (24 h or 86,400 s), a is the thermal diffusivity (m^{2}/s), and t is the time (s). The temperature at a depth x will be the highest when the part defining the time shift of the amplitude is 0. From that fact the effective thickness d_{p} of the building structure can be developed. It is defined as the depth x of the structure where the amplitude of the temperature decreases by a factor of 1/e to 0.367 • 0,. It is defined with the expression:

where a is the thermal diffusivity of materials (m^{2}/s).

The double (2d_{p}) and triple (3d_{p}) effective thickness are defined similarly, whereby the amplitude is reduced by a factor l/(2-e) to 0.184 • fy, or by a factor of l/(3-e) to 0.122 • 0j. In the design of capacity of the heat storage of the building structure, the double thermal response depth 2d_{p} is usually selected. The amount of the specific heat that is accumulated in m^{2} of building structure area during half of period t_{p} (an “realized” during the second half period) is equal to (Medved et al., 2019):

where X is the thermal conductivity of single-layer building structure (W/mK), c_{p }is the specific heat capacity (J/kgK), p is the density (kg/m^{3}), and b is the thermal effusivity (kJ/m^{2}Ks^{05}).

Case study: Determine the effective thickness and required area of the building structure made of solid concrete (a = 68 x 10^{-8} m^{2}/s, b = 2.18 kJ/(m^{2}Ks^{05}) and by solid wood (a = 14 x 10^{-8} m^{2}/s, b = 0.38 kJ/(m^{2}Ks^{05})) that will in the theory accumulate 1 kWh of daily solar gains. Assume that 6j is equal to 3K. The effective thickness 2 x d„ of the concrete building structure is ~250 mm, and of the wooden one is ~ 120 mm. To store 1 kWh of solar gain without overheating of the room ~2.5 m^{2} of concreate and ~14 m^{2} of wooden construction is needed.

In the case explaining the procedure for determining the effective thickness of the building structure for periodic accumulation of the cold, we assumed that indoor air temperature 9_{;} is equal to the surface temperature 0_{si} of the building structure. This means that convective heat transfer resistance R_{c si} was assumed to be 0 (h_{c si} = oo). In reality, this is not the case, and the capacity of cold accumulation in building structures is lower.

The convective surface’s heat transfer coefficient used to determine heat transfer in building structures is listed in ISO 6846:2017. The standard suggests h_{c si} 2.5 W/m^{2}K for vertical walls, 0.7 W/m^{2}K for floors, and 5.0 W/m^{2}K for ceiling. Nevertheless, the temperature difference between the indoor air and surface temperatures of building structures in the passive cooled room by ventilation is much higher (6 to 8 K) than in the temperature- controlled buildings. Meanwhile, the indoor air velocity is much higher compared to the thermal buoyancy-driven convection (v_{;} is in the range between 0.15 and 0.25 m/s) in the closed room. The maximum air exchange rates can be 10 lr^{1} or above, which significantly increase convective heat transfer at the surface of building structures. This is especially the case in free cooled buildings, where air exchange rates could be even larger.

Some examples available in the literature of the approximation models (ASHRAE, 2001; Khalifa and Marshall, 1989) for determination of the average surface convective heat transfer coefficient h_{c avg wall} for vertical walls dependent on the temperature difference Л9 between indoor air 0, and surface temperature 9_{sj} of the building structure are shown in Figure 15.16. In can be seen that h_{c waU} is in the range between

1.8 and 3.3 W/m^{2}K taking into account the temperature difference Д0 4K and 8K.

In the case of free cooling, room air exchange rates (ACH) are even larger, and surface convection becomes mixed, and the surface convective heat transfer coefficient combines

FIGURE 15.16 Approximation models for convective surface heat transfer coefficient dependant on temperature difference Д0; between indoor air temperature and surface temperature of wall 0_{si}.

FIGURE 15.17 Approximation models for convective surface heat transfer coefficient in case of free cooling of the buildings dependent on temperature difference of the supply air velocity vi„ and ACH.

natural and forced convection phenomena. Among several researches, an approximation model for local surface heat transfer coefficient for mix convection caused by supply air jet blown near a vertical wall was developed by Venko et al. (2015). An approximation model of the average convective surface heat transfer coefficient that includes inlet velocity of adiabatic supply air temperature and a model that includes ACH as an independent variable were presented by Fisher and Pedersen (1997). The approximation models are shown in Figure 15.17. Taking into account the range ACH between ACH 10 tr^{1} and 20 h^{_l}, the h_{c avg waU free} is in the range between 6.24 and 7.40 W/m^{2}K.

It can be concluded that in numerical modeling of thermal response of nonmechanical cooled buildings, the standardized convective surface heat transfer coefficient should be replaced with one that includes bought temperature difference and ACH as influence variables.