Four kinds of temporal operators

It was observed that ETFE-foil surfaces and the test rig’s air temperatures were strongly influenced by outdoor environment e.g. incident solar radiation, outdoor ambient temperature, longwave radiation. Harvie (1996), stated that with no thermal mass architectural fabrics affect the spaces by the amount of solar radiation they transmit and heat they introduce into space as a result of the temperature of their surface. In this study transmittance of solar radiation through different type of ETFE-foils was measured which is presented in section 5.4. Besides it was already discussed earlier that convective and radiative heat transfer particularly affects the thermal environment of test-rigs enclosed with ETFE-foil panels. Therefore, it was important to evaluate the impact of these two heat transfer mechanisms on the thermal environment of the test-rigs. This was done by calculating convective and radiative heat transfer through the surface of the ETFE-foil, on the basis of measured surface temperatures of ETFE-foil, adjacent air temperatures of foil panel and emissivity of the ETFE-foil

5-142 surface. Convective heat transfer that occurred between the surface of the ETFE and adjacent air (air-volume of the ETFE-foil panels) of Test-rig 1 and Test-rig 2 during 6^th and 11^th September 2015 is presented in Figure 5-30, whereas Figure 5-31 presents the radiative heat transfer that occurred through the surface of ETFE-foil during the same period.

It can be assumed that the convective heat transfer occurred in between the ETFE-foil surface and the internal air of test-rigs through natural convection, where the flow was induced by buoyancy forces which arise from density differences, caused by the temperature difference in the test-rig air. The rate of this convective heat transfer was calculated on the basis of Equation 5.1, stated in Incropera et al. (2013). This expression is also known as Newton’s law of cooling.

𝑞 = ℎ(𝑇_𝑠− 𝑇_𝑎) ……..(5.1) Here, 𝑞 is convective heatflux (W/m²),

𝑇𝑠 is surface temperature (K) of ETFE-foil, 𝑇𝑎 is air temperature adjacent to ETFE-foil,

ℎ (W/m² K) is the convective heat transfer co-efficient.

The convective heat transfer co-efficient was calculated according to (BSI, 1989).

As stated by Incropera et al. (2013), radiation transfer efficiently occurs in the volume of air which is similar to the test-rig’s internal environment. Radiative heat transfer depends on the emissivity of the ETFE-foil surface. The radiative heat flux emitted by the ETFE-foil surface was calculated using Equation 5.2.

𝐸 = 𝜀𝜎𝑇_𝑠⁴ .…..(5.2) Here, 𝐸 represents radiative heat flux (W/m²),

𝜀 is the emissivity,

𝑇𝑠 is the surface temperature (K) of ETFE-foil.

Boundary conditions obtained during the experiment were directly applied in these equations to calculate convective and radiative heat flux. From Figure 5-30 and Figure 5-31 it can be stated that convective heat flux governs in the heat transfer process in both of the test-rigs. Because this type of heat flux depends on temperature difference, therefore heat was transferred between each layer of the ETFE-foils and air adjacent

5-143 to it. This heat transfer was particularly significant between the external ETFE-foil surface of the multilayer panel and adjacent air-volume, which was the result of higher temperature difference.

It is known that ETFE-foil is relatively transparent to longwave radiation. Radiative heat transfer occurring in the ETFE-foil surfaces was calculated using Equation 5.2 and presented in Figure 5-31. The radiative heat transfer here represents the combined effect of shortwave and long-wave radiation. Because it was not possible to isolate the effect of long-wave radiation. It can be assumed that during the day, heat transfer occurred on the surfaces was dominated by short-wave radiation. Whereas at night due to longwave radiation losses surface temperature dropped, this, in turn, reduced heat transfers in air and ETFE-foil layers. For optically thin surfaces, the radiative heat transfer decreases with the decrease of surface emissivity (Libby et al., 1967).

Therefore, among the different layers of ETFE foils in multi-layer panels, radiative heat transfer was more pronounced on internal transparent ETFE-foil surfaces. Whereas little less in external fritted surfaces which were the result of low emissivity and the relatively lower temperature of external surfaces (Ts1) while compared with internal surfaces (Ts2 and Ts3) in each test-rig. Besides particularly at night and early morning, stable conditions occurred, however as soon as the external surface temperatures increased above the internal surface, radiative and convective heat transfer was constant for all the surfaces and increased as the temperature difference increased between the surface of ETFE-foil and adjacent air layers during the day.

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Figure 5-30: Convective heat transfer between ETFE surface and air temperature adjacent to it in Test-rig 1 and Test-rig 2

Figure 5-31: Radiative heat transfer through ETFE-foil surface in Test-rig 1 and Test-rig 2

Impact of mesh on convective heat transfer was also evident particularly on 6^th September, when a sudden increase in heat transfer was apparent at 3.00pm, one hour after the rain mesh was removed from Test-rig 2. Heat transfer accelerated

6^th Sep 15 9^th Sep 15 10^th Sep 15 11^th Sep 15

5-145 between internal surface (Ts3_B2) of the ETFE-foil and internal air temperatures (Ta_H1 B2) of Test-rig 2.

5.5.2 Impact of rain mesh on internal thermal condition of the experimental