## 3 Results
### Parametric Analysis and Optimization  
The present section examines the yearly performance of the unit parametrically by presenting the results for different combinations of the design parameters. The solar field area and the thermal tank volume are the designed parameters that are studied in detail. Figure 9 shows the influence of the collecting area on critical energy quantities of the unit while the storage tank volume is equal to 3 m\({}^{3}\) in this figure. A higher collecting area leads to a greater useful heat product from the solar field but with a decreasing rate. The decreasing rate is reasonable because a higher solar field area increases the mean operating temperature in the tank and therefore the solar efficiency is reduced. The increase in useful heat product practically gives the system a higher energy input and makes it possible to reduce the electricity consumption with the collecting area increase. This reduction is more intense in the auxiliary electrical consumption, while the compressor electricity consumption is decreased but not dramatically. More specifically, the auxiliary electrical consumption decreases from 3591 kWh to 210 kWh, while the compressor electricity consumption decreases from 5881 kWh to 1669 kWh. Figure 7: Electricity demand for the compressor and the auxiliary electrical resistance in the tank for the case with 30 m\({}^{2}\) collecting area and 3 m\({}^{3}\) tank volume (1 October to 30 April). Figure 10 depicts the influence of the tank's volume on the crucial energy quantities of the system while the collecting area is equal to 30 m\({}^{2}\) in this figure. A larger storage tank's volume makes the mean temperature of the fluid be reduced and so the thermal performance of the solar system is increased. This fact justifies the increase in the useful heat production of the solar field with the increase in the storage tank volume. Moreover, a higher storage tank capacity leads to smaller electricity consumption, especially by reducing the auxiliary electrical resistance consumption. The compressor consumption shows a very small reduction with the increase in the tank's volume. Figure 8: COP for the system and the heat pump for the case with a 30 m\({}^{2}\) collecting area and 3 m\({}^{3}\) tank volume (1 October to 30 April). Figure 9: Variation in energy quantities for different collecting areas with the storage tank volume at 3 m\({}^{3}\). The next part of this work is the depiction of the results for different combinations of the two examined design parameters. Figure 11 illustrates the mean yearly solar thermal efficiency for the different studied cases. According to the results, a higher collecting area reduces the efficiency because greater useful heat production increases the mean operating temperature, something that leads to higher thermal losses in the solar system. Moreover, the increase in the storage tank volume can lead to a slightly higher collector thermal efficiency due to the decrease in the mean operating temperature in the system. The range of the yearly solar thermal efficiency is found to be from 20.91% (for A\({}_{\rm col}\) = 50 m\({}^{2}\) and V = 1 m\({}^{3}\)) to 64.54% (for A\({}_{\rm col}\) = 10 m\({}^{2}\) and V = 5 m\({}^{3}\)). Figure 11: Mean yearly solar thermal efficiency of the collectors for different combinations of (A\({}_{\rm col}\)) and (V). Figure 10: Variation in energy quantities for different storage tank volumes with the collecting area at 30 m\({}^{2}\). Figure 12 exhibits the impact of the total electricity demand for the different combinations of the collecting areas and tank capacities. It is clear that a higher solar field area reduces the electricity demand because there is a greater available heat input in the system. Moreover, a larger storage tank also reduces the electricity demand because a greater storage tank makes the most appropriate management of useful heat production possible.