## 1 Introduction  
It is widely known that buildings consist of an intensively energy-consuming sector that is responsible for approximately 40% of the worldwide final energy demand [1]. One of the most important energy demands of the buildings regards the coverage of the heating loads. Usually, fossil fuels such as coal, oil and natural gas are used for covering the heating demand of the buildings with the use of radiative terminal units [2]. Moreover, the exploitation of renewable energy sources can be a vital weapon in the existing energy crisis [3]. On the other hand, there is the possibility of using air-driven high-temperature heat pumps for producing hot water (70-80 \({}^{\circ}\)C) for heating purposes. However, air-source heat pumps suffer from a reduced coefficient of performance (COP), usually lower or close to two [4], especially in a cold climate and at relatively low-temperature levels. Thus, this alternative faces the challenge of reduced performance, and this fact makes the superiority of this technology marginal. An alternative choice is the use of a solar- or geothermal-driven high-temperature heat pump coupled to radiative terminal units for heating purposes [5]. This technology makesthe operation possible with an increased COP due to the relatively higher temperature of the water compared to the ambient source [6]. The solar or geothermal energy feeds the heat pump with a heat input of a relatively satisfactory temperature which can be in the range of 20-40 \({}^{\circ}\)C [7] for the solar system and around 15-25 \({}^{\circ}\)C [8; 9] for the geothermal source case. So, these systems can operate without extreme electricity consumption and their operation is not so affected by the variation in the ambient source temperature. Moreover, it is useful to add that an alternative choice is the exploitation of photovoltaic technology for driving the compressor and the pumping system of the unit [10; 11]. Another important issue is the application of environmentally friendly working fluids in the heat pump aiming for sustainability [12]. The literature includes a significant number of investigations that study the utilization of solar or geothermally driven heat pumps for heating purposes. The investigation of these systems is a critical weapon for facing the existing energy crisis and developing new and green technologies for covering the buildings' thermal needs in an adequate way. Thus, this area has attracted more and more interest in the last few years. [PERSON] et al. [13] compared the utilization of a solar-assisted heat pump (SAHP) driven by solar flat-plate thermal collectors (FPC) with an air-source heat pump (ASHP). They concluded that the mean seasonal COP of the SAHP is 3.75, the ASHP presents a value of 2.94 and the payback period was found at 6.6 years. [PERSON] et al. [14] studied a SAHP with evacuated tube collectors (ETC) by applying an optimal storage control. They compared their system with a conventional electrical heater, and they found electricity savings of about 75%. In another study with a SAHP with ETC, [PERSON] et al. [15] found the yearly COP at 3.5 while the ASHP presented a value of around 3. [PERSON] et al. [16] examined the use of a triangular air heater for feeding a SAHP for heating purposes. They calculated a 64% increase in the system's COP compared to the conventional air-source heat pump. The use of a thermal photovoltaic for driving a SAHP was examined by [PERSON] et al. [17]. They covered space heating and DHW needs with the examined configuration, while its COP was found in the range of 2.64 to 3.85 depending on the operating mode. The operation of a low-concentration solar collector coupled with a SAHP was investigated by [PERSON] et al. [18]. They used compound parabolic concentrations for feeding the heat pump and they calculated the seasonal COP at 4.7. [PERSON] et al. [6] conducted a detailed comparison of the SAHP with an ASHP for different European cities and it was concluded that the SAHP leads to a 35% greater COP.