## 6 Conclusions  
The performance of a multi-functional CO\({}_{2}\) HP WHS with the functions of both hot water supply and bath heating has been analyzed by numerical simulation. First, a component model for a storage tank were revised by assuming partly perfect mixing based on the experimental results, in case that hot water retrieved from the top of the storage tank is returned to the bottom or side of the storage tank after heat exchange for bath heating. Second, component models for a heat exchanger and a bathtub have been newly created, and these models have been combined with those for the other components to form that for the system. Finally, a performance analysis has been conducted under daily repeated hot water and bath heating demands, and the system performance has been evaluated at a periodically steady state after several days. The hourly changes in the temperature distribution in the storage tank and HP COP, as well as the daily system performance values, have been investigated in comparison with those of a uni-functional system with the function only of hot water supply. In addition, the influence of the position for hot water return on the system performance has been examined. The following main results have been obtained:  
* In the multi-functional system, the temperature at the middle of the storage tank rises when hot water is returned to the bottom of the storage tank. As the position for hot water return is heightened, the part with a constant temperature at the middle of the storage tank is also heightened. * The multi-functional system has almost constant (although lower) HP COP during the middle of HP operation when hot water returned to the bottom of the storage tank. As a result, the daily HP COP in the multi-functional system decreased by 4.7% as compared to that in the uni-functional system. However, this decrease recovered when the position for hot water return heightened. * The average temperature in the storage tank in the multi-functional system became higher than that in the uni-functional system, when hot water returned to the bottom of the storage tank. Thus, the storage efficiency in the multi-functional system also decreased as compared to that in the uni-functional system, although its decrease rate remained only 0.2%. Since the average temperature in the storage tank decreased when the position for hot water return heightened, the storage efficiency became higher than that in the uni-functional system. Figure 12: Influence of position for hot water return on system performance values: (**a**) heat pump COP, and storage and system efficiencies; (**b**) volumes of stored and unused hot water. * As a whole, the system efficiency in the multi-functional system decreased by 4.9% as compared to that in the uni-functional system, when hot water returned to the bottom of the storage tank. When the position for hot water return heightened, the system efficiency also became higher than that in the uni-functional system. * The volume of unused hot water in the multi-functional system decreased by 16.3% as compared to that in the uni-functional system, when hot water returned to the bottom of the storage tank. Furthermore, when the position for hot water return heightened, the volume of unused hot water decreased. * When the constant temperature in the storage tank by the hot water return was slightly above the inlet water temperature for HP shutdown, unique temperature distributions arised. The storage and system efficiencies increased drastically, while the volume of unused hot water decreased drastically. Thus, a deficit in hot water supply may arise. The validity of the performance, especially the temperature distribution of the storage tank, of the uni-functional system evaluated by numerical simulation was investigated by experiment in the previous paper [34]. However, the validity of the performance of the multi-functional system evaluated by numerical simulation has not been investigated by experiment yet. This should be done as future work. Conceptualization, R.Y.