This paper presents a distributed mathematical model for a carbon dioxide direct expansion solar-assisted heat pump used to heat bath water. The main components are a gas cooler, a needle valve, an evaporator/collector, and a compressor. To develop the heat exchange models, mass, energy, and momentum balances were used. The model was validated for transient as well as steady state conditions using experimental data. A reasonably good agreement was observed between the predicted temperatures and experimental data. The simulations showed that the time step required to demonstrate the behavior of the heat pump in the transient regime is greater than the time step required for the steady state. The results obtained with the mathematical model revealed that a reduction in the water mass flow rate results in an increase in the water outlet temperature. In addition, when the carbon dioxide mass flow rate is reduced, the compressor inlet and outlet temperatures increase as well as the water outlet temperature.

Thermal energy storage (TES) is an innovative technology that can help mitigate environmental problems and make energy consumption in air conditioning systems more efficient. TES also helps to decouple the production and use of cooling. In this work, a mathematical model was used to obtain the thermal loads of the environment based on Brazilian standards and to simulate the operation of an air conditioning system integrated with TES. A refrigeration system capable of providing cooling capacity for the selected environment was used. It simulated the operation of refrigeration systems to evaluate the coefficient of performance of the refrigeration cycle and the refrigeration system, including the TES, for the city of Teresina, in the northeast region of Brazil. On each day, the efficiency of the air-cooled chiller coupled with a TES that used paraffin with phase change material was verified. Based on the data obtained from the mathematical model, the reduction in energy consumption achieved by coupling TES with the air conditioning system varied between 10.6% and 1.3%.