The main task of mathematical modelling of thermal and flow processes in vertical ground heat exchanger (BHE-Borehole Heat Exchanger) is to determine the unit of borehole depth heat flux obtainable or transferred during the operation of the installation. This assignment is indirectly associated with finding the circulating fluid temperature flowing out from the U-tube at a given inlet temperature of fluid in respect to other operational parameters of the installation.

The paper presents a model of thermal and flow processes in BHE consisting of two analytical models separately-handling processes occurring inside and outside of borehole. A quasi-three-dimensional model formulated by Zeng was used for modelling processes taking place inside the borehole and allowing to determine the temperature of the fluid in the U-tube along the axis of BHE. For modelling processes occurring outside the borehole a model that uses the theory of linear heat source was selected. The coupling parameters for the models are the temperature of the sealing material on the outer wall of the borehole and the average heat flow rate in BHE. Experimental verification of the proposed model was shown in relation to BHE cooperating with a heat pump in real conditions.

In recent years, European countries have experienced a noteworthy surge in the interest surrounding renewable energy sources, particularly the integration of photovoltaic (PV) panels with various types of heat pumps. This study aims to evaluate the energy performance of a grid19 connected hybrid installation, combining a PV array with an air-source heat pump (AHP), for domestic hot water preparation in a residential building located in Cracow, Poland. The primary focus of this evaluation is to assess the extent to which self-consumption (SC) of energy can be increased. The study utilizes Transient System Simulation Tool 18 software to construct and simulate various system models under different scenarios. These scenarios include building electricity consumption profiles, PV power systems, and the specified management of AHP. Analyses were conducted over a period of 1 year to assess the operational performance of the systems. In the considered installations, the differences in SC values between PV installation ranged from 9 to 25%. Notably, the highest SC values were observed during the winter months. AHP with operation control allows to obtain in some months of the year up to 35% higher value the SC parameter compared to systems without AHP. The highest annual 29 SC value recorded reached 83.9%. These findings highlight the crucial role of selecting an appropriate PV system size to maximize the SC parameter.