# МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССОВ ТЕПЛОПЕРЕНОСА ПРИ РАБОТЕ ТЕПЛОНАСОСНЫХ СИСТЕМ ИСПОЛЬЗОВАНИЯ ГЕОТЕРМАЛЬНОЙ ЭНЕРГИИ

Translated title of the contribution: Mathematical modeling of heat transfer by operation of geothermal heat pumps

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

## Abstract

The relevance. The use of heat pumps to provide heat instead of traditional systems, which get energy from the burning of different fos& sil fuel kinds, has a number of environmental and economic benefits. Heat pumps can use air, ground, and water as an energy source. They can be used for various applications: hot water supply, air conditioning, heating and cooling water for different uses, air drying/dehu& midification, vapor production, evaporation, and distillation. By the use of natural water surface (lakes, ponds, reservoirs) as a low&po& tential heat source for heat pump, ice can be formed on the evaporator pipe surface. It is important to study the heat exchange charac& teristics between the water and the evaporator pipe undergoing ice formation on its surface. The main aim of the research is mathematical modeling for non&stationary convective heat exchange between the water and the heat pump evaporator pipes under the conditions of ice formation on their surface. The object of the research is the heat pump evaporator heat exchanger which is surrounded by water. The methods of the research are numerical solutions for convective heat transfer problem under the conditions of the water phase change by the use of the finite element method in COMSOL environment. Results. The authors have established the unsteady convective heat transfer laws near the water source heat pump evaporator pipes with the temperature under water freezing point. In calculations of the heat flux and ice thickness growth rate on the surface of heat pump evaporator pipe, the natural convection in water effect must not be ignored. The authors obtained the dependence of Nusselt number on the natural convection heat exchange characteristics undergoing a phase change (Rayleigh, Fourier and Stefan numbers). It is revea& led that the drop rate in water temperature around the pipe increases with the decrease of its depth from the surface of the water source for water temperatures values higher than 277 K. For water temperatures lower than 277 K, the heat flux is maximum around the pipe, which is located deeper.

Translated title of the contribution Mathematical modeling of heat transfer by operation of geothermal heat pumps Russian 126-135 10 Bulletin of the Tomsk Polytechnic University, Geo Assets Engineering 330 4 https://doi.org/10.18799/24131830/2019/4/229 Published - 1 Jan 2019

## ASJC Scopus subject areas

• Materials Science (miscellaneous)
• Fuel Technology
• Geotechnical Engineering and Engineering Geology
• Waste Management and Disposal
• Economic Geology
• Management, Monitoring, Policy and Law