Mathematical modeling of heat transfer processes in a hydronic radiant floor heating system

Abstract

Relevance: at present, increasing the energy efficiency of buildings and the rational use of fuel and energy re
sources are among the priority directions of the energy and construction sectors in the Republic. According to
statistical data, about 40% of total energy consumption in residential and public buildings is attributed to heating
systems. Therefore, the implementation of low-temperature and energy-efficient heating technologies plays an im
portant role in solving energy and resource-saving problems. Hydronic radiant floor heating systems are character
ized by high thermal comfort, uniform temperature distribution, and the ability to operate with low-temperature
heat carriers. However, the efficient operation of such systems requires intensification of heat transfer processes,
since the complex mechanisms of heat transfer from the heat carrier to the pipe wall, through the floor structure
layers to the floor surface and indoor air directly affect energy efficiency. Therefore, mathematical modeling of
heat transfer processes in hydronic radiant floor heating systems and evaluation of their impact on energy efficiency
represent a relevant scientific and practical problem.
Aim: the aim of this study is to analyze heat transfer processes occurring in a hydronic radiant floor heating system
based on mathematical modeling, to determine the influence of heat carrier temperature, pipe spacing, and thermal
properties of the floor structure on heat flux and energy efficiency, and to substantiate optimal operating modes
from the viewpoint of energy and resource conservation.
Methods: in the study, mathematical modeling methods based on heat balance equations, heat conduction (Fou
rier’s law), convective and radiative heat transfer equations were applied to analyze heat transfer processes in the
hydronic radiant floor heating system. The flow of the heat carrier inside the pipe, heat transfer through the layers
of the floor structure, and heat release from the floor surface to the indoor air were modeled as sequential stages.
Using computational and analytical methods, heat fluxes and energy efficiency indicators were evaluated for vari
ous operating modes of the system.
Results: based on mathematical modeling, the heat output capacity and energy efficiency indicators of the hydronic
radiant floor heating system were analyzed. The calculation results showed that the heat carrier temperature and
pipe spacing have a significant influence on heat flux. It was demonstrated that sufficient heat output can be
achieved even under low-temperature operating modes, and energy-efficient operating regimes were substantiated.
The obtained results confirm the effectiveness of hydronic radiant floor heating systems as an energy-efficient
heating technology.