The calculation of the thermal mode of a room with automatic regulation of climate systems

Abstract

Introduction. The ongoing research of the indoor temperature, regulated by automatically operating climate systems, remains relevant if focused on identification of dependencies which are sufficiently accurate with regard for the majority of essential factors and represented in the engineering format. The mission of the research is to identify a dependency between indoor temperature and time in case of irregular heat supply in the context of prorated heat flow regulation by indoor climate systems. The exponential nature of this dependency serves as the research hypothesis.
 Materials and methods. The author has employed and analyzed the principal equations connecting the most important constituents of a heat flow in a room that has automated climate systems in the context of discontinuous changes. The author has employed a computational model of a non-steady temperature environment of a ventilated room. The proposed model is based on the solution of a system of differential equations describing heat conductivity and transfer on indoor surfaces. The author has composed and analytically solved the general differential equation describing the indoor thermal balance with regard for the climate system’s feedback.
 Results. The author has developed an analytical expression describing the indoor space heating rate in case of prorated temperature regulation by the climate system and irregular heat supply. The analytical expression represents an exponential function of the square root of the time span starting from the moment of a heat supply spike. The author used a residential house in Moscow to analyze the nature of indoor temperature fluctuations with and without heat regulation.
 Conclusions. The author has proven that an indoor temperature rate is mainly driven by the relation between the transmission coefficient of a climate system and the thermal inertia of “massive” building envelopes in case of irregular thermal exposure. The author makes the point that a simplified analytical solution is proven true by the results of the analysis performed with the help of a numerical model. It’s been identified that the ultimate value of an indoor temperature increment is determined as the relation between the heat gain value and the parameter which is proportionate to the transfer coefficient.