Mathematical modelling of the temperature distribution in building envelopes

Introduction. This paper provides a literature review on methods for mathematically modelling steady-state and transient temperature fields in building envelopes. It is demonstrated that the thermal state of the envelope affects the energy conservation and energy efficiency of a building. It is noted that the development of temperature calculation methods is particularly relevant given the emergence of new design solutions and thermal insulation materials, such as the use of phase-change materials, the development of zero-energy buildings, and the consideration of green building.

Materials and methods. The literature review was written using both Russian and international sources. Russian papers from the Higher Attestation Commission (HAC) list and dissertations by candidates of technical sciences (PhD) were used. International sources indexed in international databases (Scopus and Web of Science) were also included.

Results. The paper describes the work of A.V. Kolesnikova, which considers a physical and mathematical model for describing non-stationary two-dimensional heat transfer in a heterogeneous fragment. The paper of L.A. Puldas is presented, examining a multifactor thermophysical model that takes into account the multi-layered nature of structures, the non-stationarity of processes, and the presence of moisture and gaseous media. The approach of T.A. Miroshnichenko, which solves the problem of the influence of a cylindrical connector on the thermal state of a three-layer enclosing structure in a cylindrical coordinate system, is considered. The mathematical model and software of N.S. Kotlyarova, allowing one to determine the three-dimensional temperature field and additional heat losses, are studied.

Conclusions. The optimal way to determine the temperature field of a building’s enclosing structure is to use a nonlinear two-dimensional or three-dimensional transient heat equation. For complex object geometry, it is possible to divide the spatiotemporal domain into a number of subdomains with their own boundary conditions. For a combined problem, it is possible to supplement the heat equation with other equations, such as the equations for the transport of water vapor, air, water, and ice.

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