Science. Business. Society.
Vol. 11 (2026), Issue 1, pg(s) 7-10

SCIENCE

Analytical solutions for boundary value problems of transport phenomena in the design of multilayer structures

  • 1 Kazan State Power Engineering University, Russia

Abstract

This article provides a systemic analysis of the application of analytical methods for solving differential equations of heat and mass transfer for the design of building envelopes in the context of modern energy efficiency requirements and the digitalization of the construction industry. It is demonstrated that analytical solutions remain critical for the design of multilayer walls and roofs, thermal stability and vapor permeability calculations, and the verification of BIM models and smart home systems. A review of classic and new analytical results from 2015–2025 is presented, including the use of physically-informed neural networks (PINN) for real-time thermal protection optimization. Examples of implementation in regulatory documents, software, and microclimate management systems are provided.

Keywords

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