Thermal Analysis of Multilayered Building Walls Using the Thermal Quadrupole Method: Transfer Functions, Convolution-Based Predictions, and Multispot Excitation Scenarios

This study focuses on resolving the heat transfer problem in a multilayered building wall using the thermal quadrupole method. This method transforms the governing partial differential equations into algebraic forms in the Laplace domain, enabling efficient computation for complex wall geometries. To establish the relationship between inputs (external temperature and solar flux) and outputs (temperature and heat flux within the wall), transfer functions are derived using simplified input functions, such as sinusoidal variations. These transfer functions allow for the prediction of thermal responses to real climate data by employing convolution products. Real climate data are first fitted into a suitable mathematical function. The convolution of the inverse Laplace-transformed transfer functions with these fitted functions reconstructs the system’s thermal behavior in the time domain. The methodology enables systematic analysis of the thermal performance of multilayered walls under realistic environmental conditions, offering a computationally efficient alternative to direct numerical simulations. The results are validated against finite element models and the authors’ previous work on incorporating climate data directly into the quadrupole equations, ensuring reliability and accuracy of the proposed approach. Furthermore, the study extends to investigating multispot excitations scenarios for an active method of thermal resistance measurement of walls. This work is conducted within the framework of the RESBIOBAT project funded by the French national research agency (under grant ANR-21-CE22-0018).

Work In Progress