An analytical approach based on Green's function to thermal response factors for composite planar structure with experimental validation

Abstract

The unsteady heat conduction in composite planar structure, with arbitrary number of layers, using analytical approach based on Green's Functions (GF) is analyzed. The analytical solution for spatial and temporal temperature distribution is evaluated in the general form and expressed in the terms of the convolution integrals. The GF are employed in the novel approach for calculation of Thermal Response Factors (TRF) with arbitrary shape functions for unsteady heat conduction in composite planar structure. The two pairs of TRF for spatial and temporal distribution of the temperature and the thermal flux are obtained. The whole analysis is performed in the time domain. A numerical scheme for efficient evaluation of convolution integral suitable for practical application in the case of the long term measurements with lower sampling rates is developed. The in-situ measurements of inside and outside surface temperatures and outside heat flux for a building wall under real dynamical environmental conditions during the period of then days are used for validation of the presented results and to demonstrate the possible practical application. Using developed approach and recorded surface temperatures as inputs the temporal and spatial distributions of the temperature and the thermal flux are obtained. These results are compared with experimental data and numerical simulations obtained by the Finite Volume Method (FVM).