Transient heat transfer in fibrous multi-scale composites: A semi-analytical model and its numerical validation

Abstract

This article presents the development and validation of a semi-analytical (hybrid) model to describe transient heat conduction in a composite material reinforced with long unidirectional cylindrical inclusions. The development of the model relies on the existing analytical solution at the particle-scale, subject to a locally uniform but time-evolving surface temperature; this solution is used to calculate the local heat exchange with the matrix material. Following this, spatial discretization (using N nodes) at the macroscale leads to a system of Ordinary Differential Equations, yielding the matrix temperature and the surface temperature of the inclusions at each node. n0 is the number of the terms in the Bessel expansion computed without recourse to approximation. The intra-fiber thermal response is recovered analytically from the above. A fully numerical two-dimensional model of a unidirectional composite containing 1000 randomly placed fibers is developed on the OpenFOAM platform, using Gmesh for generation of the computational meshes. Comparison of the predictions of the proposed semi-analytical model with the results of several 100s of numerical simulations, spanning a large range of size ratios (macro-scale to fiber diameter) and conductivity ratios, shows excellent agreement between the semi-analytical model and the numerical results. The proposed model is portable and executable on mid-level workstations, requiring minutes of CPU time for cases in which a full numerical solution would require 10s of CPU hours. It therefore provides an attractive and accurate alternative in modeling transient heat transfer in multi-scale fibrous composites.