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

• Published in: Numerical heat transfer. Part A, Applications Vol. 77; no. 9; pp. 840 - 852
• Main Authors: Dobri, Adam, Wang, Yanwei, Papathanasiou, T. D.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.05.2020; Taylor & Francis Ltd
• Subjects: Composite materials; Computer simulation; Conduction heating; Conductive heat transfer; Diameters; Differential equations; Exact solutions; Fiber composites; Heat; Heat exchange; Inclusions; Mathematical analysis; Mathematical models; Multiscale analysis; Ordinary differential equations; Surface temperature; Thermal response; Transient heat conduction; Transient heat transfer; Two dimensional models; Unidirectional composites; Workstations
• ISSN: 1040-7782; 1521-0634
• DOI: 10.1080/10407782.2020.1746154

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. n 0 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.