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.

中文翻译：

---

纤维状多尺度复合材料中的瞬态传热：半解析模型及其数值验证

摘要 本文介绍了半解析（混合）模型的开发和验证，以描述用长单向圆柱形夹杂物增强的复合材料中的瞬态热传导。模型的开发依赖于现有的粒子尺度解析解，受制于局部均匀但随时间变化的表面温度；该解用于计算与基体材料的局部热交换。在此之后，宏观尺度的空间离散化（使用 N 个节点）导致一个常微分方程系统，产生每个节点的基质温度和夹杂物的表面温度。n0 是贝塞尔展开式中不依赖近似计算的项数。纤维内热响应从上述分析恢复。在 OpenFOAM 平台上开发了一个包含 1000 根随机放置纤维的单向复合材料的全数值二维模型，使用 Gmesh 生成计算网格。将提议的半分析模型的预测与数百个数值模拟的结果进行比较，跨越大范围的尺寸比（宏观尺度与纤维直径）和电导率比，表明半分析模型和数值结果。所提出的模型在中级工作站上是可移植和可执行的，对于完整数值解决方案需要 10 秒 CPU 小时的情况，需要几分钟的 CPU 时间。因此，它为模拟多尺度纤维复合材料中的瞬态传热提供了一种有吸引力且准确的替代方法。