Exact analytical solution of the parabolic two-step model for nanoscale heat conduction

IF 2.8 2区 数学 Q1 MATHEMATICS, APPLIED
A.S.N. Chairuca , A.J.A. Ramos , J.A.R. Nascimento , L.G.R. Miranda
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引用次数: 0

Abstract

This work presents an analytical solution to the parabolic two-step model, widely used in modeling nanoscale heat conduction, especially in metallic materials subjected to ultrashort laser pulses. The model describes the thermal coupling between the electron gas and the crystal lattice through a system of coupled differential equations. The main contribution of the article is the derivation of an explicit solution using the technique of separation of variables and Fourier series, without the need to assume the null initial velocity (NIV) condition, which is often imposed in the literature. The analytical solution provides a rigorous description of the transient behavior of the temperatures in the electronic and lattice subsystems, revealing the presence of exponential decay modes. Additionally, computational simulations are carried out to illustrate the rapid thermal dissipation in the electronic subsystem, followed by a slower redistribution in the crystal lattice, behavior that is characteristic of electron–phonon coupling at the nanoscale.
纳米尺度热传导抛物线两步模型的精确解析解
本文提出了抛物型两步模型的解析解。抛物型两步模型广泛应用于纳米尺度热传导模型,特别是金属材料在超短激光脉冲作用下的热传导模型。该模型通过一个耦合微分方程系统描述了电子气体与晶格之间的热耦合。本文的主要贡献是使用分离变量和傅立叶级数技术推导出显式解,而不需要假设文献中经常施加的零初始速度(NIV)条件。解析解提供了电子和晶格子系统温度瞬态行为的严格描述,揭示了指数衰减模式的存在。此外,还进行了计算模拟,以说明电子子系统中的快速热耗散,随后在晶格中进行较慢的重新分配,这是纳米尺度上电子-声子耦合的特征。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Applied Mathematics Letters
Applied Mathematics Letters 数学-应用数学
CiteScore
7.70
自引率
5.40%
发文量
347
审稿时长
10 days
期刊介绍: The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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