Analytical solution for three-dimensional heat conduction in a nuclear waste repository with adiabatic boundaries

IF 2.6 3区工程技术 Q1 NUCLEAR SCIENCE & TECHNOLOGY

Nuclear Engineering and Technology Pub Date : 2025-06-29 DOI:10.1016/j.net.2025.103781

Xun Xu , Liangfu Xie , De'an Sun , Luqiang He

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引用次数: 0

Abstract

Near-field temperature is a critical indicator in evaluating the safe operation of a nuclear waste repository. Analytical solutions are common methods for analyzing the thermal performance. The existing analytical solutions for temperatures from a single nuclear waste canister in a repository include compound line heat source solutions, semi-analytical solutions, and fully-analytical solutions. However, given that a repository contains thousands of canisters, existing analytical solutions are unable to accurately determine the temperature around the target canister, which is surrounded by numerous adjacent canisters. To this end, the thermal problem at the repository-scale is first transformed into an equivalent problem within a cuboid unit. This unit consists of an individual waste canister encapsulated in buffer material and wrapped in rock under specified boundary conditions. By applying Duhamel's theorem and finite Fourier sine transform, a fully-analytical solution for the temperature field of a single canister under adiabatic boundary conditions was derived. These solutions allow for a convenient and straightforward visualization of temperature evolutions and distributions at a repository-scale through explicit expressions. Furthermore, a formula for calculating the radius of the cylindrical calculation domain was developed, enabling an accurate transformation of the temperature field problem from a cuboid domain to a cylindrical domain.

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具有绝热边界的核废料贮存库三维热传导的解析解

近场温度是评价核废料处置库安全运行的重要指标。解析解是分析热性能的常用方法。现有的核废料储存库中单个核废料罐温度分析解决方案包括复合线热源解决方案、半分析解决方案和全分析解决方案。然而，考虑到储存库包含数千个罐，现有的分析解决方案无法准确确定目标罐周围的温度，目标罐周围有许多相邻的罐。为此，首先将储存库尺度上的热问题转化为长方体单元内的等效问题。该装置由一个单独的废物罐组成，在指定的边界条件下包裹在缓冲材料中并包裹在岩石中。应用Duhamel定理和有限傅里叶正弦变换，导出了绝热边界条件下单罐温度场的全解析解。这些解决方案允许通过显式表达式方便而直接地可视化存储库尺度上的温度演变和分布。建立了圆柱计算域半径的计算公式，实现了温度场问题从长方体计算域到圆柱计算域的精确转换。

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

Nuclear Engineering and Technology 工程技术-核科学技术

CiteScore

4.80

自引率

7.40%

发文量

431

审稿时长

3.5 months

期刊介绍： Nuclear Engineering and Technology (NET), an international journal of the Korean Nuclear Society (KNS), publishes peer-reviewed papers on original research, ideas and developments in all areas of the field of nuclear science and technology. NET bimonthly publishes original articles, reviews, and technical notes. The journal is listed in the Science Citation Index Expanded (SCIE) of Thomson Reuters. NET covers all fields for peaceful utilization of nuclear energy and radiation as follows: 1) Reactor Physics 2) Thermal Hydraulics 3) Nuclear Safety 4) Nuclear I&C 5) Nuclear Physics, Fusion, and Laser Technology 6) Nuclear Fuel Cycle and Radioactive Waste Management 7) Nuclear Fuel and Reactor Materials 8) Radiation Application 9) Radiation Protection 10) Nuclear Structural Analysis and Plant Management & Maintenance 11) Nuclear Policy, Economics, and Human Resource Development