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Analytical solutions of transient heat conduction in multilayered slabs and application to thermal analysis of landfills

层状结构中热传导的解析解及其在填埋场热分析中的应用

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Abstract

The study of transient heat conduction in multilayered slabs is widely used in various engineering fields. In this paper, the transient heat conduction in multilayered slabs with general boundary conditions and arbitrary heat generations is analysed. The boundary conditions are general and include various combinations of Dirichlet, Neumann or Robin boundary conditions at either surface. Moreover, arbitrary heat generations in the slabs are taken into account. The solutions are derived by basic methods, including the superposition method, separation variable method and orthogonal expansion method. The simplified double-layered analytical solution is validated by a numerical method and applied to predicting the temporal and spatial distribution of the temperature inside a landfill. It indicates the ability of the proposed analytical solutions for solving the wide range of applied transient heat conduction problems.

摘要

层状结构中瞬态热传导模型广泛应用于不同工程领域.本文建立层状结构中瞬态热传导模型, 模型的边界条件为Dirichlet, Neumann 或 Robin 边界的不同组合,模型考虑不同层中不同的产热函数. 通过叠加法,分离变量法和正交展开法得到模型的解析解.运用两层模型的解析解分析填埋场中的温 度分布并通过数值解验证解答的正确性.表明本文模型及其解析解在瞬态热传导问题中的适用性.

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Authors and Affiliations

  1. Geotechnical Engineering Research Institute, Hohai University, Nanjing, 210098, China

    Xun Wu  (吴珣), Jian-yong Shi  (施建勇), Hao Lei  (雷浩), Yu-ping Li  (李玉萍) & Leslie Okine

  2. Key Laboratory of Ministry of Education for Geomechanics and Embankment Engineering, Hohai University, Nanjing, 210098, China

    Xun Wu  (吴珣), Jian-yong Shi  (施建勇), Hao Lei  (雷浩), Yu-ping Li  (李玉萍) & Leslie Okine

  3. College of Mechanics and Materials, Hohai University, Nanjing, 211100, China

    Xun Wu  (吴珣)

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  1. Xun Wu  (吴珣)
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  2. Jian-yong Shi  (施建勇)
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  3. Hao Lei  (雷浩)
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  4. Yu-ping Li  (李玉萍)
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  5. Leslie Okine
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Correspondence to Xun Wu  (吴珣).

Additional information

Foundation item: Projects(41530637, 41877222, 41702290) supported by the National Natural Science Foundation of China

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Wu, X., Shi, Jy., Lei, H. et al. Analytical solutions of transient heat conduction in multilayered slabs and application to thermal analysis of landfills. J. Cent. South Univ. 26, 3175–3187 (2019). https://doi.org/10.1007/s11771-019-4244-y

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  • DOI: https://doi.org/10.1007/s11771-019-4244-y

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