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Analysis of non-Fourier heat conduction in a solid sphere under arbitrary surface temperature change

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Abstract

In this paper, the non-Fourier heat conduction in a solid sphere under arbitrary surface thermal disturbances is solved analytically. Four cases including sudden, simple harmonic periodic, triangular and pulse surface temperature changes are investigated step-by-step. The analytical solutions are obtained using the separation of variables method and Duhamel’s principle along with the Fourier series representation of an arbitrary periodic function and the Fourier integral representation of an arbitrary non-periodic function. Using these analytical solutions, the temperature profiles of the solid sphere are analyzed, and the differences in the temperature response between the “hyperbolic” and “parabolic” are discussed. These solutions can be applicable to all kinds of non-Fourier heat conduction analyses for arbitrary boundary conditions occurred in technology. And as application examples, particular attention is devoted to the cases of triangular surface temperature change and pulse surface temperature change. The examples presented in this paper can be used as benchmark problems for future numerical method validations.

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Authors and Affiliations

  1. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Wei Tao Zhao, Jiu Hui Wu & Zhe Chen

  2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, 710049, China

    Wei Tao Zhao, Jiu Hui Wu & Zhe Chen

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  1. Wei Tao Zhao
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  2. Jiu Hui Wu
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  3. Zhe Chen
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Correspondence to Wei Tao Zhao.

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Zhao, W.T., Wu, J.H. & Chen, Z. Analysis of non-Fourier heat conduction in a solid sphere under arbitrary surface temperature change. Arch Appl Mech 84, 505–518 (2014). https://doi.org/10.1007/s00419-013-0814-x

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  • DOI: https://doi.org/10.1007/s00419-013-0814-x

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