A Review on Analytical Heat Transfer in Functionally Graded Materials, Part II: Non-Fourier Heat Conduction

  • Amin AMIRI DELOUEI ,
  • Amin EMAMIAN ,
  • Saeed GHORBANI ,
  • Aref KHORRAMI ,
  • Karim JAFARIAN ,
  • Hasan SAJJADI ,
  • Meysam ATASHAFROOZ ,
  • Dengwei JING ,
  • Ali TAROKH
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  • 1. Department of Mechanical Engineering, Lakehead University, Thunder Bay P7B 5E1, Canada
    2. Department of Mechanical Engineering, Faculty of Advanced Technologies, Quchan University of Technology, Quchan 9477177870, Iran
    3. Department of Mechanical Engineering, University of Tehran, Tehran 14399-57131, Iran
    4. Department of Mechanical Engineering, University of Bojnord, Bojnord 945 3155111, Iran
    5. Department of Mechanical Engineering, Sirjan University of Technology, Sirjan 7813733385, Iran
    6. International Research Center for Renewable Energy, State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Online published: 2025-07-04

Copyright

Science Press, Institute of Engineering Thermophysics, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2025

Abstract

Non-Fourier heat conduction models are extended in response to heat transfer phenomena that cannot be accurately described by Fourier’s Law of heat conduction. This paper provides a review of heat conduction in functionally graded materials (FGMs) employing non-Fourier models. FGMs are designed materials with a gradual transition in composition, microstructure, or thermal conductivity throughout their volume. The spatial variation in thermal conductivity can lead to deviations from Fourier’s Law, resulting in non-Fourier heat conduction behavior in certain situations, such as at very short time scales or in materials with high thermal conductivity gradients. Researchers utilized various models, such as, Cattaneo-Vernotte, parabolic two-step model, hyperbolic two-step, phonon kinetic, dual-phase lag, and three-phase lag models to describe non-Fourier heat conduction phenomena. The objective of this review is to enhance the understanding of non-Fourier heat transfer in FGMs. As a result, the analytical studies conducted in this particular area receive a greater emphasis and focus. Various factors affecting non-Fourier heat conduction in FGMs including gradient function, material gradient index, initial conditions, boundary conditions, and type of non-Fourier model are investigated in various geometries. The literature reviews reveal that a significant portion of research efforts is centered around the utilization of dual phase lag and hyperbolic models in the field of non-Fourier heat conduction within FGMs. 

Cite this article

Amin AMIRI DELOUEI , Amin EMAMIAN , Saeed GHORBANI , Aref KHORRAMI , Karim JAFARIAN , Hasan SAJJADI , Meysam ATASHAFROOZ , Dengwei JING , Ali TAROKH . A Review on Analytical Heat Transfer in Functionally Graded Materials, Part II: Non-Fourier Heat Conduction[J]. Journal of Thermal Science, 2025 , 34(4) : 1387 -1407 . DOI: 10.1007/s11630-025-2113-6

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