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Analytical solution of non-Fourier heat conduction problem on a fin under periodic boundary conditions

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Abstract

Fourier and hyperbolic models of heat transfer on a fin that is subjected to a periodic boundary condition are solved analytically. The differential equation in Fourier and non-Fourier models is solved by the Laplace transform method. The temperature distribution on the fin is obtained using the residual theorem in a complex plan for the inverse Laplace transform method. The thermal shock is generated at the base of the fin, which moves toward the tip of the fin and is reflected from the tip. The current study of various parameters on the thermal shock location shows that relaxation time has a great influence on the temperature distribution on the fin. An unsteady boundary condition in the base fin caused the shock, which is generated continuously from the base and has interacted with the other reflected thermal shocks. Results of the current study show that the hyperbolic heat conduction equation can violate the second thermodynamic law under some unsteady boundary conditions.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Isfahan, Isfahan, 81746-73441, Iran

    H. Ahmadikia

  2. Department of Mechanical Engineering, Bu-Ali Sina University, Hamadan, Iran

    M. Rismanian

Authors
  1. H. Ahmadikia
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  2. M. Rismanian
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Correspondence to H. Ahmadikia.

Additional information

This paper was recommended for publication in revised form by Associate Editor Dongsik Kim

Hossein Ahmadikia is an assistant professor of Mechanical Engineering at the University of Isfahan, Isfahan, Iran. He received his B.Sc. degree in Ferdosi University, Mashad, Iran in 1990. He received his M.Sc. and Ph.D degrees from Isfahan University of Technology, Isfahan, Iran in 1993 and 2000, respectively. His research focuses on biological heat transfer and turbulence modeling.

Milad Rismanian received his B.Sc. degree in Mechanical Engineering from Bu-Ali Sina University, Hamadan, Iran in 2009. He is currently an M.Sc. student in Sharif University, Iran. His research interests include nano-micro mechanics and biological heat transfer.

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Ahmadikia, H., Rismanian, M. Analytical solution of non-Fourier heat conduction problem on a fin under periodic boundary conditions. J Mech Sci Technol 25, 2919–2926 (2011). https://doi.org/10.1007/s12206-011-0720-5

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  • DOI: https://doi.org/10.1007/s12206-011-0720-5

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