Non-Fourier heat conduction in a finite medium subjected to arbitrary periodic surface disturbance ☆ Amin Moosaie Department of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran 16844, Iran Available online 12 June 2007 Abstract The non-Fourier transient heat conduction in a finite medium under arbitrary periodic surface thermal disturbance is investigated analytically. In order to obtain the desired temperature field from the known solution for non-Fourier heat conduction under a harmonic disturbance, the principle of superposition along with the Fourier series representation of an arbitrary periodic function is employed. The developed method can be applied for more realistic periodic boundary conditions occurred in nature and technology. © 2007 Elsevier Ltd. All rights reserved. Keywords: Non-Fourier conduction; Hyperbolic conduction; Periodic disturbance; Finite medium 1. Introduction During the past few years there has been research concerned with departures from the classical Fourier heat conduction law. The motivation for this research was to eliminate the paradox of an infinite thermal wave speed which is in contradiction with Einstein's theory of relativity and thus provide a theory to explain the experimental data on ‘second sound’ in liquid and solid helium at low temperatures [1,2]. In addition to low temperature applications, non- Fourier theories have attracted more attention in engineering sciences, because of their applications in high heat flux conduction, short time behavior as found, for example, in laser-material interaction, etc. The classical Fourier conduction law relates the heat flux vector q to the temperature gradient ▿θ, by the relation q ¼Àkjh; ð1Þ where the material constant λ is the thermal conductivity. Eq. (1) along with the conservation of energy gives the classical parabolic heat equation aDh ¼ Ah At ; ð2Þ where a = λ/ρc, ρ, c and ▵ are thermal diffusivity, mass density, specific heat capacity and Laplace's differential operator, respectively. Eq. (2) yields temperature solutions which imply an infinite speed of heat propagation. International Communications in Heat and Mass Transfer 34 (2007) 996 – 1002 www.elsevier.com/locate/ichmt ☆ Communicated by W.J. Minkowycz. E-mail address: aminmoosaie@mail.iust.ac.ir . 0735-1933/$ - see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2007.05.002