International Journal of Thermal Sciences 42 (2003) 541–552 www.elsevier.com/locate/ijts Experiment and analysis for non-Fourier conduction in materials with non-homogeneous inner structure Wilfried Roetzel a,∗ , Nandy Putra a , Sarit K. Das b a Institut für Thermodynamik, Universität der Bundeswehr, Hamburg 22039, Germany b Heat Transfer and Thermal Power Laboratory, Mechanical Engineering Department, Indian Institute of Technology, Madras, India 600036 Received 11 October 2001; accepted 16 July 2002 Dedicated to Professor Dr.-Ing. habil. Thaddaeus M. Bes on the occasion of his 65th birthday Abstract The proposition of hyperbolic conduction (also known as the second sound wave) for materials with non-homogeneous inner structure has run into a serious controversy in recent times. While one group of investigators has observed very strong evidence of hyperbolic nature of conduction in such materials and experimentally determined the corresponding relaxation times to be of the order of tens of seconds, the other group proclaims that their experiments do not show any such relaxation behaviour and the conventional Fourier law of conduction is good enough to describe conduction in them. This paper is an effort towards resolving this controversy. In the first place the experimental philosophies and techniques of both the groups have been thoroughly examined. It has been observed that determination of thermophysical properties independent of the relaxation time measurement is an inherent inconsistency in all these experiments. Additionally the assumptions regarding temperature input might have also played a role to arrive at diverging conclusions. Based on these observations an experimental method has been suggested in this study which uses temperature oscillation in semi infinite medium to determine the thermal diffusivity and the relaxation time simultaneously from a single experiment. Using this technique the wide range of experiments conducted reveal that there exists a definite hyperbolic effect in the “bulk” conduction behaviour of such materials although it is somewhat less in extent to those reported by investigators claiming existence of hyperbolic conduction. Also a wide range of experiments with variation of parameters such as packing material, its particle size, filling gas used and its pressure and temperature have been conducted. The data presented here for the wide range of parameters can be useful for further investigations and plausible explanation of “bulk conduction” in materials with non-homogeneous inner structure.  2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. 1. Introduction Hyperbolic or non-Fourier heat conduction in material has been a theme of investigation for considerable time in the recent past. The fundamental ground for this proposition was laid by Maxwell [1] and Morse and Feshbach [2]. However, the formulation in the presently used form of flux equation for non-Fourier conduction can be attributed to Vernotte [3] and Cataneo [4] to give the unsteady flux equation of q + τ ∂q ∂t =-λ∇T (1) where τ = a C 2 * Corresponding author. E-mail address: wilfried.roetzel@unibw-hamburg.de (W. Roetzel). This equation is often referred to in literature as Cattaneo– Vernotte equation. This results in an extended equation for energy balance during conduction in the form ∂T ∂t + τ ∂ 2 T ∂t 2 = a ∇ 2 T (2) This removes one of the theoretical inconsistencies of the original Fourier’s diffusive law which actually points out an infinite propagation velocity for the heat wave meaning that a change in the temperature at any part of the medium should perturb the temperature of a finite medium at each point instantaneously. Due to its similarity with the acoustic wave this proposed wave like propagation of thermal signals is also termed as the “second sound wave”. Chester [5] accepted this name as described by Peshkov [6]. However, it is incorrect to say that this theoretical inconsistency was the seed of the development of the 1290-0729/03/$ – see front matter  2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved. doi:10.1016/S1290-0729(03)00020-6