Abstract
The process of heat transport in granular materials has generated a great deal of controversy. It has been claimed that the process is affected not only by the thermal conductivity, diffusivity and heat capacity, but also additional parameters in the form of time-phase lags must be considered. These quantities permit to take into account the thermal inertia and the micro-structural interactions of the media in such a way that they establish the non-simultaneity between the temperature and the heat flux. A highly successful model that takes into account these effects is known as the dual-phase lag model of heat conduction. It constitutes an approach that generalizes and overcomes the limitations of the classical Fourier law of heat transport. One of the most sensitive techniques for measuring thermal properties is the thermal-wave resonant cavity, which is formed by three layers. The one in the middle is semi solid, liquid or gas, whose thickness can be changed moving one of the external layers. In order to study the material in the middle, a modulated heat source is applied to one of the external layers, and the changes of temperature are registered at the surface of any of the external layers. This methodology has provided high accuracy results for the thermal properties of liquids, gases and nanofluids in the context of Fourier heat diffusion equation. However results for granular materials using this methodology are scarce and the role of the phase lags in heat transport has not been fully explored. In this work, the theoretical basis for the development of a thermal-wave resonant cavity based on dual-phase lag model is studied. It is shown that this system could be used to measure not only the thermal diffusivity but also the time-phase lags of granular materials, by performing a suitable thickness scan of the cavity. It is shown that the results obtained can be a highly useful in the development of experimental methodologies revealing the possibility of non-Fourier heat transport and how the thermal characterization of granular materials can be performed.
Similar content being viewed by others
References
Tzou D.Y.: Macro- to Microscale Heat Transfer: The Lagging Behavior. Taylor and Francis, New York (1997)
Wang L., Zhou X., Wei X.: Heat Conduction: Mathematical Models and Analytical Solutions. Springer-Verlag, Berlin, Heidelberg (2008)
Vadasz P.: Lack of oscillations in Dual-Phase-Lagging heat conduction for a porous slab subject to imposed heat flux and temperature. Int. J. Heat Mass Transf. 48, 2822–2828 (2005)
Vadasz P.: Absence of oscillations and resonance in porous media dual-phase-lagging Fourier heat conduction. J. Heat Transf-Trans. ASME 127, 307–314 (2005)
Wang L.Q., Wei X.H.: Equivalence between dual-phase-lagging and two-phase-system heat conduction processes. Int. J. Heat Mass Transf. 51, 1751–1756 (2008)
Quintard M., Whitaker S.: Transport in ordered and disordered porous-media—volume-averaged equations, closure problems, and comparison with experiment. Chem. Eng. Sci. 48, 2537–2564 (1993)
Carslaw H.S., Jaeger J.C.: Conduction of Heat in Solids. Oxford University Press, London (1959)
Vadasz P.: Exclusion of oscillations in heterogeneous and bi-composite media thermal conduction. Int. J. Heat Mass Transf. 49, 4886–4892 (2006)
Glatzmaier G.C., Ramirez W.F.: Use of volume averaging for the modeling of thermal-properties of porous materials. Chem. Eng. Sci. 43, 3157–3169 (1988)
Tzou D.Y.: Experimental support for the lagging behavior in heat propagation. J. Thermophys. Heat Transf. 9, 686–693 (1995)
Tzou D.Y.: A unified field approach for heat-conduction from macro-scales to micro-scales. J. Heat Transf.-Trans. ASME 117, 8–16 (1995)
Tzou D.Y.: The generalized lagging response in small-scale and high-rate heating. Int. J. Heat Mass Transf. 38, 3231–3240 (1995)
Antaki P.J.: New interpretation of non-Fourier heat conduction in processed meat. J. Heat Trans.-Trans. Asme 127, 189–193 (2005)
Xu M.T., Wang L.Q.: Dual-phase-lagging heat conduction based on Boltzmann transport equation. Int. J. Heat Mass Transf. 48, 5616–5624 (2005)
Ordó ñez-Miranda, J., Alvarado-Gil, J.J.: Determination of time-delay parameters in the dual-phase lagging heat conduction model. J. Heat Transf. (2010). doi:10.1115/1.4000748
Almond D.P., Patel P.M.: Photothermal Science and Techniques. Chapman and Hall, London (1996)
Quintanilla R.: Exponential stability in the dual-phase-lag heat conduction theory. J. Non-Equilib. Thermodyn. 27, 217–227 (2002)
Al-Nimr M.A., Naji M., Abdallah R.I.: Thermal behavior of a multi-layered thin slab carrying periodic signals under the effect of the dual-phase-lag heat conduction model. Int. J. Thermophys. 25, 949–966 (2004)
Khadrawi A.F., Al-Nimr M.A., Hammad M.: Thermal behavior of perfect and imperfect contact composite slabs under the effect of the hyperbolic heat conduction model. Int. J. Thermophys. 23, 581–598 (2002)
Rosencwaig A., Gersho A.: Theory of photoacoustic effect with solids. J. Appl. Phys. 47, 64–69 (1976)
Mandelis A.: Diffusion Waves Fields: Mathematical Methods and Green Functions. Springer, New York (2001)
Shen J., Mandelis A.: Thermal-wave resonator cavity. Rev. Sci. Instrum. 66, 4999–5005 (1995)
Shen J., Mandelis A., Aloysius B.D.: Thermal-wave resonant-cavity measurements of the thermal diffusivity of air: A comparison between cavity-length and modulation-frequency scans. Int. J. Thermophys. 17, 1241–1254 (1996)
Shen J., Mandelis A., Ashe T.: Pyroelectric thermal-wave resonant cavity: a precision thermal diffusivity sensor for gases and vapors. Int. J. Thermophys. 19, 579–593 (1998)
Ordóñez-Miranda J., Alvarado-Gil J.J.: Thermal wave oscillations and thermal relaxation time determination in a hyperbolic heat transport model. Int. J. Therm. Sci. 48, 2053–2062 (2009)
Ordóñez-Miranda J., Alvarado-Gil J.J.: Frequency-modulated hyperbolic heat transport and effective thermal properties in layered systems. Int. J. Therm. Sci. 49, 209–217 (2010)
Salazar A.: On thermal diffusivity. Euro. J. Phys. 24, 351–358 (2003)
Cattaneo C.: Sulla Conduzione de Calore. Atti. Semin. Mat. Fis. Univ. Modena 3, 83–101 (1948)
Vernotte P.: Les Paradoxes de la Théorie Continue de L’équation de la Chaleur. C. R. Hebd. Seances Acad. Sci. 246, 3154–3155 (1958)
Roetzel W., Putra N., Das S.K.: Experiment and analysis for non-Fourier conduction in materials with non-homogeneous inner structure. Int. J. Therm. Sci. 42, 541–552 (2003)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ordóñez-Miranda, J., Alvarado-Gil, J.J. Thermal characterization of granular materials using a thermal-wave resonant cavity under the dual-phase lag model of heat conduction. Granular Matter 12, 569–577 (2010). https://doi.org/10.1007/s10035-010-0195-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10035-010-0195-6