Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: On the stability of the exact solutions of the dual-phase lagging model of heat conduction | Ordonez-Miranda and Alvarado-Gil Nanoscale Research Letters 2011 6 327 http content 6 1 327 o Nanoscale Research Letters a SpringerOpen Journal NANO EXPRESS Open Access On the stability of the exact solutions of the dual-phase lagging model of heat conduction Jose Ordonez-Miranda and Juan Jose Alvarado-Gil Abstract The dual-phase lagging DPL model has been considered as one of the most promising theoretical approaches to generalize the classical Fourier law for heat conduction involving short time and space scales. Its applicability potential equivalences and possible drawbacks have been discussed in the current literature. In this study the implications of solving the exact DPL model of heat conduction in a three-dimensional bounded domain solution are explored. Based on the principle of causality it is shown that the temperature gradient must be always the cause and the heat flux must be the effect in the process of heat transfer under the dual-phase model. This fact establishes explicitly that the single- and DPL models with different physical origins are mathematically equivalent. In addition taking into account the properties of the Lambert W function and by requiring that the temperature remains stable in such a way that it does not go to infinity when the time increases it is shown that the DPL model in its exact form cannot provide a general description of the heat conduction phenomena. Introduction Nanoscale heat transfer involves a highly complex process as has been witnessed in the last years in which remarkable novel phenomena related to very short time and spatial scales such as enhancement of thermal conductivity in nanofluids granular materials thin layers and composite systems among others have been reported 1-5 . The traditional approach to deal with these phenomena has been to use the Fourier heat transfer equation. This methodology has proven to be extensively useful in the analysis of heat transport in a great variety of
