Abstract
The present work is devoted to define a generalized Green’s function solution for the dual-phase-lag model in homogeneous materials in a unified manner .The high-order mixed derivative with respect to space and time which reflect the lagging behavior is treated in special manner in the dual-phase-lag heat equation in order to construct a general solution applicable to wide range of dual-phase-lag heat transfer problems of general initial-boundary conditions using Green’s function solution method. Also, the Green’s function for a finite medium subjected to arbitrary heat source and arbitrary initial and boundary conditions is constructed. Finally, four examples of different physical situations are analyzed in order to illustrate the accuracy and potentialities of the proposed unified method. The obtained results show good agreement with works of [1-4].
Highlights
The dual-phase-lag (DPL) heat conduction model has stimulated considerable interest in the heat transfer community, by offering alternative interpretations and new perspectives to a large body of non-Fourier thermal behaviors in energy transportation process under special considerations, such as heat conduction in biological materials, heat transport in amorphous media, layered-film heating in superconductors, fins and reactor walls. and many commonly used devices, such as personal computers or cellular phones
The present work is devoted to define a generalized Green’s function solution for the dual-phase-lag model in homogeneous materials in a unified manner .The high-order mixed derivative with respect to space and time which reflect the lagging behavior is treated in special manner in the dual-phase-lag heat equation in order to construct a general solution applicable to wide range of dual-phase-lag heat transfer problems of general initial-boundary conditions using Green’s function solution method
Other than the notoriously annoying fictitious numerical oscillations frequently encountered in solving hyperbolic partial differential equations (HPDE), the intrinsic complexity of the DPL heat conduction equation alone poses a tremendous hindering obstacle against a general solution [5]
Summary
The dual-phase-lag (DPL) heat conduction model has stimulated considerable interest in the heat transfer community, by offering alternative interpretations and new perspectives to a large body of non-Fourier thermal behaviors in energy transportation process under special considerations, such as heat conduction in biological materials, heat transport in amorphous media, layered-film heating in superconductors, fins and reactor walls. and many commonly used devices, such as personal computers or cellular phones. Numerous efforts have been invested to the development of an explicit mathematical solution to the heat conduction equation under the DPL model. Most of these analytical solutions to the DPL heat conduction problems in the literature were formulated ad hoc, only applicable to specific formulations of initial-boundary conditions. In the present work highorder mixed derivative with respect to space and time is treated in special manner in the dual-phase-lag heat equation in order to construct a general solution applicable to wide range of dual-phase-lag heat transfer problems of general initial-boundary conditions using Green’s function solution method. For powerful reviewing of construction of several Green’s functions for different boundary and initial condition of various physical equations, the reader is referred to [10]
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