Finite integral transform techniques are applied to solve the one-dimensional (1D) dual-phase heat conduction problem, and a comprehensive analysis is provided for general time-dependent heat generation and arbitrary combinations of various boundary conditions (Dirichlet, Neumann, and Robin). Through the dependence on the relative differences in heat flux and temperature relaxation times, this analytical solution effectively models both parabolic and hyperbolic heat conduction. In order to demonstrate several exemplary physical phenomena, four distinct cases that illustrate the wavelike heat conduction behavior are presented. In the first model, following an initial temperature spike in a slab, the thermal evolution portrays immediate dissipation in parabolic systems, whereas the dual-phase solution depicts wavelike temperature propagation—the intensity of which depends on the relaxation times. Next, the analysis of periodic surface heat flux at the slab boundaries provides evidence of interference patterns formed by temperature waves. In following, the study of Joule heating driven periodic generation inside the slab demonstrates that the steady-periodic parabolic temperature response depends on the ratio of pulsatile electrical excitation and the electrical resistivity of the slab. As for the dual-phase model, thermal resonance conditions are observed at distinct excitation frequencies. Building on findings of the other models, the case of moving constant-amplitude heat generation is considered, and the occurrences of thermal shock and thermal expansion waves are demonstrated at particular conditions.
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Nonhomogeneous Dual-Phase-Lag Heat Conduction Problem: Analytical Solution and Select Case Studies
Simon Julius,
Simon Julius
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: shimonjulius@tx.technion.ac.il
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: shimonjulius@tx.technion.ac.il
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Boris Leizeronok,
Boris Leizeronok
Mem. ASME
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: borisl@technion.ac.il
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: borisl@technion.ac.il
Search for other works by this author on:
Beni Cukurel
Beni Cukurel
Mem. ASME
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: beni@cukurel.org
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: beni@cukurel.org
Search for other works by this author on:
Simon Julius
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: shimonjulius@tx.technion.ac.il
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: shimonjulius@tx.technion.ac.il
Boris Leizeronok
Mem. ASME
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: borisl@technion.ac.il
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: borisl@technion.ac.il
Beni Cukurel
Mem. ASME
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: beni@cukurel.org
Turbomachinery and Heat Transfer Laboratory,
Faculty of Aerospace Engineering,
Technion—Israel Institute of Technology,
Haifa 3200003, Israel
e-mail: beni@cukurel.org
1Corresponding author.
Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 27, 2016; final manuscript received July 16, 2017; published online October 10, 2017. Assoc. Editor: Alan McGaughey.
J. Heat Transfer. Mar 2018, 140(3): 031301 (22 pages)
Published Online: October 10, 2017
Article history
Received:
October 27, 2016
Revised:
July 16, 2017
Citation
Julius, S., Leizeronok, B., and Cukurel, B. (October 10, 2017). "Nonhomogeneous Dual-Phase-Lag Heat Conduction Problem: Analytical Solution and Select Case Studies." ASME. J. Heat Transfer. March 2018; 140(3): 031301. https://doi.org/10.1115/1.4037775
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