Understanding Thermal Lagging Behaviors in Thermoelectric Elements with the Dual-Phase-Lag Model

2021 ◽  
Author(s):  
Wing K. Yeung ◽  
Tung T. Lam
Keyword(s):  
Heat Flux ◽  
Heat Transport ◽  
Energy Transport ◽  
Cooling System ◽  
Solution Process ◽  
Single Equation ◽  
Heat Diffusion ◽  
Phase Lag ◽  
Dual Phase ◽  
Lag Model

Abstract This study investigates the heat transport mechanism in semiconductor elements within a homogeneous thermoelectric cooling system using the dual-phase-lag model. The thermal lagging behavior is analyzed and explored during the energy transport process. The coupled energy and constitutive partial differential equations are solved simultaneously to reduce the complexity of the high-order spatial and time derivatives. This approach simplifies the mathematical solution process and reduces numerical instabilities when compared to the conventional methodology in which either the temperature or heat flux are solved individually with a single equation. The effect of the thermal lagging behavior on energy transport is examined and compared to results by using the Cattaneo-Vernotte model. Furthermore, the phase-lag behavior on the temperature and heat flux profiles are investigated in detail. This study provides perceptive information for engineering applications in which microscale heat transport phenomenon plays a significant role during the design process. Adding the dual-phase-lag model to the traditional heat diffusion model will be a complementary option for engineers in the thermoelectric industry.

Inverse Estimation of Cooling Heat Flux in Spray Cooling of Hot Surface Based on Dual-Phase-Lag Model

2019 ◽  
Vol 17 (09) ◽  
pp. 1950069
Author(s):  
Wen-Lih Chen ◽  
Kuo-Chi Liu ◽  
Yu-Ching Yang ◽  
Haw-Long Lee ◽  
Win-Jin Chang
Keyword(s):  
Heat Flux ◽  
Inverse Analysis ◽  
Spray Cooling ◽  
Phase Lag ◽  
Dual Phase ◽  
Random Errors ◽  
Analysis Technique ◽  
Lag Model ◽  
Measurement Location ◽  
Hot Surface

An inverse analysis technique based on the conjugate gradient method (CGM) and the discrepancy principle is employed to estimate the time-wise variation of the unknown cooling heat flux in the spray cooling of a hot surface. In contrast to previous studies, the heat conduction equation of the cooled surface is formulated using a dual-phase-lag (DPL) model. In addition, no assumptions are made regarding the functional form of the cooling heat flux. The simulation data required to conduct the inverse analysis are generated by adding random errors to the calculated exact temperatures at the boundaries and interior of the hot body. The validity of the inverse solutions is demonstrated numerically by means of two illustrative examples. Moreover, the sensitivity of the estimation results to the measurement error and measurement location is systematically explored. Overall, the results show that the proposed method provides a robust and accurate approach for estimating the unknown time-dependent cooling heat flux in typical industrial spray cooling applications.

Dual-phase-lag thermoelastic problem in finite cylindrical domain with relaxation time

2018 ◽  
Vol 14 (5) ◽  
pp. 837-856 ◽  
Author(s):  
Gaurav Mittal ◽  
Vinayak Kulkarni
Keyword(s):  
Heat Flux ◽  
Relaxation Time ◽  
Heat Conduction ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Dual Phase ◽  
Cylindrical Domain ◽  
Content Type ◽  
Thick Circular Plate ◽  
Lag Model

Purpose The purpose of this paper is to frame a dual-phase-lag model using the fractional theory of thermoelasticity with relaxation time. The generalized Fourier law of heat conduction based upon Tzou model that includes temperature gradient, the thermal displacement and two different translations of heat flux vector and temperature gradient has been used to formulate the heat conduction model. The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. Design/methodology/approach The work presented in this manuscript proposes a dual-phase-lag mathematical model of a thick circular plate in a finite cylindrical domain subjected to axis-symmetric heat flux. The model has been designed in the context of fractional thermoelasticity by considering two successive terms in Taylor’s series expansion of fractional Fourier law of heat conduction in the two different translations of heat flux vector and temperature gradient. The analytical results have been obtained in Laplace transform domain by transforming the original problem into eigenvalue problem using Hankel and Laplace transforms. The numerical inversions of Laplace transforms have been achieved using the Gaver−Stehfast algorithm, and convergence criterion has been discussed. For illustrative purpose, the dual-phase-lag model proposed in this manuscript has been applied to a periodically varying heat source. The numerical results have been depicted graphically and compared with classical, fractional and generalized thermoelasticity for various fractional orders under consideration. Findings The microstructural interactions and corresponding thermal changes have been studied due to the involvement of relaxation time and delay time translations. This results in achieving the finite speed of thermal wave. Classical coupled and generalized thermoelasticity theories are recovered by considering the various special cases for different order of fractional derivatives and two different translations under consideration. This model has been applied to study the thermal effects in a thick circular plate subjected to a periodically varying heat source. Practical implications A dual-phase-lag model can effectively be incorporated to study the transient heat conduction problems for an exponentially decaying pulse boundary heat flux and/or for a short-pulse boundary heat flux in long solid tubes and cylinders. This model is also applicable to study the various effects of the thermal lag ratio and the shift time. These dual-phase-lag models are also practically applicable in the problems of modeling of nanoscale heat transport problems of semiconductor devices and accordingly semiconductors can be classified as per their ability of heat conduction. Originality/value To the authors’ knowledge, no one has discussed fractional thermoelastic dual-phase-lag problem associated with relaxation time in a finite cylindrical domain for a thick circular plate subjected to an axis-symmetric heat source. This is the latest and novel contribution to the field of thermal mechanics.

A dual phase lag model on photothermal interaction in an unbounded semiconductor medium with cylindrical cavity

2016 ◽  
Vol 05 (03) ◽  
pp. 1650016 ◽  
Author(s):  
Ibrahim A. Abbas
Keyword(s):  
Heat Flux ◽  
Laplace Transform ◽  
Cylindrical Cavity ◽  
Elastic Waves ◽  
Phase Lag ◽  
Dual Phase ◽  
Eigenvalue Approach ◽  
Lag Model ◽  
The Difference ◽  
Coupled Theory

In the present paper, the theory of generalized photo-thermoelasticity under dual phase lag model has been applied to study the coupled thermal, plasma and elastic waves on unbounded semiconductor medium with cylindrical cavity. The bounding surface of the cavity is traction free and loaded thermally by exponentially decaying pulse boundary heat flux. By using Laplace transform and the eigenvalue approach methodology, the solutions of all variables have been obtained analytically. Numerical computations have been done for silicon-like semiconductor material, and the results are displayed graphically to show the difference between the dual phase lag (DPL) model, Lord and Shulman’s theory (LS) and the classical dynamical coupled theory (CT).

scholarly journals Analysis of Algorithm Efficiency for Heat Diffusion at Nanoscale Based on a MEMS Structure Investigation

Energies ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2520
Author(s):  
Tomasz Raszkowski ◽  
Mariusz Zubert
Keyword(s):  
Krylov Subspace ◽  
Order Reduction ◽  
Heat Diffusion ◽  
Phase Lag ◽  
Dual Phase ◽  
Model Order ◽  
Complexity Of Algorithms ◽  
Algorithm Efficiency ◽  
Lag Model ◽  
Transfer Problems

This paper presents an analysis of the time complexity of algorithms prepared for solving heat transfer problems at nanoscale. The first algorithm uses the classic Dual-Phase-Lag model, whereas the second algorithm employs a reduced version of the model obtained using a Krylov subspace method. This manuscript includes a description of the finite difference method approximation prepared for analysis of the real microelectromechanical system (MEMS) structure manufactured by the Polish Institute of Electron Technology. In addition, an approximation scheme of the model, as well as the Krylov subspace-based model order reduction technique are also described. The paper considers simulation results obtained using both investigated versions of the Dual-Phase-Lag model. Moreover, the relative error generated by the reduced model, as well as the computational complexity of both algorithms, and a convergence of the proposed approach are analyzed. Finally, all analyses are discussed in detail.

Thermal Dispersion in Finite Medium Under Periodic Surface Disturbance Using Dual-Phase-Lag Model

2015 ◽  
Vol 138 (3) ◽  
Author(s):  
Tung T. Lam ◽  
Ed Fong
Keyword(s):  
Heat Flux ◽  
Solution Structure ◽  
Superposition Principle ◽  
Internal Heat ◽  
Transient Heat Conduction ◽  
Fourier Series Expansion ◽  
Hyperbolic Model ◽  
Phase Lag ◽  
Dual Phase ◽  
Lag Model

Transient heat conduction in finite thin films subjected to time-varying surface heat flux incidences at both boundaries and internal heat generation is investigated via the dual-phase-lag (DPL) hyperbolic model. Analytical solution of the temperature profiles inside the solid is derived by using the superposition principle and the method of Fourier series expansion in conjunction with the solution structure theorems. For comparison purposes, the classical diffusion, Cattaneo–Vernotte (C–V) model, and simplified thermomass (TM) models are deduced from the generalized DPL model. This is made possible by adjusting the temperature and heat flux relaxation parameters, and offers the opportunity to examine various interconnected non-Fourier conduction heat transfer characteristics including wave and diffusion effects as well as their interrelationship. Details of this process are examined and results are explored in this study.

NONEQUILIBRIUM DUAL-PHASE-LAG HEAT TRANSPORT THROUGH BIOLOGICAL TISSUES

2015 ◽  
Vol 18 (1) ◽  
pp. 57-69 ◽  
Author(s):  
Hossein Askarizadeh ◽  
Hossein Ahmadikia
Keyword(s):  
Heat Transport ◽  
Biological Tissues ◽  
Phase Lag ◽  
Dual Phase
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