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 novel generalized thermoelasticity with higher-order time-derivatives and three-phase lags

2019 ◽  
Vol 16 (4) ◽  
pp. 689-711
Author(s):  
Ahmed E. Abouelregal
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Taylor Series ◽  
Generalized Thermoelasticity ◽  
Phase Lag ◽  
Thermal Displacement ◽  
Content Type ◽  
Three Phase ◽  
Special Cases ◽  
Phase Lags

Purpose In this work, a modified thermoelastic model of heat conduction, including higher order of time derivative, is constructed by extending the Roychoudhuri model (TPL) (Choudhuri, 2007). In this new model, Fourier’s law of heat conduction is replaced by using Taylor series expansions, including three different phase lags for the heat flux, the thermal displacement and the temperature gradient. The generalized thermoelasticity models of Lord–Shulman (Lord and Shulman, 1967), Green and Naghdi (1991), dual-phase lag (Tzou, 1996) and three-phase lag (TPL) (Choudhuri, 2007) are obtained as special cases. The paper aims to discuss these issues. Design/methodology/approach The aim of this work is to establish a new generalized mathematical model of thermoelasticity that includes TPL in the vector of heat flux, and in the thermal displacement and temperature gradients extending TPL model (Li et al., 2019e). In this model, Fourier law of heat conduction is replaced by using Taylor series expansions to a modification of the Fourier law with introducing three different phase lags for the heat flux vector, the temperature gradient, and the thermal displacement gradient and keeping terms up with suitable higher orders. Findings The established high-order three-phase-lag heat conduction model reduces to the previous models of thermoelasticity as special cases. Originality/value In this paper, a TPL thermoelastic model is developed by extending the Roychoudhuri (Sherief and Raslan, 2017) model (TPL) considering the Taylor series approximation of the equation of heat conduction. This model is an alternative construction to the TPL model. The new model includes high order of TPL in the vector of heat flux, and in the thermal displacement and temperature gradients.

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.

Nonhomogeneous Dual-Phase-Lag Heat Conduction Problem: Analytical Solution and Select Case Studies

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Simon Julius ◽  
Boris Leizeronok ◽  
Beni Cukurel
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Generation ◽  
Integral Transform ◽  
Heat Conduction Problem ◽  
Relaxation Times ◽  
Hyperbolic Heat Conduction ◽  
Phase Lag ◽  
Dual Phase

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.

Analysis of Dual Phase Lag Heat Conduction in Gold Nanoparticle Based Hyperthermia Treatment

2008 ◽  
Author(s):  
C. Liu ◽  
B. Q. Li ◽  
C. Mi
Keyword(s):  
Heat Conduction ◽  
Gold Nanoparticle ◽  
Tissue Temperature ◽  
Surrounding Tissue ◽  
Transient Temperature ◽  
Short Time Scale ◽  
Phase Lag ◽  
Dual Phase ◽  
Hyperthermia Treatment ◽  
Lag Model

This paper addresses the fast-transient heat conduction phenomena of a gold nanoparticle embedded in cancerous tissue in hyperthermia treatment. Dual phase lag model in spherical coordinates was employed and a semi-analytical solution of 1-D non-homogenous dual phase lag equation was presented. Results show that transient temperature depends dramatically on the lagging characteristic time of the surrounding tissue. Temperature predicted by dual phase lag model greatly exceeds that predicted by a classical diffusion model, with either a constant source or a pulsed source. This phenomenon is mainly attributed by the phase lag of heat flux of tissue. The overheating in short time scale and the consequent biological effect needs to be paid more attention in the related study.

A problem of thick circular plate in modified couple stress thermoelastic diffusion with phase-lags

2016 ◽  
Vol 12 (3) ◽  
pp. 478-494
Author(s):  
Rajneesh Kumar ◽  
Shaloo Devi ◽  
Veena Sharma
Keyword(s):  
Temperature Change ◽  
Couple Stress ◽  
Chemical Potential ◽  
Phase Lag ◽  
Dual Phase ◽  
Field Equations ◽  
Thermoelastic Diffusion ◽  
Content Type ◽  
Lag Model ◽  
Modified Couple Stress

Purpose The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the context of dual-phase-lag model. Design/methodology/approach The Laplace and Hankel transforms have been applied to find the general solution to the field equations. The components of displacement, stresses, temperature change and chemical potential are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Findings The components of normal stress, tangential stress, tangential couple stress, temperature change and chemical potential are obtained numerically and depicted graphically to see the effect of dual-phase-lag diffusion (DLD), dual-phase-lag heat transfer (DLT) and TD models in the absence and presence of couple stress parameter. Originality/value Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.

Effect of rotation on micropolar generalized thermoelasticity with two temperatures using a dual-phase lag model

2014 ◽  
Vol 92 (2) ◽  
pp. 149-158 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
W.M. Hasona ◽  
Elsayed M. Abd-Elaziz
Keyword(s):  
Numerical Solutions ◽  
Generalized Thermoelasticity ◽  
Thermodynamic Temperature ◽  
Phase Lag ◽  
Dual Phase ◽  
Conductive Temperature ◽  
Mode Method ◽  
Lag Model ◽  
Two Temperatures ◽  
Physical Quantities

In the present paper, we introduce the dual-phase lag theory to study the effect of the rotation on a two-dimensional problem of micropolar thermoelastic isotropic medium with two temperatures. A normal mode method is proposed to analyze the problem and obtain numerical solutions for the displacement, the conductive temperature, the thermodynamic temperature, the microrotation, and the stresses. The results of the physical quantities have been obtained numerically and illustrated graphically. The results show the effect of phase lag of the heat flux τq, a phase lag of temperature gradient τθ and two-temperature parameter on all the physical quantities.

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