Heat-Flux Estimation in a Nonlinear Heat Conduction Problem with a Dual-Phase-Lag Model

2018 ◽  
Vol 32 (1) ◽  
pp. 196-204 ◽  
Author(s):  
M. Baghban ◽  
M. B. Ayani
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Phase Lag ◽  
Dual Phase ◽  
Nonlinear Heat Conduction ◽  
Heat Flux Estimation ◽  
Lag Model ◽  
Flux Estimation

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.

Inverse heat conduction problem using thermocouple deconvolution: application to the heat flux estimation in a tokamak

2013 ◽  
Vol 21 (5) ◽  
pp. 854-864 ◽  
Author(s):  
Jean-Laurent Gardarein ◽  
Jonathan Gaspar ◽  
Yann Corre ◽  
Stephane Devaux ◽  
Fabrice Rigollet ◽  
...  
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Heat Flux Estimation ◽  
Flux Estimation

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.

Heat flux estimation of a plasma rocket helicon source by solution of the inverse heat conduction problem

2009 ◽  
Vol 52 (9-10) ◽  
pp. 2343-2357 ◽  
Author(s):  
James M. Mulcahy ◽  
David J. Browne ◽  
Kenneth T. Stanton ◽  
Franklin R. Chang Diaz ◽  
Leonard D. Cassady ◽  
...  
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Inverse Heat Conduction ◽  
Heat Flux Estimation ◽  
Flux Estimation ◽  
Helicon Source

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.

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 Near Real-Time Solution Approach for Surface Heat Flux Estimation in One Dimensional Inverse Heat Conduction Problems With Moving Boundary

2019 ◽  
Author(s):  
Obinna Uyanna ◽  
Hamidreza Najafi
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Real Time ◽  
Surface Heat Flux ◽  
Moving Boundary ◽  
Surface Heat ◽  
Inverse Heat Conduction ◽  
Heat Flux Estimation ◽  
Flux Estimation ◽  
Inverse Heat Conduction Problems

Abstract Developing accurate and efficient solutions for inverse heat conduction problems allows advancements in the heat flux measurement techniques for many applications. In the present paper, a one-dimensional medium with a moving boundary is considered. It is assumed that two thermocouples are used to measure temperature at two locations within the medium while the front boundary is moving towards the back surface. Determining surface heat flux using measured temperature data is an inverse heat conduction problem. A filter based Tikhonov regularization method is used to develop a solution for this problem. Filter coefficients are calculated for various thicknesses of the medium. It is demonstrated that the filter coefficients can be interpolated to calculate the appropriate values for each thickness while it is continuously moving at a known rate. The use of filter method allows near real-time heat flux estimation. The developed solution is validated through several numerical test cases including a test case for a moving boundary in a medium modeled in COMSOL. It is shown that the proposed solution can effectively estimate the surface heat flux on the moving boundary in a near real-time fashion.

Sign in / Sign up

Export Citation Format

Share Document