Solution for non-Fourier dual phase lag heat conduction in a semiinfinite slab with surface heat flux

1998 ◽  
Vol 41 (14) ◽  
pp. 2253-2258 ◽  
Author(s):  
Paul J. Antaki
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Phase Lag ◽  
Dual Phase

Finite Element Formulation for Two-Dimensional Inverse Heat Conduction Analysis

1992 ◽  
Vol 114 (3) ◽  
pp. 553-557 ◽  
Author(s):  
T. R. Hsu ◽  
N. S. Sun ◽  
G. G. Chen ◽  
Z. L. Gong
Keyword(s):  
Heat Flux ◽  
Finite Element ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Discrete Point ◽  
Element Algorithm

This paper presents a finite element algorithm for two-dimensional nonlinear inverse heat conduction analysis. The proposed method is capable of handling both unknown surface heat flux and unknown surface temperature of solids using temperature histories measured at a few discrete point. The proposed algorithms were used in the study of the thermofracture behavior of leaking pipelines with experimental verifications.

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.

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 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.

Inverse Heat Flux Problem in Quenching

2000 ◽  
Author(s):  
M. Khairul Alam ◽  
Rex J. Kuriger ◽  
Rong Zhong
Keyword(s):  
Heat Flux ◽  
Heat Conduction ◽  
Surface Heat Flux ◽  
Measurement Errors ◽  
Heat Conduction Problem ◽  
Temperature Data ◽  
Surface Heat ◽  
Measured Temperature ◽  
Inverse Heat Conduction ◽  
Quenching Process

Abstract The quenching process is an important heat treatment method used to improve material properties. However, the heat transfer during quenching is particularly difficult to analyze and predict. To collect temperature data, quench probes have been used in controlled quenching experiments. The process of determination of the heat flux at the surface from the measured temperature data is the Inverse Heat Conduction Problem (IHCP), which is extremely sensitive to measurement errors. This paper reports on an experimental and theoretical study of quenching which is carried out to determine the surface heat flux history during a quenching process by an IHCP algorithm. The inverse heat conduction algorithm is applied to experimental data from a quenching experiment. The surface heat flux is then calculated, and the theoretical curve is compared with experimental results.

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