Analyses of non-Fourier heat conduction in 1-D spherical biological tissue based on dual-phase-lag bio-heat model using the conservation element/solution element (CE/SE) method: A numerical study

This work uses the “dual phase lag” (DPL) model of heat conduction to offer a new interpretation for experimental evidence of non-Fourier conduction in processed meat that was interpreted previously with hyperbolic conduction. Specifically, the DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. In addition, comparing the new interpretation to Fourier-based alternatives suggests that further study of all the interpretations could help advance the understanding of conduction in the processed meat and other biological materials such as human tissue.

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Thermal Stress Associated With Non-Fourier Heat Conduction in Femtosecond Laser Heating of Multilayer Metallic Films

Volume 8B: Heat Transfer and Thermal Engineering ◽

10.1115/imece2018-86144 ◽

2018 ◽

Author(s):

Swarup Bag ◽

M. Ruhul Amin

Keyword(s):

Thin Film ◽

Heat Conduction ◽

Thermal Stress ◽

Temperature Distribution ◽

Pulse Laser ◽

Laser Heating ◽

Laser Source ◽

Phase Lag ◽

Dual Phase ◽

Fourier Heat Conduction

In the present work, the deformation behavior in metallic film subjected to ultra-short laser heating is investigated. Static thermo-elastic behavior is predicted for 100 nm thin film of either single layer or multiple layers. The temperature distribution is estimated from dual-phase lag non-Fourier heat conduction model. The maximum temperature after single pulse is achieved 730 K. The temperature profile for this pulse laser is used to compute elastic stress and distortion field following the minimization of potential energy of the system. In the present work, the simulation has been proposed by developing 3D finite element based coupled thermo-elastic model using dual phase lag effect. The experimental basis of transient temperature distribution in ultra-short pulse laser is extremely difficult or nearly impossible, the model results have been validated with literature reported thermal results. Since the temperature distribution due to pulse laser source varies with time, the stress analysis is performed in incremental mode. Hence, a sequentially coupled thermo-mechanical model is developed that is synchronized between thermal and mechanical analysis in each time steps of transient problem. The maximum equivalent stress is achieved 0.3 GPa. Numerical results show that the predicted thermal stress may exceeds the tensile strength of the material and may lead to crack or damage the thin film.

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Notable physical anomalies manifested in non-Fourier heat conduction under the dual-phase-lag model

International Journal of Heat and Mass Transfer ◽

10.1016/j.ijheatmasstransfer.2007.07.039 ◽

2008 ◽

Vol 51 (7-8) ◽

pp. 1713-1727 ◽

Cited By ~ 54

Author(s):

B. Shen ◽

P. Zhang

Keyword(s):

Heat Conduction ◽

Phase Lag ◽

Dual Phase ◽

Lag Model ◽

Fourier Heat Conduction

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Transient Heat Conduction in Functionally Graded Hollow Cylinders and Spheres

Volume 3: Design and Analysis ◽

10.1115/pvp2012-78617 ◽

2012 ◽

Cited By ~ 1

Author(s):

A. H. Akbarzadeh ◽

Z. T. Chen

Keyword(s):

Heat Conduction ◽

Transient Heat Conduction ◽

Functionally Graded ◽

Hyperbolic Heat Conduction ◽

Phase Lag ◽

Dual Phase ◽

Conduction Theory ◽

Hollow Cylinders ◽

Fourier Heat Conduction ◽

Cylinders And Spheres

In the present work, transient heat conduction in functionally graded (FG) hollow cylinders and spheres is investigated based on the non-Fourier heat conduction theories. Since the heat transmission has been observed to propagate at a finite speed for applications with very low temperature, short-pulse thermal-heating, and micro temporal and spatial scales, dual phase lag (DPL) and hyperbolic heat conduction theories are considered in current study instead of the conventional Fourier heat conduction theory. Except the phase lags which are assumed to be constant, all the other material properties of the hollow cylinders and spheres are taken to change continuously along the radial direction according to a power-law formulation with different non-homogeneity indices. The heat conduction equations are written based on the dual phase lag theory which includes the hyperbolic heat conduction theory as well. These equations are applied for axisymmetric hollow cylinders of infinite lengths and spherically symmetric hollow spheres. Using the Laplace transform and Bessel functions, the analytical solutions for temperature and heat flux are obtained in the Laplace domain. The solutions are then converted into the time domain by employing the fast Laplace inversion technique. The exact expression is obtained for the speed of thermal wave in FG cylinders and spheres based on the DPL and hyperbolic heat conduction theories. Finally, the current results are verified with those reported in the literature based on the hyperbolic heat conduction theory.

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Tickhonov based well-condition asymptotic waveform evaluation for dual-phase-lag heat conduction

Thermal Science ◽

10.2298/tsci140410104r ◽

2016 ◽

Vol 20 (6) ◽

pp. 1891-1902

Author(s):

Sohel Rana ◽

Jeevan Kanesan ◽

Ahmed Reza ◽

Harikrishnan Ramiah

Keyword(s):

Thermal Analysis ◽

Heat Conduction ◽

High Frequency ◽

Phase Lag ◽

Dual Phase ◽

Various Boundary Conditions ◽

Fourier Heat Conduction ◽

Ill Conditioning ◽

Waveform Evaluation ◽

Asymptotic Waveform Evaluation

The Tickhonov based well condition asymptotic waveform evaluation (TWCAWE) is presented here to study the non-Fourier heat conduction problems with various boundary conditions. In this paper, a novel TWCAWE method is proposed to overwhelm ill-conditioning of the asymptotic waveform evaluation (AWE) technique for thermal analysis and also presented for time-reliant problems. The TWCAWE method is capable to evade the instability of AWE and also efficaciously approximates the initial high frequency and delay similar as well-established numerical method, such as Runge-Kutta (R-K). Furthermore, TWCAWE method is found 1.2 times faster than the AWE and also 4 times faster than the traditional R-K method.

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