Phase Lag Parameters Research Articles

Reflection of plane waves at the free surface of fiber-reinforced orthotropic thermoelastic rotating half-space with three-phase-lag model

The present article is concerned with the propagation of plane waves in a homogeneous, fiber-reinforced orthotropic thermoelastic rotating half-space in the context of three-phase-lag model. There exist three coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT) and quasi-transverse wave (qSV) in the medium. The reflection coefficients are computed numerically with the help of MATLAB programming and are depicted graphically to show the effects of rotation, fiber-reinforcement and phase lag parameters. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is depicted on velocities of various reflected waves. Some particular cases of interest have also been inferred from the present investigation.

A Non-Fourier Bioheat Transfer Model for Cryosurgery of Tumor Tissue with Minimum Collateral Damage

Background and objectivesIncorporation of non-Fourier heat conduction while studying heat transfer phenomena in biological materials has emerged has an important approach as it predicts better and more realistic results than Fourier based models. In this article we have proposed a non-Fourier computational model and applied the same to simulate cryosurgery of lung tumor and attempted minimization of freezing damage of healthy lung tissue using pulsed laser irradiation. MethodsA non-Fourier bioheat transfer model for phase change in biological tissues is solved via a Fourier heat conduction based solution approach. A unified model is proposed combining all variants of bioheat models: Fourier's heat conduction based Pennes’ bioheat model, hyperbolic heat conduction model and dual phase lag model. The proposed model takes into account the different thermophysical properties of frozen and unfrozen regions. In order to mimic the actual biotransport process, the blood perfusion and metabolic heat generation are switched off in the frozen region. Implicit source based enthalpy method is used to model phase change process. A new iterative enthalpy update equation is developed for capturing evolution of freezing front implicitly. Finite Volume based numerical discretization technique is used to discretize the governing PDE. The resulting discrete algebraic equation set is solved implicitly by Tri-diagonal Matrix Algorithm. The proposed model is verified with existing results from the literature. ResultsFor Fourier heat conduction, freezing time of 99.99% of tumor is 1247s, which increases to 1267s for τq= 5s (τT= 0s) and again reduces to 1255s for τq= 5s and τT= 3s. τq and τT are phase lag parameters for non-Fourier heat conduction. For τq= 5s and τT= 0.05s, the freezing damage of healthy tissue decreases by 23.76% when pulsed laser irradiation (Io = 106 W/m2) is used to warm the neighboring healthy tissue. ConclusionsSo non-Fourier bioheat transport models are better and more accurate in predicting temperature history, freezing time and freezing front propagation as compared to Fourier based models. Pulsed laser irradiation can prove to be a very efficient technique in minimizing collateral damage during cryosurgery.

The memory effect on thermal wave propagation in a moving thin slab

The present literature survey examines the thermal interaction due to dual-phase-lag (DPL) heat transfer for a moving finite medium due to the presence of a time-dependent laser heat source. Since, various kinds of shortcomings persist in the power-law distribution, the heat transport equation for the present problem has been defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent derivative. Incorporating the Laplace transform as a tool, the governing equation has been solved in the Laplace transform domain and a suitable numerical scheme is adopted to arrive at the solution and the corresponding numerical inversion of the Laplace transform has been carried out using Zakian method. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are constructed. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative, effect of moving velocity, effect of phase-lag parameters, delay time also. Moreover, few limiting cases of the phase-lag parameters have also been demonstrated.

Effect of three-phase-lag model on the analysis of three-dimensional free vibrations of viscothermoelastic solid cylinder

Herein we explore the effects of three-phase-lag (TPL) model of generalized thermoelasticity on the exact analysis of three-dimensional free vibrations of viscothermoelastic solid cylinder, which is assumed undeformed initially and at uniform temperature. The formulation has been put into practice with three different phase-lag parameters i.e., Phase-lag of the heat flux, Phase-lag of the temperature gradient, and Phase-lag of the thermal displacement gradient. The solution of matrix Frobenius method of continued series solution has been implemented to solve the differential equations for the evaluation of field functions i.e. stresses, displacements, and temperature by applying stress-free/rigidly-fixed thermal boundary conditions (i.e. thermally insulated and isothermal). The obtained frequency equations for the existence of different modes of TPL viscothermoelastic solid cylinder have been developed using considered stress free/rigidly fixed boundary conditions. The free vibration field functions i.e. frequency shift and thermoelastic damping have been presented graphically from the data generated by simulations and computations of numerical results. Also, the natural frequencies are presented in the form of tables which shows that with an increase in the axial wave-number and length to radius ratio, the behavior of vibrations goes on increasing. The behavior of vibrations of field functions in case of TPL model has larger in contrast to other models of generalized thermoelasticity.

Fundamental Solution and Study of Plane Waves in Bio-Thermoelastic Medium with DPL

The fundamental solution of the system of differential equations in bio-thermoelasticity with dual phase lag (DPL) in case of steady oscillations in terms of elementary function is constructed and basic property is established. The tissue is considered as an isotropic medium and the propagation of plane harmonic waves is studied. The Christoffel equations are obtained and modified with the thermal as well as bio thermoelastic coupling parameters. These equations explain the existence and propagation of three waves in the medium. Two of the waves are attenuating longitudinal waves and one is non-attenuating transverse wave. The thermal property has no effect on the transverse wave. The velocities and attenuating factors of longitudinal waves are computed for a numerical bioheat transfer model with phase lag. The variation with frequency, thermal parameters, blood perfusion parameter and phase lag parameter are presented graphically. Also the reflection of plane wave from a stress free isothermal boundary of isotropic bio-thermoelastic half space in the context of DPL theory of thermoelasticity is studied. The amplitude ratios of various reflected waves are obtained and these amplitude ratios are further used to obtain the energy ratios of various reflected waves. These energy ratios are function of the angle of incidence and bio-thermoelastic properties of the medium. The expressions of energy ratios have been computed numerically for a particular model to show the effect of Poisson ratio, blood perfusion rate and phase lag parameters.

Thermo-viscoelastic interaction under dual-phase-lag model with memory-dependent derivative

This article deals with the thermo-viscoelastic interaction in a two-dimensional homogeneous, isotropic, infinite space subjected to an instantaneous heat source. The problem is considered in the domain of dual-phase-lag (DPL) model of generalized thermo-viscoelasticity with memory-dependent derivative (MDD). The joint Laplace–Fourier transform is used as mathematical tool to obtain vector matrix differential equation and it is then solved by utilizing eigenvalue approach. Numerical estimation of displacements, stresses, and temperature are figured for a certain material by utilizing Bellman method and Gaussian quadrature formula. At last, the impact of space variable, time, kernel function, time-delay, and phase-lag parameters on the thermophysical quantities is analyzed graphically.

Skin pain sensation of epidermal electronic device/skin system considering non-Fourier heat conduction

Epidermal electronic devices (EEDs) have drawn much attention recently due to their wide applications in biological monitoring and biomedicine. Due to the thermo-mechanical coupling between EEDs and skin, skin pain sensation is susceptive to noxious stimuli from EEDs in practical applications. An analytical thermo-mechanical model is developed to predict the temperature and stress distributions in the EED/skin system accounting for the non-Fourier effect in skin tissues via Dual-Phase-Lag (DPL) model. The phase lag parameters in the DPL model are obtained from the two-temperature model and then validated by experiments. The holistic analytical frame, consisting of the thermo-mechanical model for temperature and stress, Arrhenius burn model for thermal damage, modified Hodgkin–Huxley model for nociceptor transduction and gate control theory for pain modulation and perception, is adopted to quantify the skin pain sensation in terms of the noxious stimuli from EEDs. Skin pain sensations of EED/skin system are fully investigated in both constant and periodic operation modes. The model in this paper paves the theoretical foundation to study wearing comfort of EEDs and can be easily extended to study other bio-integrated systems for different types of applications.

Linear response theory for coupled phase oscillators with general coupling functions

We develop a linear response theory by computing the asymptotic value of the order parameter from the linearized equation of continuity around the nonsynchronized reference state using the Laplace transform in time. The proposed theory is applicable to a wide class of coupled phase oscillator systems and allows for any coupling functions, any natural frequency distributions, any phase-lag parameters, and any values for the time-delay parameter. This generality is in contrast to the limitation of the previous methods of the Ott–Antonsen ansatz and the self-consistent equation for an order parameter, which are restricted to a model family whose coupling function consists of only a single sinusoidal function. The theory is verified by numerical simulations.

Thermoelastic damping analysis for size-dependent microplate resonators utilizing the modified couple stress theory and the three-phase-lag heat conduction model

Thermoelastic damping (TED) is considered to be a factor of significant energy loss in micro-scale structures, even at room temperature. The prediction of TED is therefore very important in the designing of micro-electro-mechanical system (MEMS) resonators with high-quality factors. When the thickness of the beams and plates are at microscale or nanoscale, the size-effect is needed to be considered. Couple stress theory is developed as a size-dependent continuum theory to deal with such problems. In the present work, an analytical expression for the quality factor (Q) of TED for size-dependent microplate resonators is derived by applying the modified couple stress theory (MCST) considering plane stress condition and the three-phase-lag (TPL) heat conduction model. We consider Kirchhoff microplate resonators and as case study, the effect of the length-scale parameter on the quality factor of TED are discussed in detail. To study the behavior of TED, the material of the microplate resonator is considered to be Silicon. The variations of TED as functions of the normalized frequency, microplate thickness, and length-scale parameter have been investigated. The effect of phase-lag parameters on TED has also been discussed. The results of the present model are compared to the existing results of the classical continuum theory. The present work investigates that the modified couple stress theory with small values of phase-lag parameters can increase the quality factor of microplate resonators with a smaller thickness.

Nonlocal heat conduction approach in a bi-layer tissue during magnetic fluid hyperthermia with dual phase lag model.

In this work, a nonlocal dual-phase-lag (NL DPL) model is introduced to accommodate the effects of thermomass and size-dependent thermophysical properties at nanoscale heat transport. Heat transfer at nanoscale is essentially nonlocal and quite different from that at the micro- or macro scale. To illustrate the nonlocal effect, a bi-layered structure is considered during magnetic fluid hyperthermia (MFH) treatment which is used successfully in prostate, liver, and breast tumors and the effect of size-dependent characteristic lengths is discussed in tumor and normal region of tissue. The problem is solved by using the finite difference scheme in space coordinate and Legendre wavelet Galerkin approach in time coordinate with the Dirichlet, Neumann and Robin boundary conditions. The effect of boundary conditions, characteristic lengths, phase lag parameters and nanomaterial parameters is discussed in tumor and healthy tissue domain and the results are presented graphically. This study is expected to be helpful for modeling of bioheat transfer equation at nano-scale, and may be beneficial to design nano-sized and multi-layered devices for heat transfer.

Phase-Lag Effects in Skin Tissue During Transient Heating

A three-phase-lag (TPL) model is proposed to describe heat transfer in a finite domain skin tissue with temperature dependent metabolic heat generation. The Laplace transform method is applied to solve the problem. Three special types of heat flux are applied to the boundary of skin tissue for thermal therapeutic applications. The depth of tissue is influenced by the different oscillation heat flux. The comparison between the TPL and dual-phase-lag (DPL) models is analyzed and the effects of phase lag parameters (<i>τq</i>, <i>τt</i> and <i>τv</i>) and material (<i>k</i><sup>*</sup>) on the tissue temperature distribution are presented graphically.

Study of MHD Second Grade Flow through a Porous Microchannel under the Dual-Phase-Lag Heat and Mass Transfer Model

A semi-analytical investigation has been carried out to analyze unsteady MHD second-grade flow under the Dual-Phase-Lag (DPL) heat and mass transfer model in a vertical microchannel filled with porous material. Diffusion thermo (Dufour) effects and homogenous chemical reaction are considered as well. The governing partial differential equations are solved by using the Laplace transform method while its inversion is done numerically using INVLAP subroutine of MATLAB. The numerical values of fluid velocity, fluid temperature and species concentration are demonstrated through graphs while the numerical values of skin friction, heat transfer rate and mass transfer rate presented in tabular form for different values of parameters that govern the flow. For the first time, a comparison of heat transfer utilizing the classical Fourier’s heat conduction model, hyperbolic heat conduction Cattaneo-Vernotte (CV) model, and the DPL model is carried out for the flow of a second grade fluid. It is found that the differences between them vanish at dimensionless time t=0.4 (for temperature) and at t=0.5 (for velocity), i.e. at a time where the system reaches steady state. The influence of phase lag parameters in both thermal and solutal transport on the fluid flow characteristics have been deciphered and analyzed. The results conveyed through this article would help researchers to understand non-Fourier heat and mass transfer in the flow of second-grade fluids which may play a vital role in the design of systems in polymer industries.

Effects of phase-lag on thermoelastic damping in micromechanical resonators

The present article attempts to investigate thermoelastic damping (TED) of a microbeam resonator by employing the three-phase-lag (TPL) thermoelasticity theory proposed by Roychoudhuri. An explicit formula of TED has been derived and the effects of the beam height, the phase-lag parameters on TED of the microbeam resonator have been studied. Effects of beam height and phase-lags on TED have been shown with the numerical results. A comparison of the results with the corresponding results of the theory of thermoelasticity of type GN-III is also presented. It has been observed that GN-III predicts a high-quality factor of the resonator’s sensitivity as compared to TPL model.

A note on interpreting tidal harmonic constants

The amplitudes and phase lags of tides or tidal currents, which are collectively known as tidal harmonic constants (THCs), cannot be interpolated linearly and separately. Mistreatment for the interpolations could occur, and indeed, it is seen even in the literature. This note clarifies this topic by providing correct formulas to interpret THCs. One has to perform a nonlinear and coupled interpolation of THCs to have equivalence to the liner interpolation in the time domain.Similarly, tidal current ellipse parameters (ep-parameters) cannot be interpolated linearly and separately. To interpolate ep-parameters, this note recommends that one should first convert them to amplitude and phase lag parameters (ap-parameters) and then use the nonlinear and coupled interpolants proposed herein to interpolate the ap-parameters, followed by converting the results back to ep-parameters.Examples are provided to illustrate the problems and MATLAB functions are provided in Appendix as interpolating tools.

Analytical solution of dual-phase-lag heat conduction in a finite medium subjected to a moving heat source

In the present study, the dual-phase-lag heat conduction model was employed to describe the thermal behavior of a square plate which is heated by a moving temporally non-Gaussian heat source. The Green's function approach was utilized to develop a general solution for the non-Fourier heat conduction equation in a two-dimensional finite medium. The temperature responses of the medium obtained from Fourier's law, hyperbolic heat conduction model and dual-phase-lag heat conduction model were compared to show the influences of the phase lag parameters. In addition, the effect of scanning speed of heat source on the temperature distribution was discussed. The vector diagrams of heat flux were illustrated to show its propagation.

Generalized synchronization between chimera states.

Networks of coupled oscillators in chimera states are characterized by an intriguing interplay of synchronous and asynchronous motion. While chimera states were initially discovered in mathematical model systems, there is growing experimental and conceptual evidence that they manifest themselves also in natural and man-made networks. In real-world systems, however, synchronization and desynchronization are not only important within individual networks but also across different interacting networks. It is therefore essential to investigate if chimera states can be synchronized across networks. To address this open problem, we use the classical setting of ring networks of non-locally coupled identical phase oscillators. We apply diffusive drive-response couplings between pairs of such networks that individually show chimera states when there is no coupling between them. The drive and response networks are either identical or they differ by a variable mismatch in their phase lag parameters. In both cases, already for weak couplings, the coherent domain of the response network aligns its position to the one of the driver networks. For identical networks, a sufficiently strong coupling leads to identical synchronization between the drive and response. For non-identical networks, we use the auxiliary system approach to demonstrate that generalized synchronization is established instead. In this case, the response network continues to show a chimera dynamics which however remains distinct from the one of the driver. Hence, segregated synchronized and desynchronized domains in individual networks congregate in generalized synchronization across networks.

Chimera states in two populations with heterogeneous phase-lag.

The simplest network of coupled phase-oscillators exhibiting chimera states is given by two populations with disparate intra- and inter-population coupling strengths. We explore the effects of heterogeneous coupling phase-lags between the two populations. Such heterogeneity arises naturally in various settings, for example, as an approximation to transmission delays, excitatory-inhibitory interactions, or as amplitude and phase responses of oscillators with electrical or mechanical coupling. We find that breaking the phase-lag symmetry results in a variety of states with uniform and non-uniform synchronization, including in-phase and anti-phase synchrony, full incoherence (splay state), chimera states with phase separation of 0 or π between populations, and states where both populations remain desynchronized. These desynchronized states exhibit stable, oscillatory, and even chaotic dynamics. Moreover, we identify the bifurcations through which chimeras emerge. Stable chimera states and desynchronized solutions, which do not arise for homogeneous phase-lag parameters, emerge as a result of competition between synchronized in-phase, anti-phase equilibria, and fully incoherent states when the phase-lags are near ±π2 (cosine coupling). These findings elucidate previous experimental results involving a network of mechanical oscillators and provide further insight into the breakdown of synchrony in biological systems.

On the non-Fourier thermal fracture of an edge-cracked cylindrical bar

The fracture behavior of a cylindrical bar containing a circumferential edge crack under transient thermal loading is analyzed in this paper using the dual phase lag heat conduction model. The lateral surface of the bar is subjected to an asymmetric, convective thermal boundary condition. The Laplace transform method is adopted to solve the one-dimensional, hyperbolic heat conduction equation in the un-cracked bar, and the corresponding thermal stress is obtained in the Laplace domain under plane strain condition. Then, based on the superposition method, the axial stress with minus sign is applied on the crack surface to form a mode I crack problem in the cylindrical coordinate. Love’s potential function is introduced to solve the crack problem and a singular integral equation is obtained by using the Fourier and Hankel transform methods. Furthermore, a numerical Laplace inversion technique is employed to transform all the results to the time domain. Finally, the effect of heat conduction model, phase-lag parameters, Biot number, and the crack depth on the transient temperature, thermal axial stress, stress intensity factor, and crack opening displacement is analyzed.

A Domain of Influence Theorem for Thermoelasticity with Three-Phase-Lag Model

We establish the theory of domain of influence for a potential-temperature disturbance under the generalized theory of thermoelasticity with three-phase-lag model. For a finite time t > 0, it has been proved that the potential due to the displacement and the temperature fields does not produce any disturbances outside a bounded domain and the domain of influence is dependent on the support of load, the thermoelastic coupling constant and the phase-lag parameters. It has been shown that the domain of influence of the present case reduces to the domain of influence for classical thermoelasticity theory and the thermoelasticity theory with one relaxation parameter.

Temporal evolution of the geoelectrical response on a hydrocarbon contaminated site

A geoelectrical campaign was initiated in 2009 to delineate a massive hydrocarbon spill, which occurred because of a petroleum pipe breakdown in 2009. These measurements have been compared with both field resistivity measurements made in 2009 and with laboratory measurements. From a physicochemical point of view, a hydrocarbon contamination has to be understood as a spatially and temporally varying object, responsible for a change in geoelectrical response. To evaluate the signal measured on site, geoelectrical laboratory measurements were performed on the petroleum oil extracted from the site during two stages of degradation. On the laboratory scale, the non-degraded oil shows an increase in resistivity, normalized chargeability and quadrature conductivity with oil content, whereas the degraded oil indicates a slight decrease in resistivity, but no modification of the phase-lag and chargeability parameters. In the field, resistivity measurements performed in 2009, just after the pipe breakdown, show weak changes in resistivity measured over the contaminated area. However, between 2009 and 2012, biodegradation of the oil has led to a clear decrease in the resistivity within the impacted zone. No variations in normalized chargeability or quadrature conductivity were measured in 2012 between the contaminated and the non-contaminated areas, despite the presence of biofilms. In the field, the studied hydrocarbon contamination under degradation appears not to modify the capacitive part of conduction, but rather it concerns the ohmic part of conduction. The field and laboratory measurements led us to the conclusion that to choose the most discriminatory and efficient geophysical parameters, it is necessary to have a priori information about the oil (i.e. non-degraded or partially degraded). In the present case study, there is no need to acquire chargeability and phase-lag parameters to locate the contamination in the field, as they do not undergo any change. On the other hand, the resistivity parameter is a good indicator of the presence of partially degraded oil. We also note that normalized chargeability values have been very useful in characterizing the geometry of the clayey-silt roof. • SIP laboratory measurements on a petroleum oil at different states of biodegradation • In situ temporal evolution of the resistivity response of the hydrocarbon contamination • In situ influence of petroleum oil under biodegradation on the SIP response