Assessment of Hyperbolic Heat Transfer Equation in Theoretical Modeling for Radiofrequency Heating Techniques

Theoretical modeling is a technique widely used to study the electrical-thermal performance of different surgical procedures based on tissue heating by use of radiofrequency (RF) currents. Most models employ a parabolic heat transfer equation (PHTE) based on Fourier’s theory, which assumes an infinite propagation speed of thermal energy. We recently proposed a one-dimensional model in which the electrical-thermal coupled problem was analytically solved by using a hyperbolic heat transfer equation (HHTE), i.e. by considering a non zero thermal relaxation time. In this study, we particularized this solution to three typical examples of RF heating of biological tissues: heating of the cornea for refractive surgery, cardiac ablation for eliminating arrhythmias, and hepatic ablation for destroying tumors. A comparison was made of the PHTE and HHTE solutions. The differences between their temperature profiles were found to be higher for lower times and shorter distances from the electrode surface. Our results therefore suggest that HHTE should be considered for RF heating of the cornea (which requires very small electrodes and a heating time of 0.6 s), and for rapid ablations in cardiac tissue (less than 30 s)

NUMERICAL INVESTIGATION AND PARALLEL COMPUTING FOR THERMAL TRANSPORT MECHANISM DURING NANOMACHINING

Nano-scale machining, or Nanomachining is a hybrid process in which the total thermal energy necessary to remove atoms from a work-piece surface is applied from external sources. In the current study, the total thermal energy necessary to remove atoms from a work-piece surface is applied from two sources: (1) localized energy from a laser beam focused to a micron-scale spot to preheat the work-piece, and (2) a high-precision electron-beam emitted from the tips of carbon nano-tubes to remove material via evaporation/sublimation. Macro-to-nano scale heat transfer models are discussed for understanding their capability to capture and its application to predict the transient heat transfer mechanism required for nano-machining. In this case, thermal transport mechanism during nano-scale machining involves both phonons (lattice vibrations) and electrons; it is modeled using a parabolic two-step (PTS) model, which accounts for the time lag between these energy carriers. A numerical algorithm is developed for the solution of the PTS model based on explicit and implicit finite-difference methods. Since numerical solution for simulation of nanomachining involves high computational cost in terms of wall clock time consumed, performance comparison over a wide range of numerical techniques has been done to devise an efficient numerical solution procedure. Gauss-Seidel (GS), successive over relaxation (SOR), conjugate gradient (CG), d -form Douglas-Gunn time splitting, and other methods have been used to compare the computational cost involved in these methods. Use of the Douglas-Gunn time splitting in the solution of 3D time-dependent heat transport equations appears to be optimal especially as problem size (number of spatial grid points and/or required number of time steps) becomes large. Parallel computing is implemented to further reduce the wall clock time required for the complete simulation of nanomachining process. Domain decomposition with inter-processor communication using Message Passing Interface (MPI) libraries is adapted for parallel computing. Performance tuning has been implemented for efficient parallelization by overlapping communication with computation. Numerical solution for laser source and electron-beam source with different Gaussian distribution are presented. Performance of the parallel code is tested on four distinct computer cluster architecture. Results obtained for laser source agree well with available experimental data in the literature. The results for electron-beam source are self-consistent; nevertheless, they need to be validated experimentally

A FE-FD hybrid scheme for solving parabolic two-step micro heat transport equations in irregularly shaped three dimensional double -layered thin films exposed to ultrashort -pulse lasers

Multi-layer thin films are important components in many micro-electronic devices. These films are often used when a single film layer is insufficient to meet devices specifications. The continued reduction in component size has the side effect of increasing the thermal stress on these films and consequently the devices they comprise. Understanding the transfer of heat-energy at the micro-scale is important for thermal processing using a pulse-laser. Often, micro-voids may be found in processed devices. This is due to thermal expansion. Such defects may cause an amplification of neighboring defects resulting in severe damage and consequently the failure of the device. Thus a complete understanding of thermal dissipation and defects is necessary to avoid damage and to increase the efficiency of thermal processing. A hybrid finite element - finite difference (FE-FD) method has been developed for solving three dimensional parabolic two-step heat transport in irregular double-layered thin film exposed to ultrashort pulsed lasers. This scheme first discretizes the thin film system along the xy-plane by a finite element method. Then the z-direction is discretized via a weighted finite difference scheme. The two are combined into a numerical scheme which is then coded into a computer simulation. It is shown that the scheme is unconditionally stable with respect to the initial condition and the heat source. Three distinct numerical examples are studied. The first being a 0.05 μm gold thin film disk, with 1 mm diameter, atop a same-dimensioned chromium padding layer. This disk is exposed to an ultra-fast laser burst and the thermal properties are demonstrated. Secondly, the same thin-film disk array is exposed to a double burst laser pulse and the thermal properties examined. Finally the ultrashort laser is moved in a complete circle about the center of the double-layered thin disk and the thermal properties are examined. The outcome of this study provides an efficient and reliable numerical method for solving micro-scale heat transport equations, and gives a better understanding of the nature of heat transport in such a system. Also, the hybridization procedure offers a new way to examine three dimensional heat transport systems---one that utilizes the strengths of both the finite element and the finite difference methodologies. The research results have a significant impact on the development of short-pulse laser applications in structural monitoring of thin metal films, laser patterning of such films and laser synthesis and processing of thin film deposition

A finite difference method for studying thermal deformation in two-dimensional micro scale metal thin films exposed to ultrashort pulsed lasers

Ultrashort-pulsed lasers have been attracting worldwide interest in science and engineering because the lasers with pulse durations on the order of sub-picoseconds to femtoseconds possess capabilities in limiting the undesirable spread of the thermal process zone in a heated sample during material processing at the microscale. Prevention of thermal damage is an important factor for success of ultrashort-pulsed lasers in real applications. The thermal damage induced by ultrashort pulses is intrinsically different from that induced by long-pulse or continuous lasers. It occurs after the heating pulse is over and involves the shattering of thin metal layers (without a clear signature of thermal damage by excessive temperature) rather than the melt damage caused by high temperatures. In this dissertation, by replacing the displacement components in the dynamic equations of motion using the velocity components, and employing a staggered grid, we develop a finite difference method for studying thermal deformation in two-dimensional films exposed to ultrashort-pulsed lasers, where the thin films are a single-layered thin film and a double-layered thin film with perfectly interfacial thermal contact and imperfectly interfacial thermal contact, respectively. The method is obtained based on the parabolic two-step heat transport equations. It accounts for the coupling effect between lattice temperature and strain rate, as well as for the hot electron blast effect in momentum transfer. The developed methodology allows us to avoid non-physical oscillations in the solution. Such oscillations have been an intrinsic feature of most numerical method proposed so far in the context of problem of interest. The development of physical-based, numerical-oscillation-free methods for thermal analysis of thin metal films subjected to heating of ultrashort-pulsed lasers represents challenging tools at the forefront of this practically important area of research. This method is tested for its applicability by investigating the temperature rise and deformation in (1) a single-layered gold thin film, (2) a double-layered gold and chromium thin film with perfect thermal contact at the interface, and (3) a double-layered gold and chromium thin film with imperfect thermal contact at the interface. Results show that there are no non-physical oscillations in the solutions, and the method is promising

The one-dimensional Stefan problem with non-Fourier heat conduction

We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time regimes we are able to reduce the problem to a system of two coupled ordinary differential equations describing the evolution of the solid-liquid interface and the heat flux. The reduced formulation is in good agreement with numerical simulations. In the case of silicon, differences between classical and non-classical solidification kinetics are relatively small, but larger deviations can be observed in the evolution in time of the heat flux through the growing solid. From this study we conclude that the heat flux provides more information about the presence of non-classical modes of heat transport during phase-change processes.Comment: 29 pages, 6 figures, 2 tables + Supplementary Materia

A numerical method to solve the two-step parabolic heat transport equations in a microsphere subjected to an ultrafast laser pulse

Heat transport at the microscale is the subject of intense investigation due to the growing need to fabricate microstructures for applications in nanotechnology. The need to control the spread of the thermal process zone has led to the development of high power short-pulse lasers. During thermal processing, impurities may form in the material. An amplification of the thermal energy around the impurities may result in severe damage occurring or in the failure of the thermal process. A thorough analysis of the way the impurities dissipates the thermal energy is therefore necessary to minimize the potential damage and optimize the thermal processing. The classical theory of heat diffusion, which is averaged over many grains, is inadequate in describing the transport phenomenon. Single energy equations developed to describe the transport phenomenon include a third-order mixed derivative with respect to space which makes them numerically inefficient. In this study, we will consider a microsphere subjected to an ultrafast laser pulse. The transport phenomenon is modeled by the two-step parabolic heat transport equations in three dimensional spherical coordinates. We will develop an energy estimate to establish the well-posedness of the problem, a three-level finite difference scheme to solve the transport equations, and prove that the finite difference scheme is unconditionally stable. The scheme will be applied to investigate the temperature rise in a gold sphere subjected to a short-pulse laser

A Study of Transversely Isotropic Thermoelastic Beam with Green-Naghdi Type-II and Type-III Theories of Thermoelasticity

The present research deals with the study of transversely isotropic thermoelastic beam in the context of Green-Naghdi (GN) theory of thermoelasticity of Type-II and Type-III. The mathematical model is prepared for the thin beam in a closed form with the application of Euler Bernoulli beam theory. The Laplace Transform technique has been used to find the expressions for displacement component, lateral thermal moment, deflection and axial stress in transformed domain. The general algorithm of the inverse Laplace Transform is developed to compute the results numerically in physical domain. The effect of two theories of thermoelasticity Green-Naghdi-II and Green-Naghdi-III has been depicted on the various quantities. Some particular cases have also been deduced

Imaging and inverse problems of electromagnetic nondestructive evaluation

Electromagnetic nondestructive evaluation (NDE) is used widely in industry to assess the character of structures and materials noninvasively. A major aspect of any NDE system is solving the associated inverse problem to characterize the material under study. The solution of the inverse problem is directly related to the physics of a particular electromagnetic NDE system which can be either fully dynamic, quasistatic, or static depending on the operating frequency and material parameters. In a general electromagnetic NDE system, indirect inversion techniques which utilize large amounts of a priori knowledge and some type of calibration scheme are employed to characterize materials. However, in certain test situations the governing physics of an electromagnetic NDE system allow direct inversion techniques to be employed which can be used to image flaws in a material. There has, however, been research which attempts to utilize direct inversion methods which do not rely on the underlying physics of the electromagnetic NDE system;This dissertation first describes the importance of the underlying physics to the solution of the electromagnetic NDE inverse problem. In this context, the inverse problem of fully dynamic electromagnetic NDE and magnetoquasistatic (MQS) NDE are developed to elucidate their underlying mathematical and physical properties. It is shown that the inverse problem for MQS phenomena is generally much more difficult than that of fully dynamic electromagnetic phenomena. Experiments are conducted which utilize fully dynamic millimeter wave NDE and MQS eddy current NDE to compare and contrast the physics and inverse problem of each technique. Two methods are then examined as a possible means of inverting MQS data with direct techniques. A transformation from diffusion to waves is examined as a method of inverting MQS data as a pseudo-wave field. An analytic inversion of the transformation is developed and used to gain insight into robustness issues associated with the method. Also, an averaging scheme is developed to increase the robustness of the transformation. Next, a technique is developed which utilizes phase shifts of steady state eddy current impedance measurements to directly image subsurface flaws in electrically conducting materials. A 1-D analytic study and a 2-D finite element simulation are used to gain insight into the underlying physics associated with the method. A modification to the technique is developed which utilizes the finite element model to account for phase distortions associated with the induced eddy currents in a test sample. An experiment is then carried out to demonstrate this direct inversion technique on actual eddy current data;The results of this study show that the use of direct inversion methods for imaging electromagnetic NDE must be carried out with a clear understanding of the underlying physical phenomena. There are many instances where direct inversion schemes can be applied to fully dynamic electromagnetic fields. Due to physical limitations associated with MQS phenomena, direct inversion methods are not generally applicable to MQS data. However, a transformation technique is shown to be a potential means for utilizing direct inversion techniques on MQS. A second direct inversion technique introduced for MQS data has potential for imaging subsurface flaws in electrically conducting materials. There are, however, severe limitations to both inversion methods which reduce their usefulness

Thermomagnetic behavior of a semiconductor material heated by pulsed excitation based on the fourth-order MGT photothermal model

This article proposes a photothermal model to reveal the thermo-magneto-mechanical properties of semiconductor materials, including coupled diffusion equations for thermal conductivity, elasticity, and excess carrier density. The proposed model is developed to account for the optical heating that occurs through the semiconductor medium. The Moore–Gibson–Thompson (MGT) equation of the fourth-order serves as the theoretical framework to establish the photothermal model. It is well-known that the optical and heat transfer properties of such materials behave as random functions of photoexcited-carrier density; therefore, the current model is remarkably more reliable compared to the earlier closed-form theories which are limited to a single form. The constructed theoretical framework is able to investigate the magneto-photo-thermoelastic problems in a semiconductor medium due to laser pulse excitation as a case study. Some parametric studies are used to exhibit the impact of thermal parameters, electromagnetic fields, laser pulses and thermoelectric coupling factors on the thermomagnetic behavior of physical variables. Finally, several numerical examples have been presented to draw the distributions of the examined field variables

Thermal ablation of biological tissues in disease treatment: A review of computational models and future directions

Percutaneous thermal ablation has proved to be an effective modality for treating both benign and malignant tumors in various tissues. Among these modalities, radiofrequency ablation (RFA) is the most promising and widely adopted approach that has been extensively studied in the past decades. Microwave ablation (MWA) is a newly emerging modality that is gaining rapid momentum due to its capability of inducing rapid heating and attaining larger ablation volumes, and its lesser susceptibility to the heat sink effects as compared to RFA. Although the goal of both these therapies is to attain cell death in the target tissue by virtue of heating above 50 oC, their underlying mechanism of action and principles greatly differs. Computational modelling is a powerful tool for studying the effect of electromagnetic interactions within the biological tissues and predicting the treatment outcomes during thermal ablative therapies. Such a priori estimation can assist the clinical practitioners during treatment planning with the goal of attaining successful tumor destruction and preservation of the surrounding healthy tissue and critical structures. This review provides current state-of- the-art developments and associated challenges in the computational modelling of thermal ablative techniques, viz., RFA and MWA, as well as touch upon several promising avenues in the modelling of laser ablation, nanoparticles assisted magnetic hyperthermia and non- invasive RFA. The application of RFA in pain relief has been extensively reviewed from modelling point of view. Additionally, future directions have also been provided to improve these models for their successful translation and integration into the hospital work flow