Electromagnetic field-induced thermal management of biological materials

The study of temperature profiles and heat transport within the human body when subjected to electromagnetic waves is crucial for development and improvement of radiofrequency cardiac ablation treatments (radio frequency ablation). The present study provides an analytical solution for computing the temperature profiles for blood and tissue for various biological media along with heat transfer behavior during various ablation processes. The local thermal nonequilibrium model is used to characterize the bioheat transport through the biological medium. The two energy equation model for tissue and blood phase is considered. To understand the effects induced by imposed electromagnetic field, the specific absorption rate of body tissues is also studied. The results obtained have been validated against the pertinent numerical results in the literature. This study provides benchmark analytical solutions for heat transport through biological media, thereby helping in understanding the thermophysiologic response of human body toward imposed electromagnetic radiation.     

Fundamental solution of steady and transient bio heat transfer equations especially for skin burn and hyperthermia treatments

In the field of bio heat transfer, as of now, the main concern of researchers lies in the proper and accurate thermal damage of the diseased tissues without destroying or damaging the neighboring healthy tissues during the tumor treatment. The present work aims to develop a new approach toward solving the bio heat transfer equations for the skin burn and hyperthermia treatments. Both analytical and numerical solutions are proposed. For the analytical study, a differential transform method is used to solve steady and unsteady state heat equations. The finite volume method is adopted to solve these equations numerically, which provides a better scope to solve the highly nonlinear complex equations. To obtain a complete solution, a code is developed in MATLAB and MATHEMATICA. The variation of different parameters, such as perfusion constant, space heating, surface step heating, and thermal conductivity, with time were observed. Apart from the above analysis of temperature distribution during skin burn through the spilling of hot beverage, its numerical solution was also performed for this problem at different boundary conditions. It was observed that with the help of the temperature distribution, depending on the time and the severity of the burn, different ranges of depths of the burn can be determined.     

Precise dental ablation using ultra-short-pulsed 1552 nm laser

A desktop diode pulsed laser having pulse width of 1.3 ps and wavelength of 1552 nm is utilized for precise targeted ablation of dentin, enamel, and composite material while minimizing thermal damage to the surrounding healthy tissue and nerve endings. A thermal imaging camera is used to measure the dental surface temperature rise during ablation. Following ablation, scanning electron microscopy (SEM) and optical microscopy are used to determine the quality of ablation and the volumetric ablation rate as a function of laser parameters. Surface temperature measurements are compared with the numerical modeling results obtained using the transient heat conduction equation. A good agreement between experimental and modeling results for the surface temperature is obtained which ensures accurate prediction of the temperature distribution throughout the tooth using numerical models. The SEM generates images of precise ablation of each dental material when the optimal laser parameters are used and the sample is scanned at a velocity to limit the number of overlapping pulses. During the ablation process there is minimal collateral damage to the surrounding healthy tissue and minimal heat spread throughout the tooth thus preserving the integrity of the pulp.     

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.     

Nonlinear analysis of dual-phase lag bio-heat model in living tissues induced by laser irradiation

Abstract

This paper provides a method for determining a numerical solution of the thermal damage of living tissues using a nonlinear dual phase lag model. Due to the nonlinearity of the basic equations, the finite element approach is adopted to solve such problems. The numerical outcomes obtained by the finite element technique are also compared with the existing experimental study to verify the accuracy of the numerical calculations. Based on the formulation of Arrhenius, the thermal damages to the tissues are estimated by the denatured protein range. Numerical results for temperatures are presented graphically. Also, the comparisons between the numerical outcomes and the existing experimental data show that the present mathematical models are effective tools to evaluate the bioheat transfer in a spherical living tissue.     

Mass and heat transfer study in solids of revolution via numerical simulations using finite volume method and generalized coordinates for the Cauchy boundary condition

This paper proposes a numerical solution for the diffusion equation with convective boundary condition applied to solids obtained through the revolution of arbitrary bi-dimensional geometries, using generalized coordinates. The diffusion equation was discretized using the finite volume method, with a fully implicit formulation. The solution exploits symmetry conditions and that decreases the computational effort demanded, in comparison to the traditional use of three-dimensional grids. The proposed solution was used to describe diffusion processes which have a well-known solution. There was a good agreement among the results obtained through the proposed solution and the correspondent analytical solutions, as well as the experimental data.     

Volumetric maximization of coolant usage in closed self-driven circuits

The present study numerically maximizes the heat transferred in a rectangular loop. The loop or circuit is composed of two superimposed rectangles of different sizes with coolant filling the vacant space between them. Buoyancy forces promote coolant motion, since a constant temperature difference is maintained between the two outer vertical walls of the circuit. The results are presented in terms of two quantities: the heat transfer rate per unit of length and per unit of coolant volume, for several values of the Rayleigh number. The numerical solution is obtained by applying the finite elements method to the two-dimensional numerical domain, here represented by the coolant only. The numerical results show that the relative size of the inner and outer rectangles composing the circuit are important in terms of thermal performance and that the optimal gap size between the inner and outer rectangles decreases as the Rayleigh is increased. The circuit aspect ratio (i.e., height/width) was also investigated revealing to have a positive effect on the overall thermal performance of the system if increased, while the eccentricity of the two rectangles composing the circuit presented an opposite effect. The numerical results were compared with scaling analysis showing good agreement.     

Effective thermal conductivity of wet particle assemblies

The effective thermal conductivity of mono- and poly-dispersed random assemblies of spherical particles and irregular crystals, both dry and partially or fully saturated by wetting and non-wetting liquids, has been determined computationally by numerical solution of the Fourier’s law on 3-D reconstructed media and experimentally by the transient hot wire method. The effect of spatial distribution and volume fractions of the vapour, liquid, and solid phases on effective thermal conductivity was systematically investigated. A power-law correlation for estimating the effective conductivity, valid over a wide range of phase volume fractions and relative conductivities of components, has been proposed.     

A Simulation-Experiment Method to Characterize the Heat Transfer in Ex-Vivo Porcine Hepatic Tissue with a Realistic Microwave Ablation System

A simulation-experiment method is proposed to characterize the performance of a realistic microwave ablation (MWA) device. Ex-vivo porcine livers are used in the study. The catheter is modeled without understanding its electrical structure or the actual ablation power; so, it is adaptable to other ablators. The optimized 3-D finite difference time domain (FDTD) simulation can efficiently reflect the lesion profile in heterogeneous tissues and is clinically beneficial. This method can serve as a guideline to evaluate the device performance and the treatment plan. The influence of the temperature dispersive dielectric and the thermal properties has also been discussed.     

On the junction temperature of the QFN64 electronic package subjected to free convection: Effects of the encapsulating molding compound

ABSTRACT

The thermal conductivity of the molding compound (resin) used to encapsulate the QFN64 package significantly affects the thermal behavior of this electronic package during operation when it is subjected to natural convection. These effects are quantified in this work by varying the conductivity between ?80% and +100% of its average value. The 3D numerical solution carried out by means of the control volume method clearly shows that the maximal temperature reached in the junction of the device is affected by this parameter for a wide range of the generated power and various inclinations relative to the horizontal plane. The correlation proposed in this work allows optimizing the thermal design and increases the reliability, durability, performance, and correct operating of this electronic device widely used in various engineering fields.     

高温隔热纤维结构材料绝热特性分析

高温隔热纤维结构的绝热特性是决定金属热防护系统工作性能的关键因素。文中应用有限元法及有限容积法对理想化的纤维结构模型进行了数值研究,得出了纤维结构内部稳态下的温度场、热流场及速度场分布,并在此基础上计算得到纤维结构的等效导热系数,分析了温度、内部气体压力以及纤维结构密度对等效导热系数的影响。所建物理模型和分析方法可行,计算结果与实验结果吻合较好。     

Heat transfer in a reaction–diffusion system with a moving heat source

A general formulation is presented for a moving boundary problem in which heat is generated at the boundary due to an exothermic reaction involving a species which diffuses into a dispersed phase from an external medium of finite volume. The speed of the moving boundary is prescribed based on the solution of the mass diffusion problem and an analysis is presented of the thermal dynamics of the system. The set of equations describing heat transport leads to a Green’s function type problem with time dependent boundary conditions and the Galerkin finite element method is employed to develop a numerical solution. Transformations are introduced to freeze the moving boundary and partition the domain for ease of computation, and an iterative scheme is defined to satisfy the heat flux jump boundary condition and match the temperature field across the moving boundary. The numerical results are used to set the limits of applicability of an analytical perturbation solution. Essential aspects of thermal dynamics in the system are described and parametric regions resulting in a local temperature hot spot are delineated. Computed contour plots describing thermal evolution are presented for different combinations of parameter values. These may be of utility in the prediction of thermal development, for control and avoidance of hot spot formation, and in physical parameter estimation.     

The condition requiring conjugate numerical method in study of heat transfer characteristics of tube bank fin heat exchanger

The overall heat transfer performance of a tube bank fin heat exchanger is very important for engineering applications. Developing a fin pattern with good heat transfer performance for tube bank fin heat exchanger needs more our intensive effort. There are two methods to obtain the heat transfer performances of a fin pattern, i.e., one is experimental method, and the other is numerical method. If numerical method is used, the thermal boundary condition on the fin surfaces is necessary. Generally, there are two ways to treat the thermal boundary, i.e., one is to treat fin surface with uniform temperature, and the other is to use a conjugate numerical method. The former is very easy to be applied in numerical method, but the latter needs more numerical effort. This paper reports the condition under which whether a conjugate numerical method or a numerical method just specifying uniform temperature thermal boundary condition should be used. It is found that such condition is the fin efficiency. When the fin efficiency is less than 0.8, a conjugate numerical method must be used. Otherwise, the numerical results obtained by applying an uniform temperature thermal boundary condition on the fin surfaces has only slightly differences with the results obtained by a conjugate numerical method. The reported results will provide a criterion for the researchers to choose a suitable numerical method in finding a fin pattern more efficiently and reliably.     

Engineering Analysis of Ablative Thermal Protection for Atmospheric Reentry: Improved Lumped Formulations and Symbolic – Numerical Computation

A computational approach for the engineering analysis of ablative-type thermal protection systems (TPS) in atmospheric reentry ballistic flights is communicated. We first propose an improved lumped differential approach for ablative thermal protection analysis, which involves the use of materials with low thermal diffusivity. The results obtained for a one-dimensional thermal ablation problem in a finite slab are compared against those obtained by previously reported lumped differential solutions. Benchmark results for the local nonlinear model, obtained through the generalized integral transform technique, are utilized to verify the proposed solution in a realistic ablation problem, consisting of a low thermal diffusivity material subjected to a prescribed net aerodynamic heating. In addition, an integrated symbolic–numerical system is constructed based on the Mathematica platform for the derivation and computation of all the related quantities along the flight, yielding the transient behavior of the TPS recession and thermal performance for both the constant and variable initial thickness along the vehicle nose region. An illustrative example of the computational tool and the typical results for an orbital platform in ballistic reentry flight are presented.     

A numerical solution of developing temperature for laminar developing flow in eccentric annular ducts

The energy equation expressed in bipolar coordinates is used to determine the temperature distribution in the thermal entrance region of an eccentric annular duct. An implicit alternating-direction method is used in the numerical solution. The analysis of the hydrodynamic entrance region, which provides the velocity distributions needed for the thermal solution, was obtained from a published solution by the present authors. A published Graetz solution for an eccentric annulus and a published combined thermal and hydrodynamic entrance region solution for the circular tube are used in the verification of the present solution. In the present analysis 17 combinations of fundamental thermal boundary conditions, Prandtl number, and annular geometry are considered. The annular geometry with equal relative eccentricity and radius ratio of 0.5 is used to study the effects of eccentricity and Prandtl number on the fluid temperature and surface heat flux distributions.     

An Integral Approximate Solution to Ablation of a Two-Layer Composite with a Temporal Gaussian Heat Flux

Ablation is the most common approach for thermal management for reentry of the spacecraft to the atmosphere. An analytical solution of the ablation of a two-layer composite, which includes an ablative layer and a nonablative substrate, subject to a Gaussian heat flux is presented in this paper. The problem is divided into five stages and the temperature distributions in both layers in the five stages are obtained using an integral approximate method. The locations of ablation interface, thermal penetration depth, and ablation rate are obtained and the effects of Stefan number, subcooling parameter, thickness of the ablative material, and ratio of thermal diffusivities between two materials are investigated.     

Heat flow rate at a bore-face and temperature in the multi-layer media surrounding a borehole

Assessment of the heat either delivered from high temperature rocks to the borehole or transmitted to the rock formation from circulating fluid is of crucial importance for a number of technological processes related to borehole drilling and exploitation. Normally the temperature fields in the well and surrounding rocks are calculated numerically by finite difference method or analytically by applying the Laplace-transform method. The former approach requires tedious and, in certain cases, non-trivial numerical computations. The latter method leads to rather bulky formulae that are inconvenient for further numerical evaluation. Moreover, in previous studies where the solution is obtained analytically, the heat interaction of the circulating fluid with the formation was treated on the condition of constant bore-face temperature. In the present study the temperature field in the rock formation disturbed by the heat flow from the borehole is modeled by a heat conduction equation, assuming the Newton model for the convective heat transfer on the bore-face, with boundary conditions that account for the thermal history of the borehole exploitation. The problem is solved analytically by the generalized heat balance integral method. Within this method the approximate solution of the heat conduction problem is sought in the form of a finite sum of functions that belong to a complete set of linearly independent functions defined at the finite interval bounded by the radius of thermal influence and that satisfy the homogeneous boundary conditions on the bore-face. In the present study first and second order approximations are obtained for the composite multi-layer domain. The numerical results illustrate that the second approximation is in a good agreement with the exact solution. The only disadvantage of this solution is that it depends on the radius of thermal influence, which is an implicit function of time and can only be found numerically by iterative algorithms. In order to eliminate this complication, in this study an approximate explicit formula for the radius of thermal influence and new close-form approximate solution are proposed on the basis of the approximate solution obtained by the integral-balance method. Employing the non-liner regression method the coefficients for this simplified solution are obtained. The accuracy of the approximate solution is validated by comparison with the exact analytical solution found by Carslaw and Jaeger for the homogeneous domain.     

An experimental and numerical investigation of heat transfer during technical grade paraffin melting and solidification in a shell-and-tube latent thermal energy storage unit

The latent thermal energy storage system of the shell-and-tube type during charging and discharging has been analysed in this paper. An experimental and numerical investigation of transient forced convective heat transfer between the heat transfer fluid (HTF) with moderate Prandtl numbers and the tube wall, heat conduction through the wall and solid–liquid phase change of the phase change material (PCM), based on the enthalpy formulation, has been presented. A fully implicit two-dimensional control volume Fortran computer code, with algorithm for non-isothermal phase transition, has been developed for the solution of the corresponding mathematical model. The comparison between numerical predictions and experimental data shows good agreement for both paraffin non-isothermal melting and isothermal solidification. In order to provide guidelines for system performance and design optimisation, unsteady temperature distributions of the HTF, tube wall and the PCM have been obtained by a series of numerical calculations for various HTF working conditions and various geometric parameters, and the thermal behaviour of the latent thermal energy storage unit during charging and discharging has been simulated.     

A GENETIC ALGORITHM FOR THE SHAPE OPTIMIZATION OF PARTS SUBJECTED TO THERMAL LOADING

In many technical situations, the optimization of the mechanical behavior of structures proceeds from the search for the ideal shape satisfying thermal, mechanical, technological, and geometrical constraints. In this article, the shape optimization of mono- and two-dimensional structures is handled by means of a new genetic algorithm (GA). The method is in general well suited to the resolution of nonconstrained optimization problems: The algorithm presented here has been modified by taking into account the imposed design constraints in the selection of the "individuals" belonging to a given population. The crossover operation between individuals and the mutation process in their original forms are applied to derive the optimal shape of parts subjected to thermal loadings. The algorithm exhibits a good convergence toward the optimal solution and the numerical results of its application show a good numerical accuracy.     

Acrylic acid controlled reusable temperature-sensitive hydrogel phantoms for thermal ablation therapy

Polymerization of N-isopropylacrylamide (NIPAM) with acrylic acid (AAc) has been adopted to fabricate reusable tissue-mimicking hydrogel phantoms designed for the real-time visualization and examination of thermal lesion formation in ablation and hyperthermia therapies. It is shown that the cloud point temperature of the NIPAM-based hydrogel phantoms can be adjusted by the concentration of AAc to represent the threshold temperature of pain (42 °C) or tissue damage (52 °C). The mechanical, thermal and acoustic properties of the developed phantoms are similar to those of human soft tissues. The ability of the phantoms to provide visualization of thermal lesions produced by either microwave or high-intensity focused ultrasound (HIFU) ablation was examined. Evolution of the optical transparency of the phantoms with temperature was found to be a stable hysteretic behavior and reproducible in consecutive heating–cooling cycles, demonstrating the reusability of the phantoms. By processing the optical images of the phantoms at different stages of the heating process, a thermal lesion can be considered formed (i.e., threshold temperature reached) when the grayscale value reaches the half-saturation point. The image processing method proposed for the NIPAM-based hydrogel phantoms is shown to be independent on the type of heating device used.