Computational Study On Skin Tissue Freezing Using Three Phase Lag Bioheat Model

2021 ◽  
Author(s):  
Rohit Verma ◽  
Sushil Kumar
Keyword(s):  
Phase Change ◽  
Computational Study ◽  
Time Derivative ◽  
Finite Difference Approximation ◽  
Skin Tissue ◽  
Difference Approximation ◽  
Freezing Process ◽  
Phase Lag ◽  
Three Phase ◽  
The Impact

Abstract This paper considers the three-phase lag (TPL) bioheat model, to study the phase change phenomena in skin tissue during cryosurgery. The considered TPL model is based on the model of thermoelasticity, i.e., the combination of the rate of thermal conductivity and new phase lag $\left( {{\tau _v}} \right)$ due to thermal displacement. We establish an effective heat capacity based numerical algorithm to solve the non-linear governing equation for biological tissue freezing. We use radial basis functions (RBFs) and finite difference approximation for space and time derivative, respectively. We study the impact of three non-classical models, single-phase change (SPL), dual-phase lag (DPL), and triple-phase lag (TPL) on the freezing process. The effects of phase lags involved in the models on freezing are also the part of this study.

scholarly journals Computational Study of Heat Transfer inside Different PCMs Enhanced by Al2O3 Nanoparticles in a Copper Heat Sink at High Heat Loads

Nanomaterials ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 284 ◽  
Author(s):  
Nadezhda S. Bondareva ◽  
Nikita S. Gibanov ◽  
Mikhail A. Sheremet
Keyword(s):  
Phase Change ◽  
Phase Change Materials ◽  
Computational Study ◽  
Conjugate Problem ◽  
High Heat ◽  
Solid Particles ◽  
Heat Sinks ◽  
Al2o3 Nanoparticles ◽  
Electronic Elements ◽  
The Impact

The cooling of electronic elements is one of the most important problems in the development of architecture in electronic technology. One promising developing cooling method is heat sinks based on the phase change materials (PCMs) enhanced by nano-sized solid particles. In this paper, the influence of the PCM’s physical properties and the concentration of nanoparticles on heat and mass transfer inside a closed radiator with fins, in the presence of a source of constant volumetric heat generation, is analyzed. The conjugate problem of nano-enhanced phase change materials (NePCMs) melting is considered, taking into account natural convection in the melt under the impact of the external convective cooling. A two-dimensional problem is formulated in the non-primitive variables, such as stream function and vorticity. A single-phase nano-liquid model is employed to describe the transport within NePCMs.

scholarly journals Electromagnetic Field and Three-Phase-Lag in a Compressed Rotating Isotropic Homogeneous Micropolar Thermo-Viscoelastic Half-Space

2020 ◽  
Author(s):  
S.M. Abo-Dahab ◽  
A. Abd-Alla ◽  
araby kilany
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Initial Stress ◽  
Half Space ◽  
Viscoelastic Medium ◽  
Normal Mode Analysis ◽  
Mode Analysis ◽  
Phase Lag ◽  
Three Phase ◽  
The Impact

A unified mathematical model of three-phase-lag in a compressed rotating isotropic homogeneous micropolar thermo-viscoelastic medium based on a ramp type thermal shock is developed. An application of this model is carried out to resolve the problem of a perfectly conducting half-space subjected to certain boundary conditions in the presence of an electromagnetic field. Lame’s potentials and normal mode analysis techniques are employed to get the general analytical solutions. Specific attention is paid to explore the impact of the rotation, magnetic field, ramp time, as well as initial stress on the distributions of temperature, displacement, stress, and induced electric and magnetic distribution. The findings show that the impact of the rotation, magnetic field, viscous, ramp parameter, initial stress, and phase-lag on the micropolar thermo-viscoelastic medium is noticeable.

The influence of inter-turn short circuit fault considering loop current on the electromagnetic field of permanent magnet synchronous motor

2017 ◽  
Vol 36 (4) ◽  
pp. 1028-1042 ◽  
Author(s):  
Hongbo Qiu ◽  
Wenfei Yu ◽  
Shuai Yuan ◽  
Bingxia Tang ◽  
Cunxiang Yang
Keyword(s):  
Electromagnetic Field ◽  
Permanent Magnet ◽  
Short Circuit ◽  
Phase Lag ◽  
Field Calculation ◽  
Loop Current ◽  
Content Type ◽  
Phase Current ◽  
Three Phase ◽  
The Impact

Purpose The impact of the loop current (LC) on the motor magnetic field in the analysis of the inter-turn short circuit (ITSC) fault is always ignored. This paper made a comparative study on the electromagnetic field of permanent magnet synchronous motors (PMSM). The purpose of this study is to explore the necessary of the LC existing in the fault analysis and the electromagnetic characteristics of the PMSM with the ITSC fault when taking into account the LC. Design/methodology/approach Based on the finite element method (FEM), the fault model was established, and the magnetic density of the fault condition was analyzed. The induced electromotive force (EMF) and the LC of the short circuit ring were studied. The three-phase induced EMF and the unbalance of the three-phase current under the fault condition were studied. Finally, a prototype test platform was built to obtain the data of the fault. Findings The influence of the fault on the magnetic density was obtained. The current phase lag when the ITSC fault occurs causes the magnetic enhancement of the armature reaction. The mechanism that LC hinders the flux change was revealed. The influence of the fault on the three-phase-induced EMF symmetry, the three-phase current balance and the loss was obtained. Originality/value The value of the LC in the short circuit ring and the influence of it on the motor electromagnetic field were obtained. On the basis of the electromagnetic field calculation model, the sensitivity of the LC to the magnetic density, induced EMF, current and loss were analyzed.

Solving Fully Three-Dimensional Microscale Dual Phase Lag Problem Using Mixed-Collocation, Finite Difference Discretization

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
Alaeddin Malek ◽  
Zahra Kalateh Bojdi ◽  
Parisa Nuri Niled Golbarg
Keyword(s):  
Finite Difference ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Finite Difference Approximation ◽  
Stability And Convergence ◽  
Difference Approximation ◽  
Phase Lag ◽  
Dual Phase ◽  
Linear System Of Equations ◽  
Finite Difference Discretization

In the present work, we investigate laser heating of nanoscale thin-films irradiated in three dimensions using the dual phase lag (DPL) model. A numerical solution based on mixed-collocation, finite difference method has been employed to solve the DPL heat conduction equation. Direct substitution in the model transforms the differential equation into a linear system of equations in which related system is solved directly without preconditioning. Consistency, stability, and convergence of the proposed method based on a mixed-collocation, finite difference approximation are proved, and numerical results are presented. The general form of matrices and their corresponding eigenvalues are presented.

scholarly journals Phase-Lag Effects in Skin Tissue During Transient Heating

2019 ◽  
Vol 24 (3) ◽  
pp. 603-623 ◽  
Author(s):  
R. Kumar ◽  
A.K. Vashishth ◽  
S. Ghangas
Keyword(s):  
Heat Flux ◽  
Skin Tissue ◽  
Tissue Temperature ◽  
Finite Domain ◽  
Phase Lag ◽  
Transient Heating ◽  
Transform Method ◽  
Lag Effects ◽  
Three Phase ◽  
The Laplace Transform

Abstract 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 (τq, τt and τv) and material (k*) on the tissue temperature distribution are presented graphically.

scholarly journals Simulation of continuously deforming parabolic problems by Galerkin finite-elements method

1986 ◽  
Vol 9 (3) ◽  
pp. 577-582
Author(s):  
Yahia S. Halabi
Keyword(s):  
Phase Change ◽  
Hermite Polynomials ◽  
Galerkin Approximation ◽  
Finite Difference Approximation ◽  
Parabolic Problems ◽  
Difference Approximation ◽  
Two Phase ◽  
Transition Zones ◽  
Basic Functions ◽  
Numerical Finite Element

A general numerical finite element scheme is described for parabolic problems with phase change wherein the elements of the domain are allowed to deform continuously. The scheme is based on the Galerkin approximation in space, and finite difference approximation for the time derivatives. The numerical scheme is applied to the two-phase Stefan problems associated with the melting and solidification of a substance. Basic functions based on Hermite polynomials are used to allow exact specification of flux-latent heat balance conditions at the phase boundary. Numerical results obtained by this scheme indicates that the method is stable and produces an accurate solutions for the heat conduction problems with phase change; even when large time steps used. The method is quite general and applicable for a variety of problems involving transition zones and deforming regions, and can be applied for one multidimensional problems.

UNSTEADY RESPONSE OF BLOOD FLOW THROUGH A COUPLE OF IRREGULAR ARTERIAL CONSTRICTIONS TO BODY ACCELERATION

2008 ◽  
Vol 08 (03) ◽  
pp. 395-420 ◽  
Author(s):  
NORZIEHA MUSTAPHA ◽  
SANTABRATA CHAKRAVARTY ◽  
PRASHANTA K. MANDAL ◽  
NORSARAHAIDA AMIN
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Finite Difference ◽  
Stokes Equations ◽  
Computational Study ◽  
Cylindrical Tube ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Body Acceleration ◽  
Flow Through

A two-dimensional (2D) nonlinear mathematical model to study the response of the pulsatile flow of blood through a couple of irregular stenoses influenced by externally imposed periodic body acceleration is developed. The model is 2D and axisymmetric with an outline of the stenosis obtained from the three-dimensional (3D) casting of a mildly stenosed artery. The combined influence of an asymmetric shape and surface irregularities of the constrictions is explored in a computational study of blood flow through arterial stenoses with 48% areal occlusion. The arterial wall is treated as an elastic (moving wall) cylindrical tube having a couple of stenoses in its lumen, while the streaming blood is considered to be Newtonian. Solutions of the time-dependent nonlinear Navier–Stokes equations in the cylindrical coordinate system are obtained using a finite difference method based on the nonuniform and nonstaggered grids. The finite difference approximation helps to estimate the effects of body acceleration on the doubly constricted flow phenomena through several graphical representations quantitatively in order to validate the applicability of the present, improved mathematical model.

Reverse time imaging of ground-penetrating radar and SH-seismic data including the effects of wave loss

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. H21-H32 ◽  
Author(s):  
Tieyuan Zhu ◽  
José M. Carcione ◽  
Marco A. B. Botelho
Keyword(s):  
Ground Penetrating Radar ◽  
Seismic Data ◽  
Velocity Dispersion ◽  
Time Derivative ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Reverse Time ◽  
Time Migration ◽  
Lossy Media ◽  
Ground Penetrating

The presence of wave loss (velocity dispersion and attenuation in lossy media) degrades the resolution of migrated images by distorting the phase and amplitude of the signal. These effects have to be mitigated to improve resolution. We have developed a technique to perform reverse time migration of ground-penetrating radar and SH-seismic data in lossy media, suitable for engineering and seismic applications. The method is based on the solution of the transverse magnetic (TM) Maxwell equation, which in view of the acoustic-electromagnetic analogy, is mathematically equivalent to the SH-wave equation, where attenuation is described by the Maxwell mechanical model. Attenuation compensation is performed by reversing the sign of the diffusion term (first-order time derivative). In this manner, the TM equation has the same wave-velocity dependence with frequency (same velocity-dispersion behavior) but opposite attenuation, i.e., compensating for attenuation effects when back propagating. We have solved the equations numerically with a direct grid method by using the Fourier pseudospectral operator for computing the spatial derivatives, and we used an explicit staggered second-order finite-difference approximation for computing the time derivative. Four applications illustrated the potential of the algorithm. The migrated image by correcting for attenuation loss is able to improve the illumination of the target reflectors. This migration is found to be particularly useful to balance the overall image amplitude by illuminating shadow zones. Under the assumption of low-loss media (e.g., [Formula: see text]) and thicknesses comparable with or smaller than the skin depth, the attenuation-compensated migration is stable.

Analysis of Two-Dimensional Heat Diffusion Using FEA and the Fundamental Collocation Method

2016 ◽  
Author(s):  
Amir Khalilollahi ◽  
Enayat Mahajerin ◽  
Gary Burgess
Keyword(s):  
Laplace Transform ◽  
Collocation Method ◽  
Initial Conditions ◽  
Time Derivative ◽  
Heat Diffusion ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Two Dimensional ◽  
Heat Diffusion Equation ◽  
The Laplace Transform

Finite Element Analysis (FEA) and the Laplace Transform-Based Fundamental Collocation Method (FCM) are used to solve the heat diffusion equation in two-dimensional regions having arbitrary shapes and subjected to arbitrary initial and mixed type boundary conditions. In the FEA method, the time derivative is replaced with a finite difference approximation. The resulting time dependent global equations are solved incrementally starting with the initial conditions. The FCM approach is applied in the Laplace transform domain to obtain temperatures in the s-domain, T(x,y,s). An inversion technique is used to retrieve the time domain solution, T(x,y,t). To compare applicability and accuracy of these methods, both techniques are applied to transient heat flow problems for which exact solutions are known.

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