scholarly journals Numerical two-dimensional thermal analysis of the human skin using the multigrid method

2019 ◽  
Vol 42 ◽  
pp. e40992
Author(s):  
Gylles Ricardo Stroher ◽  
Cosmo Damião Santiago
Keyword(s):  
Thermal Analysis ◽  
Steady State ◽  
Temperature Distribution ◽  
Body Temperature ◽  
Multigrid Method ◽  
Medical Diagnostics ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Bioheat Equation ◽  
Average Skin

Heat can be used as an adjuvant treatment of many diseases and also as a powerful tool to help diagnose cancers, with the advantage to be a noninvasive exam. Some tumors may be best diagnosed by evaluating body temperature distribution, for instance, it is observed that local temperatures of the skin over a tumor are higher than the average skin temperature. Certainly, it is expected from medical diagnostics to be, early, fast and very precise. Especially if the health problem is a tumor, it is necessary to know the shape and the size of the cancer. Thermal images can provide further information about the tumor, generally, the thermal diagnostic is made comparing images of the region with a bioheat model. In this context, the present study shows interesting results about the multigrid method applied to solve the Pennes bioheat equation in two dimensions, using a non-stationary and steady state cases for the skin heath and with melanoma. The multigrid method presented itself as an extremely efficient and fast tool to solve the bioheat equation with refined grids that provide good spatial precision.

Two-dimensional steady-state thermal analytical model of permanent-magnet synchronous machines operating in generator mode

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Zakarya Djelloul Khedda ◽  
Kamel Boughrara ◽  
Frédéric Dubas ◽  
Baocheng Guo ◽  
El Hadj Ailam
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Permanent Magnet ◽  
Analytical Model ◽  
Electrical Machines ◽  
Synchronous Machines ◽  
Analytical Prediction ◽  
Two Dimensional ◽  
Content Type ◽  
Proposed Model

Purpose Thermal analysis of electrical machines is usually performed by using numerical methods or lumped parameter thermal networks depending on the desired accuracy. The analytical prediction of temperature distribution based on the formal resolution of thermal partial differential equations (PDEs) by the harmonic modeling technique (or the Fourier method) is uncommon in electrical machines. Therefore, this paper aims to present a two-dimensional (2D) analytical model of steady-state temperature distribution for permanent-magnet (PM) synchronous machines (PMSM) operating in generator mode. Design/methodology/approach The proposed model is based on the multi-layer models with the convolution theorem (i.e. Cauchy’s product theorem) by using complex Fourier’s series and the separation of variables method. This technique takes into the different thermal conductivities of the machine parts. The heat sources are determined by calculating the different power losses in the PMSM with the finite-element method (FEM). Findings To validate the proposed analytical model, the analytical results are compared with those obtained by thermal FEM. The comparisons show good results of the proposed model. Originality/value A new 2D analytical model based on the PDE in steady-state for full prediction of temperature distribution in the PMSM takes into account the heat transfer by conduction, convection and radiation.

scholarly journals A SPLITTING ITERATIVE METHOD FOR SOLVING THE NEUTRON TRANSPORT EQUATION

2009 ◽  
Vol 14 (3) ◽  
pp. 271-289 ◽  
Author(s):  
Onana Awono ◽  
Jacques Tagoudjeu
Keyword(s):  
Steady State ◽  
Iterative Method ◽  
Transport Equation ◽  
Multigrid Method ◽  
Neutron Transport ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Numerical Treatment ◽  
Neutron Transport Equation ◽  
Slab Geometry

This paper presents an iterative method based on a self‐adjoint and m‐accretive splitting for the numerical treatment of the steady state neutron transport equation. Theoretical analysis shows that this method converges unconditionally to the unique solution of the transport equation. The convergence of the method is numerically illustrated and compared with the standard Source Iteration method and multigrid method on sample problems in slab geometry and in two dimensional space.

Thermal Analysis In Optical Waveguides

2012 ◽  
Author(s):  
Mohd Haniff Ibrahim ◽  
Norazan Mohd Kassim ◽  
Abu Bakar Mohammad ◽  
Nazri Kamsah
Keyword(s):  
Thermal Analysis ◽  
Steady State ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Heat Equation ◽  
Cross Section ◽  
Optical Waveguides ◽  
Finite Difference Numerical Method ◽  
Steady State Heat

Analisis haba di dalam struktur pandu gelombang optik telah dijalankan untuk mengkaji taburan suhu keratan rentas apabila dipanaskan dengan elemen pemanas. Persamaan umum haba diprogramkan menggunakan kaedah berangka pembezaan terhingga. Perbezaan keputusan yang ketara telah diperoleh apabila nilai keberaliran haba yang berbeza bagi setiap elemen pandu gelombang dan mekanisma konveksi ke persekitaran dipertimbangkan. Kata kunci: Kesan termo–optik, analisis terma, kaedah pembezaan terhingga A thermal analysis in optical waveguides structure is simulated in order to predict the temperature distribution over the waveguide cross–section, when heated by a heating element. A steady state heat equation is solved by using finite difference numerical method. It is observed that by applying different value of thermal conductivities for each waveguide element and further application of convection mechanism to the ambient, obvious differences with other researchers’ work are recorded. Key words: Thermo–optic effect, thermal analysis, finite difference method

Numerical Simulation of Inviscid Transonic Flow Through Nozzles With Fluctuating Back Pressure

1989 ◽  
Vol 111 (2) ◽  
pp. 169-180 ◽  
Author(s):  
A. Bo¨lcs ◽  
T. H. Fransson ◽  
M. F. Platzer
Keyword(s):  
Steady State ◽  
Two Dimensions ◽  
Back Pressure ◽  
Nozzle Geometry ◽  
Pressure Jump ◽  
Two Dimensional ◽  
Transonic Flows ◽  
One Dimensional ◽  
Flux Vector Splitting ◽  
Shock Position

The study presents a numerical method, based on the flux vector splitting approach, to the problem of unsteady one-dimensional and two-dimensional inviscid transonic flows, with emphasis on the numerical determination of the shock position, through nozzles with time-varying back pressure. The model is first validated by comparison with exact (one dimension) and numerical (two dimensions) steady-state solutions. It is thereafter applied to the problem of time-fluctuating back pressure in quasi-one-dimensional and two-dimensional nozzles. The one-dimensional results are validated by comparison with a small perturbation analytical unsteady solution, whereafter a few sample cases are presented with the objective of understanding fundamental aspects of unsteady transonic flows. It is concluded that both the amplitude and frequency of the imposed fluctuating exit pressure are important parameters for the location of the unsteady shock. It is also shown that the average unsteady shock position is not necessarily identical with the steady-state position, and that the unsteady shock may, under certain circumstances, propagate upstream into the subsonic flow domain. The pressure jump over the shock, as well as the unsteady post-shock pressure, is different for identical shock positions during the cycle of fluctuation, which implies that an unsteady shock movement, imposed by oscillating back pressure, may introduce a significant unsteady lift and moment. This may be of importance for flutter predictions. It is also noted that, although the sonic velocity is obtained in the throat of steady-state, quasi-one-dimensional flow, this is not necessarily true for the unsteady solution. During part of the period with fluctuating back pressure, the flow velocity may be subsonic at the throat and still reach a supersonic value later in the nozzle. This phenomenon depends on the frequency and amplitude of the imposed fluctuation, as well as on the nozzle geometry.

Research of Thermal Analysis Collaboratively Using ANSYS Workbench and SolidWorks Simulation

2011 ◽  
Vol 127 ◽  
pp. 262-266
Author(s):  
Ying Peng
Keyword(s):  
Thermal Analysis ◽  
Steady State ◽  
Temperature Distribution ◽  
Product Design ◽  
Basic Theory ◽  
Steady Temperature ◽  
Optimal Method ◽  
Ansys Workbench

This paper introduces the basic theory of thermal analysis and the use of SolidWorks Simulation and ANSYS Workbench to complete the steady-state thermal analysis about related models, thus getting steady temperature distribution of the model. By comparing the differences between SolidWorks Simulation and ANSYS Workbench, we can finally work out the optimal method for product design and simulation .

The Method of Two-Dimensional Stretching to Reduce Residual Stress in Quenched Thin-Walled Aluminum Alloy

2015 ◽  
Vol 1095 ◽  
pp. 523-526
Author(s):  
Kun Qi Wang ◽  
Wei Zheng ◽  
Dan Dan Na
Keyword(s):  
Thermal Analysis ◽  
Residual Stress ◽  
Aluminum Alloy ◽  
Steady State ◽  
Two Dimensional ◽  
One Dimensional ◽  
Thin Walled ◽  
Simulation Results ◽  
Transient Thermal ◽  
Better Than

This study aims to reduce the residual stress of quenched thin-walled aluminum alloy. The method of two-dimensional stretching was proposed to further reduce the residual stress in the alloy. The steady-state and transient thermal analysis were used in ANSYS workbench15.0. Static structural was used to simulate one-dimensional and two-dimensional stretching. The simulation results show that two-dimensional stretching method is better than one-dimensional stretching, and it can eliminate the residual stress up to 92.6% when the amount of stretching in length and width is controlled in 2.5%.

Thermal Analysis of Noncircular Bearings

1996 ◽  
Vol 118 (1) ◽  
pp. 246-254 ◽  
Author(s):  
A. Hussain ◽  
K. Mistry ◽  
S. Biswas ◽  
K. Athre
Keyword(s):  
Thermal Analysis ◽  
Temperature Distribution ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Two Dimensional

The present work is on prediction of temperature distribution in noncircular journal bearings and the surrounding solids. Three forms are studied, viz. two-lobe, elliptical and orthogonally displaced bearings. For comparison purposes, a circular bearing with two different groove locations is analyzed. The investigation includes the effects of recirculation and oil mixing at the grooves. The cavitation zone has also been investigated. The work is based on a two-dimensional treatment following McCallion’s approach. The results are presented for various geometries of journal bearing configuration, including the conventional circular bearing.

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