scholarly journals Simplified Theoretical Model for Temperature Evaluation in Tissue–Implant–Bone Systems during Ultrasound Diathermy

2020 ◽  
Vol 10 (4) ◽  
pp. 1306
Author(s):  
Chang-Wei Huang
Keyword(s):  
Temperature Distribution ◽  
Analytical Solutions ◽  
Sensitivity Analyses ◽  
Orthogonal Expansion ◽  
One Dimensional ◽  
Simplified Approach ◽  
Implant Materials ◽  
Surgical Implants ◽  
Lower Temperature ◽  
Joint Prostheses

Deep heating procedures are helpful in treating joint contractures that frequently occur with fractures and joint diseases involving surgical implants and artificial joint prostheses. This study uses a one-dimensional composite medium model consisting of parallel slabs as a simplified approach to shed light on the influences of implants during ultrasound diathermy. Analytical solutions for the one-dimensional transient heat generation and conduction problem were derived using the orthogonal expansion technique and a Green’s function approach. The analytical solutions provided deep insight into the temperature profile by therapeutic ultrasound heating in the composite system. The effects of the implant material type, tissue thickness, and ultrasound operation frequency on temperature distribution were studied for clinical application. In addition, sensitivity analyses were carried out to investigate the influences of material properties on the temperature distribution during ultrasound diathermy. Based on the derived analytical solutions, the numerical simulations indicate that materials with high density, high specific heat, and low thermal conductivity may be optimal implant materials. Among available implant materials, a tantalum implant, which can achieve a lower temperature rise within the tissue (hydrogel) and bone layers during ultrasound diathermy, is a better choice thanks to its thermodynamics.

scholarly journals Performance analysis and optimization of rectangular fin arrays used in plate-fin heat exchangers

2020 ◽  
pp. 213-213
Author(s):  
Weicheng Wu ◽  
Hassan Soliman
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Performance Analysis ◽  
Aspect Ratio ◽  
Analytical Solutions ◽  
Heat Exchangers ◽  
Two Dimensional ◽  
One Dimensional ◽  
Independent Parameters

This paper deals with longitudinal rectangular fin arrays used in plate-fin heat exchangers. The temperature distribution and rate of heat transfer were obtained using one dimensional (1-D) and two-dimensional (2-D) solutions. The ranges of independent parameters within which the 1-D solution was within 1% from the 2-D solution were determined. Simple analytical solutions were determined for the rate of heat transfer, fin effectiveness, and augmentation factor. The aspect ratio at which the rate of heat transfer reached a maximum was determined, as well as the corresponding effectiveness and augmentation factor.

Transient convective diffusion to a uniformly accessible surface under aparent slip conditions

1991 ◽  
Vol 56 (2) ◽  
pp. 334-343
Author(s):  
Ondřej Wein
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Convective Diffusion ◽  
Active Surface ◽  
Velocity Profiles ◽  
One Dimensional ◽  
Slip Conditions ◽  
Accessible Surface ◽  
Diffusion Problems

Analytical solutions are given to a class of unsteady one-dimensional convective-diffusion problems assuming power-law velocity profiles close to the transport-active surface.

INHOMOGENEOUS LARGE DEFORMATION KINETICS OF POLYMERIC GELS

2013 ◽  
Vol 05 (01) ◽  
pp. 1350001 ◽  
Author(s):  
WILLIAM TOH ◽  
ZISHUN LIU ◽  
TENG YONG NG ◽  
WEI HONG
Keyword(s):  
Large Deformation ◽  
Soft Matter ◽  
Inner Core ◽  
Kinetic Studies ◽  
Fe Model ◽  
One Dimensional ◽  
Simplified Approach ◽  
Deformation Kinetics ◽  
Polymeric Gels ◽  
Kinetics Of

This work examines the dynamics of nonlinear large deformation of polymeric gels, and the kinetics of gel deformation is carried out through the coupling of existing hyperelastic theory for gels with kinetic laws for diffusion of small molecules. As finite element (FE) models for the transient swelling process is not available in commercial FE software, we develop a customized FE model/methodology which can be used to simulate the transient swelling process of hydrogels. The method is based on the similarity between diffusion and heat transfer laws by determining the equivalent thermal properties for gel kinetics. Several numerical examples are investigated to explore the capabilities of the present FE model, namely: a cube to study free swelling; one-dimensional constrained swelling; a rectangular block fixed to a rigid substrate to study swelling under external constraints; and a thin annulus fixed at the inner core to study buckling phenomena. The simulation results for the constrained block and one-dimensional constrained swelling are compared with available experimental data, and these comparisons show a good degree of similarity. In addition to this work providing a valuable tool to researchers for the study of gel kinetic deformation in the various applications of soft matter, we also hope to inspire works to adopt this simplified approach, in particular to kinetic studies of diffusion-driven mechanisms.

scholarly journals Data visualization and distinct features extraction of the comet Ison 2013

2019 ◽  
Vol 12 (24) ◽  
pp. 122-128
Author(s):  
Salman. Z. Khalaf
Keyword(s):  
Temperature Distribution ◽  
Data Visualization ◽  
Features Extraction ◽  
Maximum Intensity ◽  
Distribution Fitting ◽  
One Dimensional ◽  
Mathematical Equations ◽  
Distinct Features

The distribution of the intensity of the comet Ison C/2013 is studied by taking its histogram. This distribution reveals four distinct regions that related to the background, tail, coma and nucleus. One dimensional temperature distribution fitting is achieved by using two mathematical equations that related to the coordinate of the center of the comet. The quiver plot of the gradient of the comet shows very clearly that arrows headed towards the maximum intensity of the comet.

Numerical Experiments of Coolant Mixing in a Lower Plenum of PWR Under Asymmetric Thermal- Hydraulics Conditions

2006 ◽  
Author(s):  
Masanori Ohtani ◽  
Akito Kozuru ◽  
Yasuyuki Kashimoto ◽  
Mitsuto Montani ◽  
Koutaro Takeda ◽  
...  
Keyword(s):  
Steady State ◽  
Temperature Distribution ◽  
Turbulent Mixing ◽  
Numerical Experiments ◽  
Time Dependent ◽  
Inlet Temperature ◽  
Velocity Fluctuations ◽  
The Core ◽  
State Calculation ◽  
Lower Temperature

Asymmetric thermal-hydraulic conditions among primary loops during a postulated steam line break (SLB) induce a non-uniform temperature distribution at a core inlet. When coolant of lower temperature intrudes into a part of core, it leads to a reactivity insertion and a local power increase. Therefore, an appropriate model for the core inlet temperature distribution is required for a realistic SLB analysis. In this study, numerical experiments were conducted to examine the core inlet temperature distribution under the asymmetric thermal-hydraulic coolant conditions among primary loops. 3D steady-state calculations were carried out for Japanese standard Pressurized Water Reactor (PWR) such as 2, 3, 4 loop types and an advanced PWR. Since the flow in a reactor vessel involves time-dependent velocity fluctuations due to a high Reynolds number condition and a complicated geometry of flow path, the turbulent mixing might be enhanced. Hence, the turbulent thermal diffusivity for the steady-state calculation was examined based on experimental results and another transient calculation. As a result, it was confirmed that (1) the turbulent mixing in a downcomer and a lower plenum were enhanced due to time-dependent velocity fluctuations and therefore the turbulent thermal diffusivity for steady-state calculation was specified to be greater, (2) the core inlet temperature distribution predicted by a steady-state calculation reasonably agreed with a experimental data, (3) the patterns of core inlet temperature distribution were comprehended to be dependent on the plant type, i.e. the number of primary loop and (4) under a low flow rate condition, the coolant of lower temperature appeared on the opposite side of the affected loop due to the effect of a natural convection.

IV.—Expansion of a Finite One-dimensional Gas Cloud into a Vacuum

1953 ◽  
Vol 64 (1) ◽  
pp. 57-70
Author(s):  
A. G. Mackie
Keyword(s):  
Density Distribution ◽  
Analytical Solutions ◽  
Initial Density ◽  
Initial Distribution ◽  
One Dimensional ◽  
Gas Streams ◽  
Subsequent Motion ◽  
Gas Cloud ◽  
Initial Density Distribution ◽  
Stationary Period

SynopsisAn investigation is made of the motion of a one-dimensional finite gas cloud which is initially at rest and is allowed to expand into a vacuum in both directions. The density of the gas at rest is assumed to rise steadily and continuously from zero at the boundaries to a maximum in the interior of the cloud.If the subsequent motion is continuous, it is completely specified by analytical solutions in seven different regions of the x-t plane joined together along characteristics. The motion of one of the boundaries is discussed, and conditions found for it to have (i) an initial stationary period or (ii) a final constant velocity of advance into the vacuum. The gas streams in both directions from a dividing point at zero velocity. This point ultimately tends to the mid-point of the initial distribution.The possible breakdown of the continuity of the motion is discussed, and a condition on the initial density distribution found for shock-free flow to be maintained.

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