Numerical study on the nonlinear effects of heat diffusion in composites and its potential in nondestructive testing

2003 ◽  
Vol 74 (1) ◽  
pp. 462-464 ◽  
Author(s):  
Georgios Kalogiannakis ◽  
Danny Van Hemelrijck
Keyword(s):  
Nondestructive Testing ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Heat Diffusion

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

scholarly journals The transformation of an interfacial solitary wave of elevation at a bottom step

2009 ◽  
Vol 16 (1) ◽  
pp. 33-42 ◽  
Author(s):  
V. Maderich ◽  
T. Talipova ◽  
R. Grimshaw ◽  
E. Pelinovsky ◽  
B. H. Choi ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Ocean Model ◽  
Gardner Equation ◽  
Fully Nonlinear ◽  
Layer Flow ◽  
The One ◽  
Bottom Step

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.

scholarly journals Visualization Of Thermal Distribution During Machining of Dental Implants

2021 ◽  
Vol 12 (4) ◽  
pp. 4637-4648
Keyword(s):  
Dental Implants ◽  
Thermal Field ◽  
Numerical Study ◽  
Physical Property ◽  
Heat Diffusion ◽  
Dimensional Error ◽  
3 Dimensional ◽  
Thermal Distribution ◽  
Cooling Strategy ◽  
Thermo Physical Properties

Dental implants used are usually metallic. One of the most widely used materials for the same is Titanium-based alloy like Ti-6Al-4V, which suffers difficulty processing and machining due to its thermo-physical properties. The thermo-physical property of the material plays a significant role in the biocompatibility and safety to use them as dental implants. Due to its hardness and difficult-to-machine characteristics, a large amount of heat gets generated while machining, creating dimensional error. Hence before assembly of parts, they must be processed so that stress deformation of the assembly due to heat can be avoided. During machining of Ti-6Al-4V, the cooling strategy needs prior information on the thermal field, and hence, the distribution of temperature in the material is an essential domain to study. To understand the thermal distribution in the material during machining, 3-dimensional heat diffusion equations have been solved using a Finite Difference scheme coupled with the Liebmann method to generate the thermal distribution in the material. An efficient parallelized code for the same has been written in MATLAB and utilized in this numerical study. This study reveals the variation of the temperature gradient with time and space, all along with the three orthogonal directions, which will be helpful for the scientists, engineers, and surgeons to ascertain the sustainability [1, 2], suitability, and longevity of the implants.

scholarly journals A Numerical Study of Diffusion of Nanoparticles in a Viscous Medium During Solidification

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Kazi M. Rahman ◽  
M. Ruhul Amin ◽  
Ahsan Mian
Keyword(s):  
Fluid Flow ◽  
Marangoni Number ◽  
Numerical Study ◽  
Control Volume ◽  
Mathematical Formulation ◽  
Heat Diffusion ◽  
Solidification Time ◽  
Original Position ◽  
Heat Diffusion Equation ◽  
Metal Matrix Nanocomposites

Abstract In the field of additive manufacturing process, laser cladding is widely considered due to its cost effectiveness, small localized heat generation, and full fusion to metals. Introducing nanoparticles with cladding metals produces metal matrix nanocomposites, which in turn improves the material characteristics of the clad layer. The governing equations that control the fluid flow are standard incompressible Navier–Stokes and heat diffusion equation, whereas the Euler–Lagrange approach has been considered for particle tracking. The mathematical formulation for solidification is adopted based on enthalpy porosity method. Liquid titanium has been considered as the initial condition where particle distribution has been assumed uniform throughout the geometry. A numerical model implemented in a commercial software based on control volume method has been developed, which allows to simulate the fluid flow during solidification as well as tracking nanoparticles during this process. A detailed parametric study has been conducted by changing the Marangoni number, convection heat transfer coefficient, constant temperature below the melting point of titanium, and insulated boundary conditions to analyze the behavior of the nanoparticle movement. The influence of increase in Marangoni number results in a higher concentration of nanoparticles in some portions of the geometry and lack of nanoparticles in rest of the geometry. The high concentration of nanoparticles decreases with a decrease in Marangoni number. Furthermore, an increase in the rate of solidification time limits the nanoparticle movement from its original position which results in different distribution patterns with respect to the solidification time.

scholarly journals Numerical Study on the Characteristics of Boger Type Viscoelastic Fluid Flow in a Micro Cross-Slot under Sinusoidal Stimulation

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 64
Author(s):  
Chao Yuan ◽  
Hong-Na Zhang ◽  
Li-Xia Chen ◽  
Jun-Long Zhao ◽  
Xiao-Bin Li ◽  
...  
Keyword(s):  
Flow Pattern ◽  
Natural Frequency ◽  
Viscoelastic Fluid ◽  
Numerical Study ◽  
Nonlinear Effects ◽  
Weissenberg Number ◽  
Stimulation Frequency ◽  
External Stimulation ◽  
Inlet Velocity ◽  
The Cross

The cross-slot geometry plays an important role in the study of nonlinear effects of viscoelastic fluids. The flow of viscoelastic fluid in a micro cross-slot with a high channel aspect ratio (AR, the ratio of channel depth to width) can be divided into three types, which are symmetric flow, steady-state asymmetric flow and time-dependent flow under the inlet condition with a constant velocity. However, the flow pattern of a viscoelastic fluid in the cross-slot when a stimulation is applied at inlets has been rarely reported. In this paper, the response of cross-slot flow under an external sinusoidal stimulation is studied by numerical simulations of a two-dimensional model representing the geometry with a maximum limit of AR. For the cases under constant inlet velocity conditions, three different flow patterns occur successively with the increase of Weissenberg number (Wi). For the cases under sinusoidal varying inlet velocity conditions, when the stimulation frequency is far away from the natural frequency of a viscoelastic fluid, the frequency spectrum of velocity fluctuation field shows the characteristics of a fundamental frequency and several harmonics. However, the harmonic frequency disappears when the stimulation frequency is close to the natural frequency of the viscoelastic fluid. Besides, the flow pattern shows spatial symmetry and changes with time. In conclusion, the external stimulation has an effect on the flow pattern of viscoelastic fluid in the 2D micro cross-slot channel, and a resonance occurs when the stimulation frequency is close to the natural frequency of the fluid.

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