Development of a mathematical model for propagation of ultrasonic waves in thick-walled cylinders in the presence of a thermal gradient - Case of axial scanning

Ultrasonics ◽  
2021 ◽  
pp. 106628
Author(s):  
R. Shabani ◽  
F. Honarvar
Keyword(s):  
Mathematical Model ◽  
Thermal Gradient ◽  
Ultrasonic Waves ◽  
Axial Scanning

scholarly journals Ultrasonic Waves in Bubbly Liquids: An Analytic Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1309
Author(s):  
P. R. Gordoa ◽  
A. Pickering
Keyword(s):  
Mathematical Model ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Waves ◽  
Elliptic Functions ◽  
Coupled System ◽  
Ultrasonic Waves ◽  
Partial Differential ◽  
Special Cases ◽  
Spherical Bubbles

We consider the problem of the propagation of high-intensity acoustic waves in a bubble layer consisting of spherical bubbles of identical size with a uniform distribution. The mathematical model is a coupled system of partial differential equations for the acoustic pressure and the instantaneous radius of the bubbles consisting of the wave equation coupled with the Rayleigh–Plesset equation. We perform an analytic analysis based on the study of Lie symmetries for this system of equations, concentrating our attention on the traveling wave case. We then consider mappings of the resulting reductions onto equations defining elliptic functions, and special cases thereof, for example, solvable in terms of hyperbolic functions. In this way, we construct exact solutions of the system of partial differential equations under consideration. We believe this to be the first analytic study of this particular mathematical model.

Computer Simulation of Thermomigration Process

1997 ◽  
Vol 490 ◽  
Author(s):  
V. Yu. Gershanov ◽  
S. I. Garmashov ◽  
A. R. Minyaev ◽  
A. V. Beletskaya
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Computer Simulation ◽  
Thermal Gradient ◽  
Thermal Conditions ◽  
Diffuse Interface ◽  
Cross Sectional ◽  
Nucleation Mechanisms ◽  
Liquid Phase Composition ◽  
Sectional Shape

ABSTRACTMathematical model of thermomigration of liquid inclusions through a crystal under stationary and non-stationary thermal conditions is presented. It is assumed that the mass-transfer is provided by diffusion only, the crystallization and dissolution processes are carried out in accordance with the diffuse interface mechanism for atomic-rough (non-singular) interfaces and screw-dislocation or two-dimension nucleation mechanisms for singular interfaces.The package of computer programs based on this model enables simulation of the evolution of the cross-sectional shape of cylindrical liquid inclusions. It is possible to simulate the cases of various inclusion sizes, various relationship between the interface and volume mass-transfer restrictions, various liquid phase composition, thermal gradient under stationary and non-stationary thermal conditions as well. The main results of the simulation are presented.

High Temperature Thermal Gradient Interaction Chromatography (HT-TGIC) for Blends of Ethylene/1-Octene Copolymers: A Mathematical Model

2015 ◽  
Vol 354 (1) ◽  
pp. 361-366 ◽  
Author(s):  
Nantiya Inwong ◽  
Siripon Anantawaraskul ◽  
João B. P. Soares ◽  
Abdulaal Z. Al-Khazaal
Keyword(s):  
Mathematical Model ◽  
High Temperature ◽  
Thermal Gradient

Mathematical Model and Simulation of a Thermal Diffusion Column

2003 ◽  
Vol 125 (2) ◽  
pp. 266-273 ◽  
Author(s):  
Juan E. Vela´squez ◽  
Farid Chejne ◽  
Alan F. J. Hill
Keyword(s):  
Mathematical Model ◽  
Temperature Gradient ◽  
Thermal Diffusion ◽  
Thermal Gradient ◽  
Gas Mixture ◽  
Two Dimensional ◽  
Model And Simulation ◽  
Total Reflux ◽  
Diffusion Column ◽  
Composition Profiles

A two-dimensional mathematical model, in stationary state was developed for the separation of species in a thermal diffusion column working with total reflux. The model was applied to a gas mixture of CO2 and N2. The existence of convective currents along the column was verified, the separation of species due to the temperature gradient was predicted and the effect of the thermal gradient and of the operation pressures on the composition profiles was analyzed.

Quantitative Evaluation of an Internal Flaw of a Structural Component Using Electromagnetic Acoustic Transducers

2001 ◽  
Author(s):  
Shinichi Maruyama ◽  
Toshihiko Sugiura ◽  
Akihiro Inoue ◽  
Masatsugu Yoshizawa
Keyword(s):  
Mathematical Model ◽  
Nondestructive Evaluation ◽  
Ultrasonic Waves ◽  
Local Optimum ◽  
Electromagnetic Acoustic Transducers ◽  
Acoustic Transducers ◽  
Time Period ◽  
Internal Flaw ◽  
Inspection Process ◽  
The Mathematical Model

Abstract Electromagnetic acoustic transducers (EMATs) can transmit and detect ultrasonic waves in a conductive specimen out of any contact with it. This process can be given theoretical modeling and formulation based on elastodynamics and electromagnetics. It suggests a possibility of quantitative nondestructive evaluation using EMATs. This research deals with a numerical method of flaw identification from a receiver signal obtained by EMATs. Experimental results of the receiver signals agree well with numerical ones, which verified the mathematical model of the inspection process. Flaw identification is formulated as a problem of parameter optimization. To avoid being trapped in a local optimum, initial parameters were successfully evaluated from the height and the time period of peaks in the receiver signals. Flaw parameters were identified from the receiver signals obtained by numerical simulations and experiments, which verified the method of flaw identification presented here.

Nonlinear ultrasonic waves in a magneto-flexo-thermally actuated single walled armchair carbon nanotube embedded on polymer matrix

2020 ◽  
Vol 18 (1) ◽  
pp. 1-13
Author(s):  
Rajendran Selvamani ◽  
M. Mahaveer Sree Jayan ◽  
Farzad Ebrahimi
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotube ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Ultrasonic Waves ◽  
Dimensionless Frequency ◽  
Single Walled Carbon Nanotube ◽  
Content Type ◽  
Analytical Formulation ◽  
Nonlinear Ultrasonic

Purpose The purpose of this paper is concerned with the study of nonlinear ultrasonic waves in a magneto-flexo-thermo (MFT) elastic armchair single-walled carbon nanotube (ASWCNT) resting on polymer matrix. Design/methodology/approach A mathematical model is developed for the analytical study of nonlinear ultrasonic waves in a MFT elastic armchair single walled carbon nanotube rested on polymer matrix using Euler beam theory. The analytical formulation is developed based on Eringen’s nonlocal elasticity theory to account small scale effect. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been analysed numerically by using the nonlinear foundations supported by Winkler-Pasternak model. The solution is obtained by ultrasonic wave dispersion relations. Findings From the literature survey, it is evident that the analytical formulation of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix is not discussed by any researchers. So, in this paper the analytical solutions of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix are studied. Parametric studies is carried out to scrutinize the influence of the nonlocal scaling, magneto-electro-mechanical loadings, foundation parameters, various boundary condition and length on the dimensionless frequency of nanotube. It is noticed that the boundary conditions, nonlocal parameter and tube geometrical parameters have significant effects on dimensionless frequency of nanotubes. Originality/value This paper contributes the analytical model to find the solution of nonlinear ultrasonic waves in an MFT elastic ASWCNT embedded on polymer matrix. It is observed that the increase in the foundation constants raises the stiffness of the medium and the structure is able to attain higher frequency once the edge condition is C-C followed by S-S. Further, it is noticed that the natural frequency is arrived below 1% in both local and nonlocal boundary conditions in the presence of temperature coefficients. Also, it is found that the density and Poisson ratio variation affects the natural frequency with below 2%. The results presented in this study can provide mechanism for the study and design of the nano devices such as component of nano oscillators, micro wave absorbing, nano-electron technology and nano-electro--magneto-mechanical systems that make use of the wave propagation properties of ASWCNTs embedded on polymer matrix.

Fission Gas Bubbles in Fractured UO2

1968 ◽  
Vol 26 ◽  
pp. 286-287
Author(s):  
O. M. Katz
Keyword(s):  
Electron Microscopy ◽  
Thermal Gradient ◽  
Gas Bubbles ◽  
Inert Gas ◽  
Thermal Gradients ◽  
Fission Gas ◽  
Beam Heating ◽  
Limited Application ◽  
Bubble Characteristics ◽  
Electron Beam Heating

The swelling of irradiated UO2 has been attributed to the migration and agglomeration of fission gas bubbles in a thermal gradient. High temperatures and thermal gradients obtained by electron beam heating simulate reactor behavior and lead to the postulation of swelling mechanisms. Although electron microscopy studies have been reported on UO2, two experimental procedures have limited application of the results: irradiation was achieved either with a stream of inert gas ions without fission or at depletions less than 2 x 1020 fissions/cm3 (∼3/4 at % burnup). This study was not limited either of these conditions and reports on the bubble characteristics observed by transmission and fractographic electron microscopy in high density (96% theoretical) UO2 irradiated between 3.5 and 31.3 x 1020 fissions/cm3 at temperatures below l600°F. Preliminary results from replicas of the as-polished and etched surfaces of these samples were published.

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