Three-Dimensional Interaction in Thermoelastic Medium with Two Relaxation Times Due to Thermal Source

2015 ◽  
Vol 03 (03n04) ◽  
pp. 1550003 ◽  
Author(s):  
Ibrahim A. Abbas ◽  
Rajneesh Kumar ◽  
A. Lahiri
Keyword(s):  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Three Dimensional ◽  
Specific Model ◽  
Mode Analysis ◽  
Thermal Source ◽  
Thermoelastic Medium ◽  
Coupled Equations ◽  
Dimensional Interaction ◽  
Element Technique

The present study is concerned with the interaction in thermoelastic medium with two relaxation times due to thermal source. The finite element technique under normal mode analysis is used to solve the resulting nondimensional coupled equations. As an application of the approach, the particular type of thermal source has been considered. The components of displacement, stress and temperature change are computed numerically. The numerical stimulated results are depicted graphically for a specific model. The effect of rotation has been shown on the resulting quantities. Effect of relaxation times is shown on the resulting quantities by a comparison between the absence and presence of relaxation times.

Kelvin-Helmholtz and Rayleigh-Taylor Instability of Two Superimposed Magnetized Fluids with Suspended Dust Particles

2009 ◽  
Vol 64 (7-8) ◽  
pp. 455-466 ◽  
Author(s):  
Ramprasad Prajapati ◽  
Raj Kamal Sanghvi ◽  
Rajendra Kumar Chhajlani ◽  
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Particle Density ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Mhd Equations ◽  
Mode Analysis ◽  
Dust Particles ◽  
Suspended Dust ◽  
The Magnetic Field

AbstractThe effect of a magnetic field and suspended dust particles on both the Kelvin-Helmholtz (K-H) and the Rayleigh-Taylor (R-T) instability of two superimposed streaming magnetized plasmas is investigated. The magnetized fluids are assumed to be incompressible and flowing on top of each other. The usual magnetohydrodynamic (MHD) equations are considered with suspended dust particles. The basic equations of the problem are linearized and the dispersion relation is obtained using normal mode analysis by applying the appropriate boundary conditions. The general dispersion relation is found to be modified due to the presence of the suspended dust particles and of the magnetic field. The effect of the magnetic field appears in the dispersion relation if three-dimensional perturbations of the system are considered. The general conditions of the K-H instability as well as the R-T instability are derived for the considered medium. The stability of the system for both cases is discussed by applying the Routh-Hurwitz criterion. Numerical analysis is performed to show the effect of various parameters on the growth rates of the K-H and R-T instabilities. Three different cases of the present configurations are considered and the conditions of instability are obtained. It is found that the conditions for the K-H and R-T instabilities depend on the magnetic field, on the suspended dust particles and on the relaxation frequency of the particles. The magnetic field and particle density have stabilizing influence, while the density difference between the fluids has a destabilizing influence on the growth rate of the K-H and R-T configurations.

Mode-Wise Phonon Properties of Bismuth Telluride

2012 ◽  
Author(s):  
Yaguo Wang ◽  
Xianfan Xu
Keyword(s):  
Bismuth Telluride ◽  
Thermal Transport ◽  
Phonon Dispersion ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Mode Analysis ◽  
Phonon Modes ◽  
Time Resolved ◽  
Transport Control ◽  
Phonon Properties

Thermal transport properties and thermal transport control are important for many materials, for example, low thermal conductivity is desirable for thermoelectric materials. Knowledge of mode-wise phonon properties is crucial to identify dominant phonon modes for thermal transport and design effective phonon barriers for thermal transport control. In this paper, we adopt the normal mode analysis to investigate spectral phonon properties, and to calculate phonon dispersion relations and phonon relaxation times in bismuth telluride. Our results agree with previously reported data for long-wavelength longitudinal acoustic phonon and A1g optical phonon obtained from ultrafast time-resolved measurements. By combing the frequency dependent anharmonic phonon group velocities and lifetime, mode-wise thermal conductivities are predicted to reveal the contributions of heat carriers with different polarizations and wavelength.

scholarly journals Two-Dimensional Deformation in a Thermoelastic Solid with Microtemperatures Subjected to an Internal Heat Source

2018 ◽  
Vol 23 (1) ◽  
pp. 5-21 ◽  
Author(s):  
P. Ailawalia ◽  
S. Budhiraja ◽  
J. Singh
Keyword(s):  
Heat Source ◽  
Half Space ◽  
Normal Mode Analysis ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Thermoelastic Medium ◽  
Generalized Thermoelastic ◽  
Thermoelastic Solid

AbstractThe purpose of this paper is to study the two dimensional deformation in a generalized thermoelastic medium with microtemperatures having an internal heat source subjected to a mechanical force. The force is acting along the interface of generalized thermoelastic half space and generalized thermoelastic half space with microtemperatures having an internal heat source. The normal mode analysis has been applied to obtain the exact expressions for the considered variables. The effect of internal heat source and microtemperatures on the above components has been depicted graphically.

Three-Dimensional Thermoelastic Problem Under Two-Temperature Theory

2017 ◽  
Vol 14 (03) ◽  
pp. 1750030 ◽  
Author(s):  
Abhik Sur ◽  
M. Kanoria
Keyword(s):  
Thermal Loading ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Thermodynamic Temperature ◽  
Mode Analysis ◽  
Phase Lag ◽  
Field Equations ◽  
Conductive Temperature ◽  
Lag Model ◽  
Two Temperature

The present paper deals with the problem of thermoelastic interactions in a homogeneous, isotropic three-dimensional medium whose surface suffers a time dependent thermal loading. The problem is treated on the basis of three-phase-lag model and dual-phase-lag model with two temperatures. The medium is assumed to be unstressed initially and has uniform temperature. Normal mode analysis technique is employed onto the non-dimensional field equations to derive the exact expressions for displacement component, conductive temperature, thermodynamic temperature, stress and strain. The problem is illustrated by computing the numerical values of the field variables for a copper material. Finally, all the physical fields are represented graphically to analyze the difference between the two models. The effect of the two temperature parameter is also discussed.

A Study on the Generalized Thermoelastic Problem for an Anisotropic Medium

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Debkumar Ghosh ◽  
Abhijit Lahiri
Keyword(s):  
Stress Component ◽  
Normal Mode Analysis ◽  
Thermal Strain ◽  
Three Dimensional ◽  
Mode Analysis ◽  
Governing Equations ◽  
Eigenvalue Approach ◽  
Matrix Differential ◽  
Vector Matrix ◽  
Component Temperature

A vector–matrix differential equation is formulated using normal mode analysis from the governing equations of a three-dimensional anisotropic half space in presence of heat source and gravity. The corresponding solution is obtained with the help of eigenvalue approach. Numerical computations for displacement, thermal strain and stress component, temperature distribution are evaluated and presented graphically.

Normal Mode Analysis of Three-Dimensional Propagation Over a Small-Slope Cosine Shaped Hill

2015 ◽  
Vol 23 (03) ◽  
pp. 1550005 ◽  
Author(s):  
Megan S. Ballard ◽  
Benjamin M. Goldsberry ◽  
Marcia J. Isakson
Keyword(s):  
Parabolic Equation ◽  
Normal Mode ◽  
Hybrid Model ◽  
Mode Coupling ◽  
Transmission Loss ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Mode Analysis ◽  
The Hill ◽  
Horizontal Refraction

Three-dimensional propagation over an infinitely long cosine shaped hill is examined using an approximate normal mode/parabolic equation hybrid model that includes mode coupling in the out-going direction. The slope of the hill is relatively shallow, but it is significant enough to produce both mode-coupling and horizontal refraction effects. In the first part of the paper, the modeling approach is described, and the solution is compared to results obtained with a finite element method to evaluate the accuracy of the solution in light of assumptions made in formulating the model. Then the calculated transmission loss is interpreted in terms of a modal decomposition of the field, and the solution from the hybrid model is compared to adiabatic and N × 2D solutions to assess the relative importance of horizontal refraction and mode-coupling effects. An analysis using a horizontal ray trace is presented to explain differences in the modal interference pattern observed between the 3D and N × 2D solutions. The detailed discussion provides a thorough explanation of the observed 3D propagation effects and demonstrates the usefulness of the approximate normal mode/parabolic equation hybrid model as a tool to understand measured transmission loss in complex environments.

Effect of Rotation to a Half-Sapce in Magneto-Thermoelasticity with Thermal Relaxations

2007 ◽  
Vol 353-358 ◽  
pp. 3018-3021
Author(s):  
Ying Pan ◽  
Zi Hou Zhang ◽  
Li Hou Liu
Keyword(s):  
Magnetic Field ◽  
Half Space ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Generalized Thermoelasticity ◽  
Mode Analysis ◽  
Two Dimensional ◽  
Induced Magnetic Field ◽  
Coupled Problem ◽  
Analytical Expressions

Based on Green and Lindsay’s generalized thermoelasticity theory with two relaxation times, a two-dimensional coupled problem in electromagneto-thermoelasticity for a rotating half-space solid whose surface is subjected to a heat is studied in this paper. The normal mode analysis is used to obtain the analytical expressions for the considered variables. It can be found electromagneto-thermoelastic coupled effect in the medium, and it also can be found that rotation acts to significantly decrease the magnitude of the real part of displacement and stress and insignificantly affect the magnitude of temperature and induced magnetic field.

Non-modal growth of perturbations in density-driven convection in porous media

2008 ◽  
Vol 609 ◽  
pp. 285-303 ◽  
Author(s):  
SAIKIRAN RAPAKA ◽  
SHIYI CHEN ◽  
RAJESH J. PAWAR ◽  
PHILIP H. STAUFFER ◽  
DONGXIAO ZHANG
Keyword(s):  
Stability Theory ◽  
Initial Conditions ◽  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Linear Stability Theory ◽  
Mode Analysis ◽  
Geologic Sequestration ◽  
Onset Of Convection ◽  
Static Approximation ◽  
Modal Theory

In the context of geologic sequestration of carbon dioxide in saline aquifers, much interest has been focused on the process of density-driven convection resulting from dissolution of CO2 in brine in the underlying medium. Recent investigations have studied the time and length scales characteristic of the onset of convection based on the framework of linear stability theory. It is well known that the non-autonomous nature of the resulting matrix does not allow a normal mode analysis and previous researchers have either used a quasi-static approximation or solved the initial-value problem with arbitrary initial conditions. In this manuscript, we describe and use the recently developed non-modal stability theory to compute maximum amplifications possible, optimized over all possible initial perturbations. Non-modal stability theory also provides us with the structure of the most-amplified (or optimal) perturbations. We also present the details of three-dimensional spectral calculations of the governing equations. The results of the amplifications predicted by non-modal theory compare well to those obtained from the spectral calculations.

Perturbed normal-mode analysis of induction times, relaxation times, and reaction rates in unimolecular reactions

1979 ◽  
Vol 57 (13) ◽  
pp. 1723-1730 ◽  
Author(s):  
Andrew W. Yau ◽  
Huw O. Pritchard
Keyword(s):  
Normal Mode ◽  
Transition Probabilities ◽  
Normal Mode Analysis ◽  
Relaxation Times ◽  
Normal Modes ◽  
Reaction Rates ◽  
Mode Analysis ◽  
Decomposition Reactions ◽  
Induction Times ◽  
Network Relationship

A perturbed normal-mode analysis is presented of the induction (or incubation) time, the relaxation rate, and the reaction rate of a diluted unimolecular system. At high temperature, the unimolecular rate approaches the Lindemann behaviour and the low-pressure rate is related to the normal modes of relaxation of the reactive states in a simple manner. In a step-ladder model system, the network relationship between the normal modes and the microscopic transition probabilities leads to explicit theoretical correlations between the respective experimental quantities. Illustrative calculations of such correlations are presented for the decomposition reactions of N2O and CO2 diluted in Ar at shock wave temperatures, and are compared with experiment.

Three-Dimensional Analysis of a Thermo-Viscoelastic Half-Space due to Thermal Shock in Temperature-Rate-Dependent Thermoelasticity

2016 ◽  
Vol 32 (4) ◽  
pp. 401-411 ◽  
Author(s):  
S. Kumar ◽  
J. S. Sikka ◽  
S. Choudhary
Keyword(s):  
Normal Mode Analysis ◽  
Three Dimensional ◽  
Displacement Component ◽  
Mode Analysis ◽  
Field Equations ◽  
Finite Speed Of Propagation ◽  
Rate Dependent ◽  
Coupled Field Equations ◽  
Temperature Rate ◽  
Thermoelastic Waves

AbstractThe present paper is aimed at studying the effects of viscosity and time on the propagation of thermoelastic waves in a homogeneous and isotropic three-dimensional medium whose surface is acted upon by a thermal load under the purview of temperature-rate-dependent thermoelasticity. The normal mode analysis technique has been employed to solve the resulting non-dimensional coupled field equations and hence the exact expressions for displacement component, stress, temperature field and strain are obtained. The problem is further illustrated by computing the numerical values of the field variables for a copper- like material and depicting them graphically. Numerical results predict finite speed of propagation for thermoelastic waves.

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