scholarly journals Finite Element Analysis of Thermal-Diffusions Problem for Unbounded Elastic Medium Containing Spherical Cavity under DPL Model

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2782
Author(s):  
Aatef D. Hobiny ◽  
Ibrahim A. Abbas
Keyword(s):  
Finite Element ◽  
Chemical Potential ◽  
Phase Lag ◽  
Dual Phase ◽  
Element Analysis ◽  
Spherical Cavities ◽  
Lag Model ◽  
Phase Lags ◽  
Unbounded Elastic Medium ◽  
Element Technique

In this work, the thermo-diffusions interaction in an unbounded material with spherical cavities in the context dual phase lag model is investigated. The finite element technique has been used to solve the problem. The bounding surface of the inner hole is loaded thermally by external heat flux and is traction-free. The delay times caused in the microstructural interactions, the requirement for thermal physics to take account of hyperbolic effects within the medium, and the phase lags of chemical potential and diffusing mass flux vector are interpreted. A comparison is made in the case of the presence and the absence of mass diffusions between coupled, Lord-Shulman and dual phase lag theories. The numerical results for the displacement, concentration, temperature, chemical potential and stress are presented numerically and graphically.

A problem of thick circular plate in modified couple stress thermoelastic diffusion with phase-lags

2016 ◽  
Vol 12 (3) ◽  
pp. 478-494
Author(s):  
Rajneesh Kumar ◽  
Shaloo Devi ◽  
Veena Sharma
Keyword(s):  
Temperature Change ◽  
Couple Stress ◽  
Chemical Potential ◽  
Phase Lag ◽  
Dual Phase ◽  
Field Equations ◽  
Thermoelastic Diffusion ◽  
Content Type ◽  
Lag Model ◽  
Modified Couple Stress

Purpose The purpose of this paper is to investigate the two-dimensional axisymmetric problem in a homogeneous, isotropic modified couple stress thermoelastic diffusion (TD) medium in the context of dual-phase-lag model. Design/methodology/approach The Laplace and Hankel transforms have been applied to find the general solution to the field equations. The components of displacement, stresses, temperature change and chemical potential are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Findings The components of normal stress, tangential stress, tangential couple stress, temperature change and chemical potential are obtained numerically and depicted graphically to see the effect of dual-phase-lag diffusion (DLD), dual-phase-lag heat transfer (DLT) and TD models in the absence and presence of couple stress parameter. Originality/value Comparisons are made in the absence and presence of couple stress DLD, DLT and TD models.

The Reflection of Magneto-Thermoelastic P and SV Waves at a Solid Half Space Using Dual-Phase-Lag Model

2011 ◽  
Vol 3 (6) ◽  
pp. 745-758
Author(s):  
Ahmed E. Abouelregal
Keyword(s):  
Reflection Coefficients ◽  
Transfer Model ◽  
Phase Lag ◽  
Dual Phase ◽  
Angle Of Incidence ◽  
Lag Model ◽  
Phase Lags ◽  
Energy Ratios ◽  
Thermoelastic Solid ◽  
P And Sv Waves

AbstractThe dual-phase-lag heat transfer model is employed to study the reflection phenomena of P and SV waves from a surface of a semi-infinite magneto-thermoelastic solid. The ratios of reflection coefficients to that of incident coefficients are obtained for P- and SV-wave cases. The results for partition of the energy for various values of the angle of incidence are computed numerically under the stress-free and rigidly fixed thermally insulated boundaries. The reflection coefficients are depending on the angle of incidence, magnetic field, phase lags and other material constants. Results show that the sum of energy ratios is unity at the interface. The results are discussed and depicted graphically.

Effects of thermal and diffusion phase-lags in a plate with axisymmetric heat supply

2016 ◽  
Vol 12 (2) ◽  
pp. 275-290 ◽  
Author(s):  
Rajneesh Kumar ◽  
Nidhi Sharma ◽  
Parveen Lata
Keyword(s):  
Heat Supply ◽  
Mass Concentration ◽  
Chemical Potential ◽  
Phase Lag ◽  
Dual Phase ◽  
Content Type ◽  
Thermal Phase ◽  
Diffusion Phase ◽  
Phase Lags ◽  
And Diffusion

Purpose – The purpose of this paper is to depict the effect of time and thermal and diffusion phase-lags due to axisymmetric heat supply in a ring. The problem is discussed within the context of dual-phase-lag heat transfer and dual-phase-lag diffusion models. The upper and lower surfaces of the ring are traction free and subjected to an axisymmetric heat supply. Design/methodology/approach – The solution is found by using Laplace and Hankel transform technique and a direct approach without the use of potential functions. The analytical expressions of displacements, stresses and chemical potential, temperature and mass concentration are computed in transformed domain. Numerical inversion technique has been applied to obtain the results in the physical domain. Numerically simulated results are depicted graphically. The effect of time and diffusion and thermal phase-lags are shown on the various components. Some particular cases of result are also deduced from the present investigation. Findings – It is observed that change in time changes the behaviour of deformations of the various components of stresses, displacements, chemical potential function, temperature change and mass concentration. The authors find that for t=0.2, trends are oscillatory in all the cases whereas for t=0.1, trends are quite different. A sound impact of diffusion and thermal phase-lags on the various quantities is observed. A lot of difference in the trends of single phase lag and dual phase lag is observed. The use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient. Originality/value – This problem is totally new because dual phase lag is applied in heat conduction and diffusion equation while considering the problem of plate in axisymmetric heat supply.

A Two Dimensional Axisymmetric Thermoelastic Diffusion Problem of Micropolar Porous Circular Plate with Dual Phase Lag Model

2020 ◽  
Vol 22 (4) ◽  
pp. 1389-1406
Author(s):  
Rajneesh Kumar ◽  
Aseem Miglani ◽  
Rekha Rani
Keyword(s):  
Circular Plate ◽  
Chemical Potential ◽  
Volume Fraction ◽  
Diffusion Problem ◽  
Phase Lag ◽  
Dual Phase ◽  
Two Dimensional ◽  
Thermoelastic Diffusion ◽  
Field Temperature ◽  
Lag Model

AbstractIn the present work, we consider a two dimensional axisymmetric problem of micropolar porous circular plate with thermal and chemical potential sources in the context of the theory of dual phase lag generalized thermoelastic diffusion. The potential functions are used to analyze the problem. The Laplace and Hankel transforms techniques are used to find the expressions of displacements, microrotation, volume fraction field, temperature distribution, concentration and stresses in the transformed domain. The inversion of transforms based on Fourier expansion techniques is applied to obtain the results in the physical domain. The numerical results for resulting quantities are obtained and depicted graphically. Effect of porosity, LS theory and phase lag are presented on the resulting quantities. Some particular cases are also deduced.

The initial stress effect on a thermoelastic micro-elongated solid under the dual-phase-lag model

2021 ◽  
Vol 127 (9) ◽  
Author(s):  
Mohamed I. A. Othman ◽  
Sarhan Y. Atwa ◽  
Ebtesam E. M. Eraki ◽  
Mohamed F. Ismail
Keyword(s):  
Initial Stress ◽  
Stress Effect ◽  
Phase Lag ◽  
Dual Phase ◽  
Lag Model

Thermoelastic Bresse system with dual-phase-lag model

2021 ◽  
Vol 72 (3) ◽  
Author(s):  
Noelia Bazarra ◽  
Ivana Bochicchio ◽  
José R. Fernández ◽  
Maria Grazia Naso
Keyword(s):  
Phase Lag ◽  
Dual Phase ◽  
Bresse System ◽  
Lag Model

Axisymmetric Finite-Element Analysis for Interface Migration-Controlled Shape Instabilities of Plate-Like Double-Crystal Grains

2012 ◽  
Vol 460 ◽  
pp. 230-235
Author(s):  
Pei Zhen Huang ◽  
Zhou Zhou Zhang ◽  
Jian Wei Guo ◽  
Jun Sun
Keyword(s):  
Finite Element ◽  
Grain Boundary ◽  
Chemical Potential ◽  
Boundary Energy ◽  
Element Analysis ◽  
Interface Motion ◽  
Double Crystal ◽  
Energy Principle ◽  
Chemical Potential Difference ◽  
Interface Migration

An axisymmetric finite-element method is developed to predict the evolution behavior of microstructures by interface migration. The formulation of the method is conducted on the basis of the energy principle during the interface motion. The computations extend earlier models by accounting in detail for the effects of grain-boundary energy, surface energy and chemical potential difference. The eventual shape of the plate-like double-crystal grain depends on both the initial β and the thermal grooving angle Ψ. For a given β, a critical Ψcexists. When Ψ>Ψc, the eventual shape is one made of two sphere segments with a thermal groove. When Ψ≤Ψc, grain splitting along the grain boundary occurs, and the splitting segments evolve into two spheres, respectively. Both the spheroidization time and the splitting time increase with Ψ and β increasing. The volume shrinkage rate decreases with increasing Ψ.

Determination of Stress Concentration Around an Oblique Hole by a Finite-Element Technique

1983 ◽  
Vol 105 (2) ◽  
pp. 206-212 ◽  
Author(s):  
Hua-Ping Li ◽  
F. Ellyin
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Maximum Stress ◽  
Plate Thickness ◽  
Two Dimensional ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Parametric Studies ◽  
Element Technique

A plate weakened by an oblique penetration of a circular cylindrical hole has been investigated. The stress concentration around the hole is determined by a finite-element method. The results are compared with experimental data and other analytical works. Parametric studies of effects of angle of inclination, plate thickness, and width are performed. The maximum stress concentration factor (SCF) obtained from the finite-element analysis is higher than experimental results, and this deviation increases with the increase of angle of skewness. The major reason for this difference is attributed to the shear-action between layers parallel to the plate surface which cannot be directly included in the two-dimensional elements. An empirical formula is derived which accounts for the shear-action and renders the finite-element predictions in line with experimentally observed data.

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