scholarly journals On the Effect of Thomson and Initial Stress in a Thermo-Porous Elastic Solid under G-N Electromagnetic Theory

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 413 ◽  
Author(s):  
Elsayed Abd-Elaziz ◽  
Marin Marin ◽  
Mohamed Othman
Keyword(s):  
Initial Stress ◽  
Numerical Solutions ◽  
Elastic Solid ◽  
Electromagnetic Theory ◽  
Type Ii ◽  
Thomson Effect ◽  
Heat Condition ◽  
Mode Method ◽  
Condition Equation ◽  
Thomson Coefficient

The present work investigated the effect of Thomson and initial stress in a thermo-porous elastic solid under G-N electromagnetic theory. The Thomson coefficient affects the heat condition equation. A constant Thomson coefficient, instead of traditionally a constant Seebeck coefficient, is assumed. The charge density of the induced electric current is taken as a function of time. A normal mode method is proposed to analyze the problem and to obtain numerical solutions. The results that were obtained for all physical sizes are graphically illustrated and we offer a comparison between the type II G-N theory and the G-N theory of type III, both in the present case and in the absence of specific parameters, as initial stress, pores and the Thomson effect. Some particular cases are also discussed in the context of the problem. The results indicate that the effect of initial stress, Thomson coefficient effect, and magnetic field are very pronounced.

Buoyancy-driven crack propagation: the limit of large fracture toughness

2007 ◽  
Vol 580 ◽  
pp. 359-380 ◽  
Author(s):  
S. M. ROPER ◽  
J. R. LISTER
Keyword(s):  
Fracture Toughness ◽  
Pressure Gradient ◽  
Viscous Flow ◽  
Numerical Solutions ◽  
Elastic Solid ◽  
Propagation Rate ◽  
Fluid Viscosity ◽  
Viscous Effects ◽  
Vertical Propagation ◽  
Viscous Pressure

We study steady vertical propagation of a crack filled with buoyant viscous fluid through an elastic solid with large effective fracture toughness. For a crack fed by a constant flux Q, a non-dimensional fracture toughness K=Kc/(3μQm3/2)1/4 describes the relative magnitudes of resistance to fracture and resistance to viscous flow, where Kc is the dimensional fracture toughness, μ the fluid viscosity and m the elastic modulus. Even in the limit K ≫ 1, the rate of propagation is determined by viscous effects. In this limit the large fracture toughness requires the fluid behind the crack tip to form a large teardrop-shaped head of length O(K2/3) and width O(K4/3), which is fed by a much narrower tail. In the head, buoyancy is balanced by a hydrostatic pressure gradient with the viscous pressure gradient negligible except at the tip; in the tail, buoyancy is balanced by viscosity with elasticity also playing a role in a region within O(K2/3) of the head. A narrow matching region of length O(K−2/5) and width O(K−4/15), termed the neck, connects the head and the tail. Scalings and asymptotic solutions for the three regions are derived and compared with full numerical solutions for K ≤ 3600 by analysing the integro-differential equation that couples lubrication flow in the crack to the elastic pressure gradient. Time-dependent numerical solutions for buoyancy-driven propagation of a constant-volume crack show a quasi-steady head and neck structure with a propagation rate that decreases like t−2/3 due to the dynamics of viscous flow in the draining tail.

scholarly journals Causal cosmology with braneworld gravity including Gauss Bonnet coupling

2020 ◽  
Vol 35 (26) ◽  
pp. 2050216
Author(s):  
Partha Sarathi Debnath
Keyword(s):  
Numerical Solutions ◽  
Analytic Solutions ◽  
Causal Theory ◽  
Type Ii ◽  
Dissipative Effects ◽  
Exponential Expansion ◽  
Linear Field Equation ◽  
The Universe ◽  
Special Case ◽  
Linear Field

Causal cosmological evolutions in Randall Sundrum type II (RS) braneworld gravity with Gauss Bonnet coupling and dissipative effects are discussed here. Causal theory of dissipative effects are illustrated by Full Israel Stewart theory are implemented. We consider the numerical solutions of evolutions and analytic solutions as a special case for extremely non-linear field equation in Randall Sundrum type II braneworld gravity with Gauss Bonnet coupling. Cosmological models admitting Power law expansion, Exponential expansion and evolution in the vicinity of the stationary solution of the universe are investigated for Full Israel Stewart theory. Stability of equilibrium or fixed points related to the dynamics of evolution in Full Israel Stewart theory in Randall Sundrum type II braneworld gravity together with Gauss Bonnet coupling are disclosed here.

Simulation and Optimized Analysis of Channel for Injection Molding of Bottle Cap Based on Moldflow

2014 ◽  
Vol 889-890 ◽  
pp. 587-590
Author(s):  
Cong Zhang ◽  
Lei Lei Han ◽  
De Yang ◽  
Hui Min Zhang
Keyword(s):  
Injection Molding ◽  
Surface Quality ◽  
Simulation Optimization ◽  
Channel Number ◽  
Heat Condition ◽  
Quality Requirements ◽  
Cooling Circuit ◽  
Condition Equation ◽  
Model Scheme ◽  
Simulation Scheme

A simulation optimization of a two-cavity injection molding for the bottle cap was studied. It included the preprocessor of the model, scheme one which used a series recommended parameters from Moldflow software. Though the result could meet surface quality requirements, the mold structure was too complicated especially the channel. The deformation of different factors were analyzed and uneven cooling had little effect on the deformation. And some relative heat condition equation were used to calculate the channel number. Therefore the optimized scheme two was put forward. According to the cooling circuit and deformation factors, the channel number was greatly reduced. After the simulation, scheme two could also meet surface quality requirements. At the same time, the mold structure can get simplified.

Effect of Thermal Conductivity of the Soil Cover on the Air Temperature Dynamics under Natural Conditions and at Anthropogenic Loads

2012 ◽  
Vol 260-261 ◽  
pp. 852-855
Author(s):  
E.E. Kholoden ◽  
O.M. Morina ◽  
S.A. Lobanov
Keyword(s):  
Thermal Conductivity ◽  
Air Temperature ◽  
Soil Cover ◽  
Linear Trend ◽  
Russian Far East ◽  
Far East ◽  
Temperature Fields ◽  
Heat Condition ◽  
Condition Equation ◽  
Natural Mechanism

By the example of the southern Russian Far East territory, it was stated that a sign of the linear trend of the long-term air temperature variations in the warm and cold periods of the year depended essentially on the soil thermal conductivity. It was shown that the mechanism of the soil temperature fields’ formation was controlled by the Fourier heat condition equation. In this case, the modern anthropogenic loads on the soil cover can only slightly enhance or weaken the natural mechanism of forming the temperature fields of soil and air.

Effect of rotation on micropolar generalized thermoelasticity with two temperatures using a dual-phase lag model

2014 ◽  
Vol 92 (2) ◽  
pp. 149-158 ◽  
Author(s):  
Mohamed I.A. Othman ◽  
W.M. Hasona ◽  
Elsayed M. Abd-Elaziz
Keyword(s):  
Numerical Solutions ◽  
Generalized Thermoelasticity ◽  
Thermodynamic Temperature ◽  
Phase Lag ◽  
Dual Phase ◽  
Conductive Temperature ◽  
Mode Method ◽  
Lag Model ◽  
Two Temperatures ◽  
Physical Quantities

In the present paper, we introduce the dual-phase lag theory to study the effect of the rotation on a two-dimensional problem of micropolar thermoelastic isotropic medium with two temperatures. A normal mode method is proposed to analyze the problem and obtain numerical solutions for the displacement, the conductive temperature, the thermodynamic temperature, the microrotation, and the stresses. The results of the physical quantities have been obtained numerically and illustrated graphically. The results show the effect of phase lag of the heat flux τq, a phase lag of temperature gradient τθ and two-temperature parameter on all the physical quantities.

Contact Stresses Between an Elastic Cylinder and a Layered Elastic Solid

1974 ◽  
Vol 96 (2) ◽  
pp. 250-257 ◽  
Author(s):  
P. K. Gupta ◽  
J. A. Walowit
Keyword(s):  
Integral Equation ◽  
Layer Thickness ◽  
Contact Pressure ◽  
Contact Zone ◽  
Numerical Solutions ◽  
Elastic Solid ◽  
Elastic Cylinder ◽  
Elastic Solids ◽  
Actual Contact ◽  
Wide Range

The generalized plane strain problem of the contact of layered elastic solids is reduced to an integral equation using Green’s function approach. Approximate numerical solutions are obtained by replacing the integral equation by a matrix inversion when the trapezoidal rule is used to represent the integral. Results for determining the actual contact pressure at the center of the contact zone and size of contact zone for a wide range of layer thicknesses are presented for two most practical cases, (i) when the indenter is rigid, and (ii) when the indenter is elastic having a modulus of elasticity equal to that of the substrate of the indented body. When the layer is softer than the substrate it is found that the actual contact pressure distribution is very closely determined by a weighted sum of elliptic and parabolic functions. For a substrate softer than the layer the pressures substantially deviate from an elliptical or parabolic behavior, for the cases when the layer thickness is finite. The analysis checks with the Hertzian solution in the extreme cases when the layer thickness either tends to zero or approaches infinity.

I. On a relation between the coefficient of the Thomson effect and certain other physical properties of metals

1884 ◽  
Vol 37 (232-234) ◽  
pp. 25-28 ◽  
Keyword(s):  
Physical Properties ◽  
Specific Heat ◽  
Electrical Resistance ◽  
Specific Resistance ◽  
Close Relation ◽  
Specific Electrical Resistance ◽  
Definite Function ◽  
Thomson Effect ◽  
Physical Constants ◽  
Thomson Coefficient

The magnitude and direction of the Thomson effect depend upon a coefficient which is always the same for the same metal, but varies with different metals. Professor Everett, in his “Units and Physical Constants,” p. 151, gives a table based upon Tait’s thermoelectric diagram (“Trans. R. S. E.,” vol. xxvii, p. 125), in which the thermoelectric values of a number of metals, referred to lead as zero, are given in the form α + βt ,where β is a number which for a given metal is proportional to the tangent of the inclination of the line representing the metal in Tait’s diagram, and therefore to the coefficient of the Thomson effect. Since all the physical properties of a metal are to some extent affected by h.eat, it seemed probable that a connexion might be found to exist between certain of these properties and the Thomson effect. A short examination showed that, as a rule, the coefficient of the Thomson effect is positive in those metals which have a great specific electrical resistance and specific heat, and negative in those which are distinguished by a great coefficient of expansion. I therefore made several attempts to ascertain whether the Thomson coefficient might not be some definite function of the specific resistance, specific heat, and coefficient of expansion; and though I have not been perfectly successful, it appears from the subjoined table that there is a close relation between them.

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