scholarly journals A homogenization method for thermomechanical continua using extensive physical quantities

2012 ◽  
Vol 468 (2142) ◽  
pp. 1696-1715 ◽  
Author(s):  
Kranthi K. Mandadapu ◽  
Arkaprabha Sengupta ◽  
Panayiotis Papadopoulos
Keyword(s):  
Heat Flux ◽  
Continuum Mechanics ◽  
Equations Of Motion ◽  
Homogenization Method ◽  
Deformation Condition ◽  
Balance Laws ◽  
Macroscopic Stress ◽  
Stress Deformation ◽  
The One ◽  
Physical Quantities

This article proposes a continuum thermomechanical homogenization method inspired by the Irving–Kirkwood procedure relating the atomistic equations of motion to the balance laws of continuum mechanics. This method yields expressions for the macroscopic stress and heat flux in terms of microscopic kinematic and kinetic quantities. The resulting equation for macroscopic stress affords a rational comparison with the widely used Hill–Mandel stress-deformation condition, while the one for heat flux reduces, under certain assumptions, to a Hill–Mandel-like condition involving heat flux and the gradient of temperature.

Experimental Study on the Identification of the Saturation of a Porous Media through Thermal Analysis

2014 ◽  
Vol 611-612 ◽  
pp. 1576-1583
Author(s):  
Maxime Villière ◽  
Sébastien Guéroult ◽  
Vincent Sobotka ◽  
Nicolas Boyard ◽  
Joel Breard ◽  
...  
Keyword(s):  
Thermal Analysis ◽  
Heat Flux ◽  
Porous Medium ◽  
Thermophysical Properties ◽  
Saturated Porous Medium ◽  
Homogenization Method ◽  
Saturation Curve ◽  
Mechanisms Of Formation ◽  
Mechanical Performances ◽  
The One

Resin Transfer Molding (RTM) is among the most commonly used fabrication processes for producing high quality and complex composite structural parts. RTM process consists of placing a dry fibrous preform into a mold cavity. A liquid resin is subsequently injected into that cavity. The consolidation of the part is then obtained by crosslinking in case of a thermosetting resin or by crystallization in case of thermoplastic one. Voids can be created in the porous medium during the flow of the resin. Presence of residual voids in the composite part at the end of the filling drastically affect mechanical performances. Even if several authors have contributed to a better understanding and modeling of the mechanisms of formation and transport of voids during injection, few experimental approaches allowed a direct measurement of the saturation curve. The aim of this study is then to identify the saturation of a fibrous preform by a liquid through thermal analysis. To address this issue, an experimental bench that allows the injection of a fluid into a textile preform has been used. This apparatus combines the measurement of temperatures and wall heat flux densities at several locations. A simplified modeling of the filling front has been performed with FEM using Comsol Multiphysics™. The saturation curve is modeled using several geometric parameters. Saturation is taken into account through the evolution of thermophysical properties. Effective thermophysical properties of the dry and completely-saturated porous medium in transverse and longitudinal directions have been measured by several methods, and their results have been then cross-checked and compared with good accuracy. The evolution between these two states has been modeled. A particular attention has been paid for the modeling of the transverse thermal conductivity. This parameter has been modeled using a periodic homogenization method as a function of the micro- and macro-saturation. The saturation curve parameters are determined by minimizing the cost function defined as the square difference between the measured and computed heat flux. The obtained saturation curve is finally compared with the one measured by a conductometric sensor.

scholarly journals On the polar nature and invariance properties of a thermomechanical theory for continuum-on-continuum homogenization

2021 ◽  
pp. 108128652199432
Author(s):  
Kranthi K. Mandadapu ◽  
B. Emek Abali ◽  
Panayiotis Papadopoulos
Keyword(s):  
Heat Flux ◽  
Angular Momentum ◽  
Balance Laws ◽  
Polar Medium ◽  
Thermomechanical Theory ◽  
Form Invariance ◽  
Couple Stresses ◽  
Invariance Properties ◽  
Macroscopic Stress ◽  
The Continuum

This paper makes a rigorous case for considering the continuum derived by the homogenization of extensive quantities as a polar medium in which the balances of angular momentum and energy contain contributions due to body couples and couple stresses defined in terms of the underlying microscopic state. The paper also addresses the question of invariance of macroscopic stress and heat flux and form-invariance of the macroscopic balance laws.

Statistical Mechanics of Thermotransport of a Heavy Impurity in an Insulating Solid

1971 ◽  
Vol 26 (1) ◽  
pp. 10-17 ◽  
Author(s):  
A. R. Allnatt
Keyword(s):  
Heat Flux ◽  
Time Correlation ◽  
Three Dimensions ◽  
Time Correlation Functions ◽  
Single Vacancy ◽  
One Dimensional ◽  
Enthalpy Of Activation ◽  
Heavy Impurity ◽  
The One ◽  
Non Equilibrium

AbstractA kinetic equation is derived for the singlet distribution function for a heavy impurity in a lattice of lighter atoms in a temperature gradient. In the one dimensional case the equation can be solved to find formal expressions for the jump probability and hence the heat of transport, q*. for a single vacancy jump of the impurity, q* is the sum of the enthalpy of activation, a term involving only averaging in an equilibrium ensemble, and two non-equilibrium terms in­volving time correlation functions. The most important non-equilibrium term concerns the cor­relation between the force on the impurity and a microscopic heat flux. A plausible extension to three dimensions is suggested and the relation to earlier isothermal and non-isothermal theories is indicated

Fluid turbulence simulations of divertor heat load for ITER hybrid scenario using BOUT++

2021 ◽  
Author(s):  
Xueyun Wang ◽  
Xueqiao Xu ◽  
Philip B Snyder ◽  
Zeyu Li
Keyword(s):  
Heat Flux ◽  
Steady State ◽  
Energy Loss ◽  
Heat Load ◽  
Type I ◽  
Fluid Turbulence ◽  
Drift Model ◽  
Steady State Operation ◽  
Different Types ◽  
The One

Abstract The BOUT++ six-field turbulence code is used to simulate the ITER 11.5MA hybrid scenario and a brief comparison is made among ITER baseline, hybrid and steady-state operation (SSO) scenarios. Peeling-ballooning instabilities with different toroidal mode numbers dominate in different scenarios and consequently yield different types of ELMs. The energy loss fractions (ΔWped/Wped) caused by unmitigated ELMs in the baseline and hybrid scenarios are large (~2%) while the one in the SSO scenario is dramatically smaller (~1%), which are consistent with the features of type-I ELMs and grassy ELMs respectively. The intra ELM divertor heat flux width in the three scenarios given by the simulations is larger than the estimations for inter ELM phase based on Goldston’s heuristic drift model. The toroidal gap edge melting limit of tungsten monoblocks of divertor targets imposes constraints on ELM energy loss, giving that the ELM energy loss fraction should be smaller than 0.4%, 1.0%, and 1.2% for ITER baseline, hybrid and SSO scenarios, correspondingly. The simulation shows that only the SSO scenario with grassy ELMs may satisfy the constraint.

Indentation of a Transversely Isotropic Thermoporoelastic Half-Space by a Rigid Circular Cylindrical Punch

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Yilan Huang ◽  
Guozhan Xia ◽  
Weiqiu Chen ◽  
Xiangyu Li
Keyword(s):  
Half Space ◽  
Original Problem ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
The Finite Element Method ◽  
Thermal Fields ◽  
Cylindrical Punch ◽  
The One ◽  
Physical Quantities ◽  
Potential Theory Method

Exact solutions to the three-dimensional (3D) contact problem of a rigid flat-ended circular cylindrical indenter punching onto a transversely isotropic thermoporoelastic half-space are presented. The couplings among the elastic, hydrostatic, and thermal fields are considered, and two different sets of boundary conditions are formulated for two different cases. We use a concise general solution to represent all the field variables in terms of potential functions and transform the original problem to the one that is mathematically expressed by integral (or integro-differential) equations. The potential theory method is extended and applied to exactly solve these integral equations. As a consequence, all the physical quantities of the coupling fields are derived analytically. To validate the analytical solutions, we also simulate the contact behavior by using the finite element method (FEM). An excellent agreement between the analytical predictions and the numerical simulations is obtained. Further attention is also paid to the discussion on the obtained results. The present solutions can be used as a theoretical reference when practically applying microscale image formation techniques such as thermal scanning probe microscopy (SPM) and electrochemical strain microscopy (ESM).

scholarly journals Thermal-hydraulic behavior of physical quantities at critical velocities in a nuclear research reactor core channel using plate type fuel

2012 ◽  
Vol 27 (3) ◽  
pp. 229-238
Author(s):  
Ali Sidi ◽  
Zaki Boudali ◽  
Rachid Salhi
Keyword(s):  
Heat Flux ◽  
Critical Velocity ◽  
Nuclear Reactor ◽  
Reactor Core ◽  
Thermal Characteristics ◽  
Nuclear Research ◽  
Coolant Fluid ◽  
Critical Velocities ◽  
Set Up ◽  
Physical Quantities

The thermal-hydraulic study presented here relates to a channel of a nuclear reactor core. This channel is defined as being the space between two fuel plates where a coolant fluid flows. The flow velocity of this coolant should not generate vibrations in fuel plates. The aim of this study is to know the distribution of the temperature in the fuel plates, in the cladding and in the coolant fluid at the critical velocities of Miller, of Wambsganss, and of Cekirge and Ural. The velocity expressions given by these authors are function of the geometry of the fuel plate, the mechanical characteristics of the fuel plate?s material and the thermal characteristics of the coolant fluid. The thermal-hydraulic study is made under steady-state; the equation set-up of the thermal problem is made according to El Wakil and to Delhaye. Once the equation set-up is validated, the three critical velocities are calculated and then used in the calculations of the different temperature profiles. The average heat flux and the critical heat flux are evaluated for each critical velocity and their ratio reported. The recommended critical velocity to be used in nuclear channel calculations is that of Wambsganss. The mathematical model used is more precise and all the physical quantities, when using this critical velocity, stay in safe margins.

THE VILKOVISKY EFFECTIVE ACTION IN THE EVEN-DIMENSIONAL QUANTUM GRAVITY

1989 ◽  
Vol 04 (07) ◽  
pp. 633-644 ◽  
Author(s):  
I. L. BUCHBINDER ◽  
E. N. KIRILLOVA ◽  
S. D. ODINTSOV
Keyword(s):  
Numerical Calculation ◽  
Effective Potential ◽  
Effective Action ◽  
Equations Of Motion ◽  
Flat Space ◽  
Einstein Gravity ◽  
Quantum Field ◽  
Dimensional Torus ◽  
Spontaneous Compactification ◽  
The One

The one-loop Vilkovisky effective potential which is not dependent on a gauge and a parametrization of quantum field, is investigated. We have considered Einstein gravity on a background manifold of (flat space) × (d−4- sphere) or × (d−4- dimensional torus ), d is even, and of R3 × (1- sphere ), where R3 is flat space. The numerical calculation for the cases R4 × Td−4 (d = 6,8,10) and R3 × S1 is done. The solution to the one-loop corrected equations of motion is found, although the spontaneous compactification is not stable in these cases.

Flow between Stretchable Rotating Disks in an Anisotropic Porous Medium with Cattaneo Christov Heat Flux

2019 ◽  
Vol 393 ◽  
pp. 138-148
Author(s):  
K. Gowthami ◽  
P. Hari Prasad ◽  
B. Mallikarjuna ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Thermal Relaxation ◽  
Relaxation Parameter ◽  
Transport Processes ◽  
Rotation Parameter ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Anisotropic Porous Medium ◽  
Physical Quantities

A study on fully developed fluid flow between 2two stretchable disks in a 1porous medium is presented. The porous medium is assumed to be an anisotropic porous medium and described using Darcy’s model. Moreover Cattaneo - Christov heat flux 1model is used for heat transport processes. Numerical method 1is used to compute the solutions of non-dimensionalized equations and obtained results are discussed with the aid of graphs and table values on physical quantities (fluid velocity, fluid temperature, skin frication coefficients and Nusselt numbers) for various values of physical parameters, Darcy’ number in different directions, stretchable disk parameters, rotation parameter and thermal relaxation parameter. Increasing stretchable disks parameter reports opposite behavior on physical quantities at different disks. Positive and negative values of rotation parameter impact on physical quantities are presented and discussed. As increase in thermal relaxation parameter fluid temperature transfers in different directions between disks and Nusselt number values are enhanced at both disks.

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