Balance equations and the problem of constitutive relations in varied dimensions curvilinear media

2007 ◽  
pp. 69-79
Author(s):  
Roger Prud’homme
Keyword(s):  
Constitutive Relations ◽  
Balance Equations

MATERIAL ELEMENT MODEL AND THE GEOMETRY OF THE ENTROPY FORM

2010 ◽  
Vol 07 (06) ◽  
pp. 1021-1042 ◽  
Author(s):  
M. DOLFIN ◽  
M. FRANCAVIGLIA ◽  
S. PRESTON ◽  
L. RESTUCCIA
Keyword(s):  
Phase Space ◽  
Constitutive Relations ◽  
Element Model ◽  
Continuum Thermodynamics ◽  
Balance Equations ◽  
Ferroelectric Crystal ◽  
Material Element ◽  
Closure Conditions ◽  
The Continuum ◽  
Crystal Element

In this work we analyze and compare the model of the material (elastic) element and the entropy form developed by Coleman and Owen with that one obtained by localizing the balance equations of the continuum thermodynamics. This comparison allows one to determine the relation between the entropy function S of Coleman–Owen and that one imported from the continuum thermodynamics. We introduce the Extended Thermodynamical Phase Space (ETPS) [Formula: see text] and realize the energy and entropy balance expressions as 1-forms in this space. This allows us to realizes I and II laws of thermodynamics as conditions on these forms. We study the integrability (closure) conditions of the entropy form for the model of thermoelastic element and for the deformable ferroelectric crystal element. In both cases closure conditions are used to rewrite the dynamical system of the model in term of the entropy form potential and to determine the constitutive relations among the dynamical variables of the model. In a related study (to be published) these results will be used for the formulation of the dynamical model of a material element in the contact thermodynamical phase space of Caratheodory and Hermann similar to that of homogeneous thermodynamics.

Grain Size Reduction in Granular Flows of Spheres: The Effects of Critical Impact Energy

1992 ◽  
Vol 59 (2S) ◽  
pp. S17-S22 ◽  
Author(s):  
M. W. Richman ◽  
A. A. Oyediran
Keyword(s):  
Impact Energy ◽  
Constitutive Relations ◽  
Granular Flows ◽  
Binary Collision ◽  
Granular Temperature ◽  
Balance Equations ◽  
Shear Rates ◽  
Time Variations ◽  
Granular Shear ◽  
Induced Stresses

We extend methods employed to derive recent kinetic theories for rapid noncomminuting granular flows, to homogeneous flows in which a fraction of the repeated collisions produce tiny fractures on the particles’ peripheries and gradually reduce their effective diameters. The theory consists of balance equations for mass, momentum, and energy, as well as constitutive relations for the pressure tensor and collisional rates of mass and energy lost. We improve upon the work of Richman and Chou (1989) by incorporating into the constitutive theory the critical impact energy below which no mass loss occurs in a binary collision. The theory is applied to granular shear flows and, for fixed shear rates, predicts the time variations of the solid fraction, granular temperature, and induced stresses, as well as their extreme sensitivities to small changes in the critical impact energy.

Effects of Ambipolar Diffusion on Prominence Thread Models

1994 ◽  
Vol 144 ◽  
pp. 315-321 ◽  
Author(s):  
M. G. Rovira ◽  
J. M. Fontenla ◽  
J.-C. Vial ◽  
P. Gouttebroze
Keyword(s):  
Energy Balance ◽  
Transition Region ◽  
Ambipolar Diffusion ◽  
Line Profiles ◽  
Balance Equations ◽  
Model Calculations ◽  
Partial Frequency ◽  
Frequency Redistribution ◽  
Partial Frequency Redistribution ◽  
Theoretical Structure

AbstractWe have improved previous model calculations of the prominence-corona transition region including the effect of the ambipolar diffusion in the statistical equilibrium and energy balance equations. We show its influence on the different parameters that characterize the resulting prominence theoretical structure. We take into account the effect of the partial frequency redistribution (PRD) in the line profiles and total intensities calculations.

Parametric Study of Photovoltaic Thermal Solar Collector Using An Improved Parallel Flow

2020 ◽  
Vol 2 (1) ◽  
pp. 19-24
Author(s):  
Sakhr Mohammed Sultan ◽  
Chih Ping Tso ◽  
Ervina Efzan Mohd Noor ◽  
Fadhel Mustafa Ibrahim ◽  
Saqaff Ahmed Alkaff
Keyword(s):  
Thermal Conductivity ◽  
Energy Balance ◽  
Parametric Study ◽  
Solar Collector ◽  
Parallel Flow ◽  
Operating Conditions ◽  
Balance Equations ◽  
Conductivity Type ◽  
Pv Module ◽  
Sunny Weather

Photovoltaic Thermal Solar Collector (PVT) is a hybrid technology used to produce electricity and heat simultaneously. Current enhancements in PVT are to increase the electrical and thermal efficiencies. Many PVT factors such as type of absorber, thermal conductivity, type of PV module and operating conditions are important parameters that can control the PVT performance. In this paper, an analytical model, using energy balance equations, is studied for PVT with an improved parallel flow absorber. The performance is calculated for a typical sunny weather in Malaysia. It was found that the maximum electrical and thermal efficiencies are 12.9 % and 62.6 %, respectively. The maximum outlet water temperature is 59 oC.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

Potential impacts of slum urbanisation on channel bank storage in the Bang Pakong River, Thailand

2012 ◽  
Vol 7 (4) ◽  
Author(s):  
K. Harriden
Keyword(s):  
Water Quality ◽  
Balance Equations ◽  
Physical Processes ◽  
Social Phenomena ◽  
Urban Settlements ◽  
Recharge Rates ◽  
Water Quality Deterioration ◽  
Informal Urban Settlements ◽  
Storage Processes

Generally regarded as social phenomena, this paper regards slum urbanisation as an environmental actor. Specifically, how slum developments modify hydrogeomorphological processes motivates this research. Using the Bang Pakong River, eastern Thailand, as a case study, a literature review was conducted. The literature reviewed indicated changes in physical processes such as channel bank stability, water quality, flow regimes and the hydrological balance equations can occur with slum development. Given the importance of channel banks as the physical basis of many slum sites, this paper focuses on the possible changes to channel bank storage in the Bang Pakong River following slum urbanisation. The research highlights possible changes to channel bank storage processes, notably decreased storage recharge rates; increased anthropogenic extraction; and probable water quality deterioration. Deeper scientific understanding of how river processes are affected by specific forms of urban development can contribute to better management of both informal urban settlements and rivers.

Thermal Performance Analysis of a Rectangular Longitudinal Finned Solar Air Heater With Semicircular Absorber Plate

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Satyender Singh ◽  
Prashant Dhiman
Keyword(s):  
Thermal Performance ◽  
Numerical Solutions ◽  
Solar Air Heater ◽  
Duct Flow ◽  
Balance Equations ◽  
Absorber Plate ◽  
Ansys Fluent ◽  
Air Heater ◽  
Glass Cover ◽  
Good Agreement

Thermal performance of a single-pass single-glass cover solar air heater consisting of semicircular absorber plate finned with rectangular longitudinal fins is investigated. The analysis is carried out for different hydraulic diameters, which were obtained by varying the diameter of the duct from 0.3–0.5 m. One to five numbers of fins are considered. Reynolds number ranges from 1600–4300. Analytical solutions for energy balance equations of different elements and duct flow of the solar air heater are presented; results are compared with finite-volume methodology based numerical solutions obtained from ansys fluent commercial software, and a fairly good agreement is achieved. Moreover, analysis is extended to check the effect of double-glass cover and the recycle of the exiting air. Results revealed that the use of double-glass cover and recycle operation improves the thermal performance of solar air heater.

scholarly journals Phase-field gradient theory

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Luis Espath ◽  
Victor Calo
Keyword(s):  
Free Energy ◽  
Field Equation ◽  
Field Gradient ◽  
Phase Field ◽  
Constitutive Relations ◽  
The Body ◽  
Second Grade ◽  
Gradient Theory ◽  
Boundary Edge ◽  
Field Equations

AbstractWe propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second gradients of the phase field describe long-range interactions. By considering a nontrivial interaction inside the body, described by a boundary-edge microtraction, we characterize the existence of a hypermicrotraction field, a central aspect of this theory. On surfaces, we define the surface microtraction and the surface-couple microtraction emerging from internal surface interactions. We explicitly account for the lack of smoothness along a curve on surfaces enclosing arbitrary parts of the domain. In these rough areas, internal-edge microtractions appear. We begin our theory by characterizing these tractions. Next, in balancing microforces and microtorques, we arrive at the field equations. Subject to thermodynamic constraints, we develop a general set of constitutive relations for a phase-field model where its free-energy density depends on second gradients of the phase field. A priori, the balance equations are general and independent of constitutive equations, where the thermodynamics constrain the constitutive relations through the free-energy imbalance. To exemplify the usefulness of our theory, we generalize two commonly used phase-field equations. We propose a ‘generalized Swift–Hohenberg equation’—a second-grade phase-field equation—and its conserved version, the ‘generalized phase-field crystal equation’—a conserved second-grade phase-field equation. Furthermore, we derive the configurational fields arising in this theory. We conclude with the presentation of a comprehensive, thermodynamically consistent set of boundary conditions.

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