scholarly journals Functional analysis of thermal conductivity and viscosity of quasi-solid capillary-porous bodies under varying air environment conditions during museum storage

2020 ◽  
Vol 34 ◽  
pp. 7-15
Author(s):  
Volodymyr Dovhaliuk ◽  
Y. Chоvniuk ◽  
M. Shyshyna ◽  
A. Moskvitina
Keyword(s):  
Thermal Conductivity ◽  
Equilibrium State ◽  
Stress Tensor ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Irreversible Processes ◽  
Dissipative Function ◽  
Convection And Heat Transfer ◽  
Museum Exhibits ◽  
Porous Bodies

Fundamental analysis of the thermal conductivity and viscosity of quasi-solid capillary-porous bodies (CPBs), which are museum exhibits’ materials, is presented. The air environment parameters change leads to a temperature gradient in the CPBs. Non-uniform heating of the solid medium, in particular, quasi-solid CPB, is not accompanied by convection, and heat transfer is carried out only due to the mechanism of thermal conductivity. In order to create a mathematical model of this process in CPB, a system of partial differential equations in time and space coordinates is obtained. The resulting system adequately describes the thermal conductivity process in quasi-solid CPBs. The anisotropy of CPB’s thermal parameters, especially, its coefficients of thermal expansion and thermal conductivity, is also taken into account. Theoretically, the deformation process during motion in quasi-solid CPB is taken as reversible. In real conditions, the process is thermodynamically reversible only when it occurs at an infinitesimal speed. Then at each point in time, the CPB is able to establish a thermodynamic equilibrium state. Real motion occurs at a finite velocity, the CPB is not in an equilibrium state at any given moment, so there are endogenous processes that try to get it into a balanced condition. The occurrence of these processes causes the irreversibility of motion, which acts, in particular, through the dissipation of mechanical energy, which eventually turns into heat. The energy dissipation is caused by irreversible processes of thermal conductivity and processes of internal friction or viscosity. The dissipative function for isotropic and anisotropic cases was determined in order to analyze the viscosity of quasi-solid CPBs. The viscosity in the equations of motion can be considered by replacing the stress tensor with a tensor, which additionally takes into account the "dissipative" stress tensor.

Conservation Principles for Systems With a Varying Number of Degrees-of-Freedom

1998 ◽  
Vol 65 (3) ◽  
pp. 719-726 ◽  
Author(s):  
S. Djerassi
Keyword(s):  
Angular Momentum ◽  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Linear Momentum ◽  
Dynamical Equations ◽  
The Third ◽  
Conservation Principles

This paper is the third in a trilogy dealing with simple, nonholonomic systems which, while in motion, change their number of degrees-of-freedom (defined as the number of independent generalized speeds required to describe the motion in question). The first of the trilogy introduced the theory underlying the dynamical equations of motion of such systems. The second dealt with the evaluation of noncontributing forces and of noncontributing impulses during such motion. This paper deals with the linear momentum, angular momentum, and mechanical energy of these systems. Specifically, expressions for changes in these quantities during imposition and removal of constraints are formulated in terms of the associated changes in the generalized speeds.

Generalized hydrodynamics and heat waves

1992 ◽  
Vol 70 (1) ◽  
pp. 62-71 ◽  
Author(s):  
R. E. Khayat ◽  
Byung Chan Eu
Keyword(s):  
Thermal Conductivity ◽  
Evolution Equations ◽  
Pulse Propagation ◽  
Heat Waves ◽  
Fluid Dynamic ◽  
Propagation Speed ◽  
Heat Pulse ◽  
Irreversible Processes ◽  
Large Temperature ◽  
Generalized Hydrodynamics

By using the evolution equations of generalized hydrodynamics we investigate heat-pulse propagation in a Lennard–Jones liquid contained in the annulus between two concentric cylinders at different temperatures. It is found that the heat pulse propagates as a wave of a finite speed when a composite fluid dynamic number [Formula: see text] that depends on the thermal conductivity and wall temperature ratio is above a critical value, but in the subcritical region the heat pulse propagates diffusively as if predicted by a parabolic differential equation with an infinite speed of propagation. Therefore the question of the hyperbolicity of the system of differential (evolution) equations used is mainly determined by the parameter [Formula: see text]. This implies that the hyperbolicity of evolution equations, i.e., the finiteness of pulse-propagation speed, cannot be the main reason for extending the thermodynamics of irreversible processes as believed by some authors in the literature. This study indicates that for a liquid of high thermal conductivity or a large temperature difference the Fourier law of heat conduction is inadequate for use in the description of the temporal evolution of heat and a suitable generalization of hydrodynamics is necessary. The generalized hydrodynamic equations presented in this and previous papers are examples for such a generalization.

On sound generated aerodynamically I. General theory

1952 ◽  
Vol 211 (1107) ◽  
pp. 564-587 ◽  
Keyword(s):  
Fluid Flow ◽  
Mach Number ◽  
General Theory ◽  
Stress Tensor ◽  
High Power ◽  
Velocity Vector ◽  
Unit Volume ◽  
Equations Of Motion ◽  
Sound Field ◽  
Velocity Of Sound

A theory is initiated, based on the equations of motion of a gas, for the purpose of estimating the sound radiated from a fluid flow, with rigid boundaries, which as a result of instability contains regular fluctuations or turbulence. The sound field is that which would be produced by a static distribution of acoustic quadrupoles whose instantaneous strength per unit volume is ρv i v j + p ij - a 2 0 ρ δ ij , where ρ is the density, v i the velocity vector, p ij the compressive stress tensor, and a 0 the velocity of sound outside the flow. This quadrupole strength density may be approximated in many cases as ρ 0 v i v j . The radiation field is deduced by means of retarded potential solutions. In it, the intensity depends crucially on the frequency as well as on the strength of the quadrupoles, and as a result increases in proportion to a high power, near the eighth, of a typical velocity U in the flow. Physically, the mechanism of conversion of energy from kinetic to acoustic is based on fluctuations in the flow of momentum across fixed surfaces, and it is explained in § 2 how this accounts both for the relative inefficiency of the process and for the increase of efficiency with U . It is shown in § 7 how the efficiency is also increased, particularly for the sound emitted forwards, in the case of fluctuations convected at a not negligible Mach number.

scholarly journals Fractional formulation of Podolsky Lagrangian density

2022 ◽  
Vol 9 (2) ◽  
pp. 136-141
Author(s):  
Amer D. Al-Oqali ◽  
Keyword(s):  
Field Theory ◽  
Stress Tensor ◽  
Fractional Derivatives ◽  
Lagrangian Density ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Classical Field Theory ◽  
Higher Order ◽  
Classical Field ◽  
Energy Stress

Lagrangians which depend on higher-order derivatives appear frequently in many areas of physics. In this paper, we reformulate Podolsky's Lagrangian in fractional form using left-right Riemann-Liouville fractional derivatives. The equations of motion are obtained using the fractional Euler Lagrange equation. In addition, the energy stress tensor and the Hamiltonian are obtained in fractional form from the Lagrangian density. The resulting equations are very similar to those found in classical field theory.

The two-body problem and radiative losses

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Mechanical Energy ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Radiation Reaction ◽  
Compact Objects ◽  
Einstein Equations ◽  
Two Body Problem ◽  
System P ◽  
Radiative Losses ◽  
Radiation Reaction Force

This chapter begins by finding the field created by compact objects in the post-linear approximation of general relativity. The second quadrupole formula is then completely proven. Next, the chapter finds the equations of motion of the bodies in the field which they create to second order in the perturbations, assuming that their velocities are small. It shows that, to correctly describe the radiation reaction at 2.5 PN order, it will prove necessary to iterate Einstein equations a third time. This leads the discussion to the equations of motion, which generalize to order 1/c5 the EIH equations of order 1/c⁲. Finally, the chapter studies the effect of the radiation reaction force on the sources, and shows that there is an energy balance at 2.5 PN order between the energy radiated to infinity and the mechanical energy lost by the system.

scholarly journals Observable and Unobservable Mechanical Motion

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 737
Author(s):  
J. Gerhard Müller
Keyword(s):  
Information Gain ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Minimum Energy ◽  
Radiation Energy ◽  
Mechanical Motion ◽  
Radiation Emission ◽  
Physical Action ◽  
Hamilton's Equations ◽  
Hamilton’S Equations

A thermodynamic approach to mechanical motion is presented, and it is shown that dissipation of energy is the key process through which mechanical motion becomes observable. By studying charged particles moving in conservative central force fields, it is shown that the process of radiation emission can be treated as a frictional process that withdraws mechanical energy from the moving particles and that dissipates the radiation energy in the environment. When the dissipation occurs inside natural (eye) or technical photon detectors, detection events are produced which form observational images of the underlying mechanical motion. As the individual events, in which radiation is emitted and detected, represent pieces of physical action that add onto the physical action associated with the mechanical motion itself, observation appears as a physical overhead that is burdened onto the mechanical motion. We show that such overheads are minimized by particles following Hamilton’s equations of motion. In this way, trajectories with minimum curvature are selected and dissipative processes connected with their observation are minimized. The minimum action principles which lie at the heart of Hamilton’s equations of motion thereby appear as principles of minimum energy dissipation and/or minimum information gain. Whereas these principles dominate the motion of single macroscopic particles, these principles become challenged in microscopic and intensely interacting multi-particle systems such as molecules moving inside macroscopic volumes of gas.

Simulation of thermomechanical processes in disc brakes of wheeled vehicles

2021 ◽  
Vol 1 (104) ◽  
pp. 11-20
Author(s):  
O. Hrevtsev ◽  
N. Selivanova ◽  
P. Popovych ◽  
L. Poberezhny ◽  
V. Sakhno ◽  
...  
Keyword(s):  
Differential Equation ◽  
Thermal Conductivity ◽  
Theoretical Basis ◽  
Equations Of Motion ◽  
Operational Reliability ◽  
Technical Condition ◽  
Heat Fluxes ◽  
Disc Brakes ◽  
Thermomechanical Processes ◽  
Fourier Type

Purpose: Ensuring the required operational reliability of disc brakes by forecasting their technical condition taking into account thermomechanical processes. Design/methodology/approach: Differential equations of rotation of a rigid body around a fixed axis are solved, it is established that the equations of motion and the equations of thermal conductivity are indirectly related. The use of these analytical dependences provides a better understanding of thermomechanical transients. Findings: The solution is obtained on the basis of the differential equation of thermal conductivity of the hyperbolic type, which does not allow an infinite velocity of propagation of temperature perturbations in contrast to the differential equation of thermal conductivity of the parabolic Fourier type. The obtained analytical dependences provide a better understanding of thermomechanical transients and develop a theoretical basis for determining stresses and heat fluxes in solving problems of reliability and durability of disc brakes. Research limitations/implications: The work uses generally accepted assumptions and limitations for thermomechanical calculations. Practical implications: It is shown, that transients in a mechanical system - a brake disk at impulse loadings cause emergence of thermal effects which arise under the influence of external loadings. Originality/value: The application of these analytical dependences provides a better understanding of thermomechanical transients and develops a theoretical basis for solving problems of reliability and durability of disc brakes.

Accounting Viscous Dissipation at Round Tubes Filling

2016 ◽  
Vol 685 ◽  
pp. 191-194
Author(s):  
E.I. Borzenko ◽  
O.Yu. Frolov ◽  
G.R. Shrager
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Mechanical Energy ◽  
Equations Of Motion ◽  
Dissipative Heating ◽  
Mathematical Basis ◽  
One Dimensional ◽  
Parametric Studies ◽  
Initial And Boundary Conditions ◽  
Formulation Of Problems

The fountain nonisothermal flow of a viscous fluid realized during circular pipe filling is investigated. The mathematical basis of the process is formed by equations of motion, continuity and energy with respective initial and boundary conditions with due account of the temperature dependence of viscosity, the presence of a free boundary and dissipation of mechanical energy. To solve the problem numerically a finite difference method is required. Depending on the values defining the dimensionless parameters the results of parametric studies in temperature, viscosity, dynamic and kinematic characteristics of the flow are shown. Flow patterns for the formulation of problems with different initial and boundary conditions are given. The separation of flow into the zone of spatial flow in the vicinity of the free surface and one dimensional flow away from it, and changing the shape of the free boundary, depending on the level of dissipative heating are demonstrated.

Molecular Dynamics Simulation of Thermal Conductivity of Aluminum

2013 ◽  
Vol 336 ◽  
pp. 47-55
Author(s):  
Jamal Davoodi ◽  
Samaneh Khoshkhatti
Keyword(s):  
Thermal Conductivity ◽  
Molecular Dynamics ◽  
Molecular Dynamics Simulation ◽  
Equations Of Motion ◽  
Fixed Number ◽  
Dynamics Simulation ◽  
Many Body ◽  
Macro Scale ◽  
Body Potential ◽  
Increasing Temperature

In this research, the thermal conductivity of aluminum (Al) in macro scale was investigated by the molecular dynamics simulation technique. We used FORTRAN programming in the simulations and used a fixed number of atoms, N, confined to a fixed pressure, P, and maintained at a constant preset temperature, T, i.e. the NPT ensemble. The Sutton-Chen many-body potential was used to calculate energy and force. The temperature and pressure of the system were controlled by Nosé-Hoover thermostat and Berendsen barostat respectively. We could solve the equations of motion using the Velocity Verlet algorithm. We calculated the thermal conductivity of Al in the macro scale using the Green-Kubo method. Moreover, we have studied the effect of increasing temperature on the value of the thermal conductivity of Al. The obtained results showed that the computed thermal conductivities are in good agreement with experimental data.

FEM-CBS algorithm for convective transport of nanofluids in inclined enclosures filled with anisotropic non-Darcy porous media using LTNEM

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sameh Elsayed Ahmed
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Porous Medium ◽  
Equilibrium State ◽  
Thermal Equilibrium ◽  
Volume Fraction ◽  
Nanofluid Flow ◽  
Content Type ◽  
Thermal Fields ◽  
Nanoparticles Volume Fraction

Purpose The Galerkin finite element method (FEM) based on the characteristic-based split (CBS) scheme is applied to simulate the nanofluid flow and thermal fields inside an inclined geometry filled by a heat-generating hydrodynamically and thermally anisotropic non-Darcy porous medium using the local thermal non-equilibrium model (LTNEM). Property of the hydrodynamic anisotropy is taken in both the Forchheimer coefficient and permeability and these tools are considered as functions of inclination of the principal axes. Also, the thermal conductivity for the porous phase is assumed to be anisotropic. Design/methodology/approach The Galerkin FEM based on the CBS scheme is applied to solve the partial differential equations governing the flow and thermal fields. Findings It is noted that the net rate of the heat transfer between the nanofluid and solid phases are influenced by variations of the anisotropic properties. Also, the system is reached to the thermal equilibrium state at H > 100. Further, the maximum nanofluid temperature is reduced by 12.27% when the nanoparticles volume fraction is varied from 0% to 4%. Originality/value This paper aims to study the nanofluid flow and heat transfer characteristics inside an inclined enclosure filled with a heat-generating, hydrodynamically and thermally anisotropic porous medium using the CBS scheme. The LTNEM is considered between the nanofluid and porous phases while the local thermal equilibrium model (LTEM) between the base fluid (water) and the nanoparticles (alumina) is taken into account. The Galerkin FEM is introduced to discretize the governing system of equations. Also, examine influences of the anisotropic properties (permeability, Forchheimer terms and thermal conductivity of the porous medium), inclination angle and nanoparticles volume fraction on the net rate of the heat transfer between the nanofluid and porous phases and on the local thermal non-equilibrium state is one of the concerns of this paper.

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