Equivalence Between Higher-Order Stress Power and Heat Flux in Energy Equation Based on Lattice Dynamics

1999 ◽  
Vol 121 (2) ◽  
pp. 240-246 ◽  
Author(s):  
Y. Yasui ◽  
K. Shizawa ◽  
K. Takahashi
Keyword(s):  
Heat Flux ◽  
Lattice Dynamics ◽  
Energy Equation ◽  
Solid Mechanics ◽  
Higher Order ◽  
First Law Of Thermodynamics ◽  
Internal Forces ◽  
Order Stress ◽  
As Stress

The essence of macroscopic quantities in solid mechanics can be grasped by expressing these quantities in terms of kinematic and mechanical quantities of atoms. In this paper, a method is proposed for obtaining the microscopic definitions of internal forces of continua such as stress, higher-order stresses and heat flux. Moreover, the relation between higher-order stress power and heat flux is discussed expressing the first law of thermodynamics with microscopic quantities in the mesodomain. Comparing heat flux with higher-order stress power, it is clarified that the divergence of heat flux is equivalent to the total of each order power due to higher-order stresses.

scholarly journals Dynamics of Extreme Stratospheric Negative Heat Flux Events in an Idealized Model

2018 ◽  
Vol 75 (10) ◽  
pp. 3521-3540 ◽  
Author(s):  
Etienne Dunn-Sigouin ◽  
Tiffany Shaw
Keyword(s):  
Heat Flux ◽  
Wave Propagation ◽  
Recent Work ◽  
Wave Interaction ◽  
Higher Order ◽  
Negative Events ◽  
Flow Mechanism ◽  
Mean Flow ◽  
Idealized Model

Recent work has shown that extreme stratospheric wave-1 negative heat flux events couple with the troposphere via an anomalous wave-1 signal. Here, a dry dynamical core model is used to investigate the dynamical mechanisms underlying the events. Ensemble spectral nudging experiments are used to isolate the role of specific dynamical components: 1) the wave-1 precursor, 2) the stratospheric zonal-mean flow, and 3) the higher-order wavenumbers. The negative events are partially reproduced when nudging the wave-1 precursor and the zonal-mean flow whereas they are not reproduced when nudging either separately. Nudging the wave-1 precursor and the higher-order wavenumbers reproduces the events, including the evolution of the stratospheric zonal-mean flow. Mechanism denial experiments, whereby one component is fixed to the climatology and others are nudged to the event evolution, suggest higher-order wavenumbers play a role by modifying the zonal-mean flow and through stratospheric wave–wave interaction. Nudging all tropospheric wave precursors (wave-1 and higher-order wavenumbers) confirms they are the source of the stratospheric waves. Nudging all stratospheric waves reproduces the tropospheric wave-1 signal. Taken together, the experiments suggest the events are consistent with downward wave propagation from the stratosphere to the troposphere and highlight the key role of higher-order wavenumbers.

scholarly journals Lattice Dynamics of Simple Harmonic and Anharmonic Shell Models

1967 ◽  
Vol 20 (5) ◽  
pp. 495 ◽  
Author(s):  
J Oitmaa
Keyword(s):  
Dipole Moment ◽  
Shell Model ◽  
Lattice Dynamics ◽  
Higher Order ◽  
Force Constants ◽  
Dynamical Equations ◽  
Normal Coordinates ◽  
Shell Models ◽  
Rigid Ion Model ◽  
Explicit Expressions

The lattice dynamics of harmonic and anharmonic shell models are reviewed. It is shown that the various dynamical equations for the shell model can be expressed in the same form as those for the rigid ion model, but with modified force constants. The anharmonic shell model leads to higher order contributions to the dipole moment, quadratic and cubic in the normal coordinates, for which explicit expressions are obtained.

Normal-Velocity Relaxation and Higher Order Algebraic Heat Flux Models Applicable to an Axisymmetric Impinging Jet

2012 ◽  
Vol 33 (4) ◽  
pp. 556-564 ◽  
Author(s):  
Farzad Bazdidi-Tehrani ◽  
Alireza Imanifar ◽  
Siavash Khajehhasani ◽  
Mehran Rajabi-Zargarabadi
Keyword(s):  
Heat Flux ◽  
Impinging Jet ◽  
Higher Order ◽  
Normal Velocity ◽  
Order Algebraic

Analytical Solutions for Crack-Tip Higher Order Stress Fields in Thermal Barrier Coating

2008 ◽  
Vol 47-50 ◽  
pp. 1023-1026
Author(s):  
Yao Dai ◽  
Chang Qing Sun ◽  
Sun Qi ◽  
Wei Tan
Keyword(s):  
Crack Tip ◽  
Higher Order ◽  
Functionally Graded ◽  
Stress Fields ◽  
Thermal Barrier ◽  
Barrier Coating ◽  
Graded Material ◽  
Stress Functions ◽  
Order Stress ◽  
Analytical Expressions

Analytical expressions for crack-tip higher order stress functions for a plane crack in a special functionally graded material (FGM), which has an variation of elastic modulus in 1 2 power form along the gradient direction, are obtained through an asymptotic analysis. The Poisson’s ratio of the FGM is assumed to be constant in the analysis. The higher order fields in the asymptotic expansion display the influence of non-homogeneity on the structure of crack-tip fields obviously. Furthermore, it can be seen from expressions of higher order stress fields that at least three terms must be considered in the case of FGMs in order to explicitly account for non-homogeneity effects on the crack- tip stress fields. These results provide the basis for fracture analysis and engineering applications of this FGM.

Unsteady in-cylinder heat transfer in a spark ignition engine: Experiments and modelling

2001 ◽  
Vol 215 (6) ◽  
pp. 747-760 ◽  
Author(s):  
D J Oude Nijeweme ◽  
J. B. W. Kok ◽  
C. R. Stone ◽  
L Wyszynski
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Combustion Chamber ◽  
Energy Equation ◽  
Spark Ignition ◽  
Surface Heat ◽  
Spark Ignition Engine ◽  
Unexpected Result ◽  
Reynolds Analogy ◽  
Law Of The Wall

Instantaneous heat flux measurements have shown that, in the expansion stroke, heat can flow from the wall into the combustion chamber, even though the bulk gas temperature is higher than the wall temperature. This unexpected result has been explained by modelling of the unsteady flows and heat conduction within the gas side thermal boundary layer. This modelling has shown that these unsteady effects change the phasing of the heat flux, compared with that which would be predicted by a simple convective correlation based on the bulk gas properties. Twelve fast response thermocouples have been installed throughout the combustion chamber of a pent roof, four-valve, single-cylinder spark ignition engine. Instantaneous surface temperatures and the adjacent steady reference temperatures were measured, and the surface heat fluxes were calculated for motoring and firing at different speeds, throttle settings and ignition timings. To make comparisons with these measurements, the combustion system was modelled with computational fluid dynamics (CFD). This was found to give very poor agreement with the experimental measurements, so this led to a review of the assumptions used in boundary layer modelling. The discrepancies were attributed to assumptions in the law of the wall and Reynolds analogy, so instead the energy equation was solved within the boundary layer. The one-dimensional energy conservation equation has been linearized and normalized and solved in the gas side boundary layer for a motored case. The results have been used for a parametric study, and the individual terms of the energy equation are evaluated for their contribution to the surface heat flux. It was clearly shown that the cylinder pressure changes cause a phase shift of the heat flux forward in time.

Localized Deformation Using Higher Order Stress/Strain Theory

1990 ◽  
Vol 112 (1) ◽  
pp. 51-53 ◽  
Author(s):  
M. A. Koenders
Keyword(s):  
Slip Band ◽  
Failure Modes ◽  
Tangential Force ◽  
Higher Order ◽  
Strain Theory ◽  
Granular Soils ◽  
Localized Deformation ◽  
Contact Points ◽  
Force Ratio ◽  
Order Stress

A material is considered which consists of rough interacting blocks. The interaction, which is expressed in terms of the ratio of the normal and tangential force at the contact points of the blocks, is pure frictional if a certain maximal force ratio is reached, and elastic otherwise. The shape of the blocks is determined by the double shearing geometry. Failure modes for this material depend on the thickness of the slip band. The investigation is relevant to granular soils and rocks.

Application of a Simplified Velocity Profile to the Prediction of Pipe-Flow Heat Transfer

1968 ◽  
Vol 90 (2) ◽  
pp. 191-198 ◽  
Author(s):  
R. D. Haberstroh ◽  
L. V. Baldwin
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Velocity Profile ◽  
Pipe Flow ◽  
Energy Equation ◽  
Momentum Equation ◽  
Turbulent Pipe Flow ◽  
Transfer Coefficients ◽  
Constant Property ◽  
Wide Range

The temperature profiles and heat-transfer coefficients are predicted for fully developed turbulent pipe flow with constant wall heat flux for a wide range of Prandtl and Reynolds numbers. The basis for integrating the energy equation comes from a continuously differentiable velocity profile which fits the physical boundary conditions and is a rigorous (though not necessarily unique) solution of the Reynolds equations. This velocity profile is the semiempirical relation proposed by S. I. Pai, reference [12]. The assumptions are those of steady, incompressible, constant-property, fully developed, turbulent flow of Newtonian fluids in smooth, circular pipes with constant heat flux at the wall. The ratio of the turbulent thermal diffusivity to the turbulent momentum diffusivity is taken to be unity. The thermal quantities are obtained by numerical integration of the energy equation, and they are presented as curves and tables. A compact formula for the Nusselt number is given for a wide range of Reynolds and Prandtl numbers. The results degenerate identically to the case of laminar flow. The heat-transfer calculation requires neither adjustable factors nor data-fitting beyond the empirical constants in the momentum equation; thus this analysis constitutes a heat-transfer prediction to be tested against heat-transfer data.

scholarly journals Application of higher-order heat flux model for predicting turbulent methane-air combustion

2019 ◽  
pp. 415-415
Author(s):  
Ali Ershadi ◽  
Mehran Rajabi-Zargarabadi
Keyword(s):  
Heat Flux ◽  
Stokes Equations ◽  
Eddy Diffusivity ◽  
Turbulent Heat Flux ◽  
Higher Order ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Generalized Gradient ◽  
No Emission ◽  
Turbulent Reactive Flows

The present study addresses a new effort to improve the prediction of turbulent heat transfer and NO emission in non-premixed methane-air combustion. In this regard, a symmetric combustion chamber in a stoichiometric condition is numerically simulated using the Reynolds averaged Navier-Stokes equations. The Realizable k-? model and Discreate Ordinate are applied for modeling turbulence and radiation, respectively. Also, the eddy dissipation model is adopted for predicting the turbulent chemical reaction rate. Zeldovich mechanism is applied for estimating the NO emission. Higher-order generalized gradient diffusion hypothesis (HOGGDH) is employed for predicting the turbulent heat flux in turbulent reactive flows. Results show that the HOGGDH model is capable of predicting temperature distribution in good agreement with the available experimental data. Comparison of the results obtained by the simple eddy diffusivity (SED) and HOGGDH models shows that applying the HOGGDH significantly improves the over-prediction of NO emission. Finally, the average turbulent Prandtl number for the non-premixed methane-air combustion has been calculated.

scholarly journals Memory and nonlocal effects of heat transport in a spherical nanoparticle

2021 ◽  
Vol 2116 (1) ◽  
pp. 012055
Author(s):  
Francesc Font
Keyword(s):  
Heat Flux ◽  
Heat Transport ◽  
Energy Equation ◽  
Hydrodynamic Equation ◽  
Radial Component ◽  
Radial Symmetry ◽  
Temperature Profiles ◽  
Governing Equations ◽  
Nonlocal Effects ◽  
Classical Energy

Abstract In this paper a mathematical model describing the heat transport in a spherical nanoparticle subject to Newton heating at its surface is presented. The governing equations involve a phonon hydrodynamic equation for the heat flux and the classical energy equation that relates the heat flux and the temperature. Assuming radial symmetry the model is reduced to two partial differential equation, one for the radial component of the flux and one for the temperature. We solve the model numerically by means of finite differences. The resulting temperature profiles show characteristic wave-like behaviour consistent with the non Fourier components in the hydrodynamic equation.

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