Temperature Gradient Boundary Research Articles

Computational Model of Effective Thermal Conductivity of Green Insulating Fibrous Media.

Modelling effective thermal properties is crucial for optimizing the thermal performance of materials such as new green insulating fibrous media. In this study, a numerical model is proposed to calculate the effective thermal conductivity of these materials. The fibers are considered to be non-overlapping and randomly oriented in space. The numerical model is based on the finite element method. Particular attention is paid to the accuracy of the results and the influence of the choice of the representative elementary volume (REV) for calculation (cubic or rectangular parallelepiped slice). The calculated effective thermal conductivity of fibrous media under different boundary conditions is also investigated. A set of usual mixed boundary conditions is considered, alongside the uniform temperature gradient conditions. The REV rectangular slice and uniform temperature gradient boundary conditions provide a more accurate estimate of the effective thermal conductivity and are therefore recommended for use in place of the usual cubic representative elementary volume and the usual mixed boundary conditions. This robust model represents a principal novelty of the work. The results are compared with experimental and analytical data previously obtained in the literature for juncus maritimus fibrous media, for different fiber volume fractions, with small relative deviations of 7%. Analytical laws are generally based on simplified assumptions such as infinitely long fibers, and may neglect heat transfer between different phases. Both short and long fiber cases are considered in numerical calculations.

On effective thermal conductivity of heterogeneous material: From periodic unit inclusion cell to large representative volume element

The custom design of a composite material requires the knowledge of its effective behavior which depends on several parameters such as the properties of the constituents, their distributions, shapes and sizes. In thermal conductivity, all these parameters have a direct and significant influence on the effective thermal conductivity (ETC) of composites. These parameters act differently on the behavior of the composite according to its use as much as a good conductor by improving its ETC or by reducing it by considering it as an insulator. The main goal of this work is an extensive study of all possible situations of ETC by a numerical homogenization technique based on the Finite Elements Method. For this purpose, the two main categories of composites, namely the periodic composites represented by the unit cell and the random RVE, are considered. For each category of composite, different contrasts, different particles’ volume fractions, aspect ratios, positions, and orientations are studied. In order to ensure the simulation results are effective and representative, two boundary conditions, namely Uniform Temperature Gradient Boundary Conditions (UGT) and Periodic Thermal Boundary Conditions (PBC), were imposed on all considered microstructures. The results of this study constitute a synthesis of the effective thermal conductivities of all the possible situations which can be summarized as follows: On the one hand, the reinforcements shape effect is very important irrespective of the nature of the periodic and random composites and on the other hand, the two types of composites do not have the same behavior as that for the reinforcements with a circular or almost circular shape. This study also emphasizes the situations where the ETC can be estimated analytically and when homogenization is necessary. From a practical point of view, and on the basis of the obtained results, this study made it possible to show clearly in which situation the composite becomes more conducting and in the opposite case when it becomes more insulating.

Thermomechanical deformation in a transversely isotropic magneto-thermoelastic rotating solids under initial stress

The present research deals with the mathematical model for study of the disturbance due to mechanical (horizontal or vertical) and thermal source in two dimensional transversely isotropic magneto thermoelastic solid under initial stress due to time-harmonic source with generalized Lord–Shulman (LS) theory of thermoelasticity with two temperatures. The Fourier transform has been used to find the solution of the problem. The displacement components, stress components and temperature distribution are calculated numerically in the transformed domain. The effect of time harmonic source, relaxation time and initial stress is depicted graphically on the resulting quantities for the insulated boundary and the temperature gradient boundary.

Finite element modelling and simulations on effective thermal conductivity of particulate composites

In this paper, the finite element simulation approach for studying the steady-state heat transfer and predicting the effective thermal conductivity of composites has been proposed. 3D representative volume elements considering the polyhedral- and spherical-shaped inclusions are generated. Different meshing approaches for meshing these complex structured composites have been used, and the mesh quality is studied based on mesh metrics: element quality and skewness, and next, a convergence study is conducted to ensure mesh-independent results. Three different boundary conditions: mixed, constant temperature gradient and uniform flux has been used to predict the effective thermal conductivity of composites. The predicted results from simulations are in good agreement with the experimental values reported in the literature. It has been observed that the random orientation and interpenetration of particles lead to a much better heat flow and hence the higher values of effective thermal conductivity of composites. For high volume fraction composites, as the number of particles having interpenetration increases, their effective thermal conductivity increases. For low volume fraction composites, constant temperature gradient boundary condition overpredicts the effective thermal conductivity and for high volume fraction composites, uniform heat flux and mixed boundary conditions predict higher values. A design point study was conducted, considering the ratio of thermal conductivity of constituents, as a design parameter. It has been observed that by reinforcing the high thermal conductivity inclusions as an interpenetrating phase, the effective thermal conductivity of composites can be increased substantially. The reinforcement of very high conductivity material cannot yield the desired ETCs if the reinforced particles are rendered uniformly oriented with no contacts between them.

Variabilities and their upper and lower bounds of the equivalent thermal conductivity and resistance defined by the entransy dissipation rate

The prediction of equivalent thermal conductivity (ETC) and resistance (ETR) is an important topic in the composite material field. Many expressions of ETCs and ETRs have been proposed using different homogenization methods in last several decades. Especially, expressions defined by the entransy dissipation rate, keff and Reff, excel for their wide range of application. Usually, it was agreed that keff and Reff were determined by the thermal conductivity distribution inside. However, we find that they are also vary with the boundary temperature gradient distribution (TGD). In this paper, we simulate and mathematically prove the influence of boundary TGD on keff. The results indicate that keff with uniform boundary TGD is higher than that with non-uniform boundary TGD. In addition, the mathematical proof after a little adjustment is applied to confirm the minimum thermal resistance principle based on the uniform TGD inside. The results show that keff is the maximum when TGD are uniform in all regions including boundaries, and keff reaches the minimum when the non-uniformity of TGD extends to the limit. Upper and lower bounds of keff and Reff found in this paper are greatly valuable for optimizing the heat transfer ability and heat insulation ability of materials. And the methodology as well as conclusion in this paper can be reproduced in some generalized irreversible transport systems.

Elastodynamic Response of a Three-Phase-Lag Model of Orthorhombic Thermoviscoelastic Material with Reference Temperature Dependent Properties

A three-phase-lag model of a homogeneous thermally conducting orthorhombic thermoviscoelastic material under the effect of the dependence of reference temperature on all elastic and thermal parameters is investigated. The Laplace and Fourier transform and eigenvalue approach techniques are used to solve the resulting nondimensional coupled equations. As an application of the problem, harmonically varying and sinusoidal pulse functions are considered. Numerical results for the field quantities are given in the physical domain and illustrated graphically. Comparisons are made for thermoviscoelastic temperature dependent, thermoviscoelastic and thermoelastic materials, respectively, for different values of time, for temperature gradient boundary.

Penetration of boundary-driven flows into a rotating spherical thermally stratified fluid

Motivated by the dynamics within terrestrial bodies, we consider a rotating, strongly thermally stratified fluid within a spherical shell subject to a prescribed laterally inhomogeneous heat-flux condition at the outer boundary. Using a numerical model, we explore a broad range of three key dimensionless numbers: a thermal stratification parameter (the relative size of boundary temperature gradients to imposed vertical temperature gradients), $10^{-3}\leqslant S\leqslant 10^{4}$, a buoyancy parameter (the strength of applied boundary heat-flux anomalies), $10^{-2}\leqslant B\leqslant 10^{6}$, and the Ekman number (ratio of viscous to Coriolis forces), $10^{-6}\leqslant E\leqslant 10^{-4}$. We find both steady and time-dependent solutions and delineate the regime boundaries. We focus on steady-state solutions, for which a clear transition is found between a low $S$ regime, in which buoyancy dominates the dynamics, and a high $S$ regime, in which stratification dominates. For the low-$S$ regime, we find that the characteristic flow speed scales as $B^{2/3}$, whereas for high-$S$, the radial and horizontal velocities scale respectively as $u_{r}\sim S^{-1}$, $u_{h}\sim S^{-3/4}B^{1/4}$ and are confined within a thin layer of depth $(SB)^{-1/4}$ at the outer edge of the domain. For the Earth, if lower mantle heterogeneous structure is due principally to chemical anomalies, we estimate that the core is in the high-$S$ regime and steady flows arising from strong outer boundary thermal anomalies cannot penetrate the stable layer. However, if the mantle heterogeneities are due to thermal anomalies and the heat-flux variation is large, the core will be in a low-$S$ regime in which the stable layer is likely penetrated by boundary-driven flows.

Experimental study of hot cracking at circular welding joints of 42CrMo steel

The hot cracking at circular welding joints of quenched and tempered 42CrMo steel were studied. The flow of the molten pool and the solidification process of weld were observed with a high-speed video camera. The information on the variations in the weld temperature was collected using an infrared (IR) thermal imaging system. The metallurgical factors of hot cracking were analyzed via metallographic microscope and scanning electron microscope (SEM). The result shows that leading laser laser-metal active gas (MAG) hybrid welding process has a smaller solid–liquid boundary movement rate (VSL) and a smaller solid–liquid boundary temperature gradient (GSL) compared with leading arc laser-MAG hybrid welding process and laser welding process. Additionally, the metal in the molten pool has superior permeability while flowing toward the dendritic roots and can compensate for the inner-dendritic pressure balance. Therefore, leading laser laser-MAG hybrid welding process has the lowest hot cracking susceptibility.

A method to derive thermoelastic Green’s functions for bounded domains (on examples of two-dimensional problems for parallelepipeds)

This article presents new constructive formulas to steady-state thermoelastic Green’s functions for a plane generalized boundary value problem of thermoelasticity for a generalized rectangle. The constructive formulas are expressed in terms of Green’s functions for Poisson’s equation. These results are formulated in a special theorem, which is proved using the author’s developed harmonic integral representations method. On the base of derived constructive formulas, it is possible to obtain many analytical expressions for Green’s functions for thermoelastic displacements and stresses to 28 concrete boundary value problems for: rectangle-16, half-strip-8, strip-4. An example of such kind is presented for a concrete plane boundary value problem for a rectangle, Green’s functions of which are presented in the form of a sum of elementary functions and ordinary series. These results are presented in another theorem, which is proved on the base of derived general constructive formulas. In the particular case for a half-strip and strip, ordinary series vanish and Green’s functions are presented in elementary functions. New analytical expressions for thermal stresses to a particular plane problem for a thermoelastic rectangle subjected to a constant boundary temperature gradient are also derived. Numerical investigation has shown that the infinite series are convergent. All solutions obtained for thermal stresses, caused by a constant temperature gradient and by a unit heat source are validated by checking the respective equilibrium equation and continuity of deformation equations (Beltrami–Michel equations), written in the terms of thermal stresses. The graphics for thermal stresses and their infinite series also are presented.

Laminar-Turbulent Bifurcation Scenario in 3D Rayleigh-Benard Convection Problem

We are considering two initial-boundary value problems for Rayleigh-Benard convection in Oberbeck-Boussinesq approximation for incompressible fluid in 3D-rectangular domain with 4:4:1 geometric ratio with periodicity in two directions and cubic domain with 1:1:1 ratio and zero velocity and temperature gradient boundary conditions. For this purpose, we use two numerical method: one is a Pseudo-Spectral-Galerkin method with trigonometric-Chebyshev polynomials and the other is finite element/volume method with WENO interpolation for advection term. Numerical methods are presented shortly and are benchmarked against known DNS data and against one another (for quasi-periodic domain problem). Then we perform stability analysis using analytical expression for main stationary solutions and eigenvalue numerical analysis by applying Implicitly Restarted Arnoldi (IRA) method. The IRA is used to perform linear stability analysis, find bifurcations of stationary points and analyze eigenvalues of monodromy matrices. Thus characteristic exponents of the system for time periodic solutions (limited cycles of various periods and resonance invariant tori) are computed. We show, numerically, the existence of multistable rotes to chaos through chaotic fractal attractors, full Feigenbaum-Sharkovski cascades and multidimensional torus attractors (Landau-Hopf scenario). The existence of these attractors is shown through analysis of phase subspaces projections, Poincare sections and eigenvalue analysis of numerically computed DNS data. These attractors burst into chaos with the increase of Rayleigh number either through resonance and phase-locking or through emergence of singular chaotic attractors.

Objective function choice for control of a thermocapillary flow using an adjoint-based control strategy

The problem of suppressing flow oscillations in a thermocapillary flow is addressed using a gradient-based control strategy. The physical problem addressed is the “open boat” process of crystal growth, the flow in which is driven by thermocapillary and buoyancy effects. The problem is modeled by the two-dimensional unsteady incompressible Navier–Stokes and energy equations under the Boussinesq approximation. The goal of the control is to suppress flow oscillations which arise when the driving forces are such that the flow becomes unsteady. The control is a spatially and temporally varying temperature gradient boundary condition at the free surface. The control which minimizes the flow oscillations is found using a conjugate gradient method, where the gradient of the objective function with respect to the control variables is obtained from solving a set of adjoint equations. The issue of choosing an objective function that can be both optimized in a computationally efficient manner and optimization of which provides control that damps the flow oscillations is investigated. Almost complete suppression of the flow oscillations is obtained for certain choices of the objective function.

Modeling movement of viscose rayon through a spinneret by the finite element method

By modeling the movement of viscose rayon through a spinneret by the finite element method, we establish the dependence of the filament quality on the stability of a number of factors. We demonstrate the relationship of the boundary temperature gradients and the shape of the heat flux distribution in the solution. The mathematical model developed allows us to use the identified relationships in synthesis of control systems.

S162014 境界面に温度分布を有する分子気体潤滑問題の改良DSMC解析 : MGL解析との比較([S162]情報機器メカニクスとヘッドディスクインターフェイス)

As molecular gas-film lubrication problem with boundary temperature gradient, the characteristics of ultra-thin parallel gas bearing whose boundary walls has an inverse V-shaped temperature distribution and are separated with submicron spacing were analyzed using DPMC (Deviational Particle Monte Carlo) method. The pressure distributions obtained by DPMC method show good agreement with those by molecular gas-film lubrication equation with thermal effects (t-MGL) equation.

Robust thermal boundary conditions applicable to a wall along which temperature varies in lattice-gas cellular automata

We show that the heat exchange between fluid particles and boundary walls can be achieved by controlling the velocity change rate following the particles' collision with a wall in discrete kinetic theory, such as the lattice-gas cellular automata and the lattice Boltzmann method. We derive a relation between the velocity change rate and temperature so that we can control the velocity change rate according to a given temperature boundary condition. This relation enables us to deal with the thermal boundary whose temperature varies along a wall in contrast to the previous works of the lattice-gas cellular automata. In addition, we present simulation results to compare our method to the existing and give an example in a microchannel with a high temperature gradient boundary condition by the lattice-gas cellular automata.

A Test of Coupled Soil Heat and Water Transfer Prediction under Transient Boundary Temperatures

Diffusion‐based coupled soil heat and water transfer theory includes capability to describe transient behavior. Unfortunately, laboratory tests of theory typically include a single initial water content distribution with a single set of boundary conditions, rather than providing a set of experimental conditions with a range of measurements for comparison with predictions. Agreement between theory and measurements can result from calibration, but this provides an incomplete test of theory. The objective of this work was to test diffusion‐based coupled heat and water transfer theory by comparing theory‐based predictions with measured transient temperature and water content distributions. Data from a single boundary condition were used for calibration of each of two soils, silt loam and sand. Subsequent testing was performed at additional boundary and initial conditions using measurements from the same soil. Results indicate that the theory can be calibrated for a single boundary condition with adjustment of soil saturated hydraulic conductivity and/or the vapor enhancement factor, which adjust the liquid and vapor fluxes, respectively. For silt loam, calibration reduced Root Mean Square Error (RMSE) by 67 and 18% for water content and temperature distributions, respectively. For sand, RMSE was reduced by 14 and 46% for water content and temperature, respectively. Using this calibration, there was agreement between calculated and measured distributions for additional boundary and initial conditions with RMSE ≤ 0.03 m3m−3 and 1.28°C for water content and temperature distributions, respectively. However, when the boundary temperature gradient was instantly reversed, noticeable differences occurred between measured and calculated patterns of heat and moisture redistribution. The theory described observations well when boundary temperature conditions were changed gradually, but results suggested a need for further development of coupled heat and water transfer theory combined with testing under transient conditions to make improvements in the description of transfer mechanisms.

Linear instability of broad baroclinic zones

Baroclinic energy conversions play a central role in mid-latitude synoptic-scale dynamics, drawing energy from the meridional temperature gradient and feeding it into the eddy dynamics. The physical mechanisms underlying these conversions can be investigated through the theory of small-amplitude instabilities growing on a steady basic state. In a recent study the author analysed the instability associated with a boundary temperature transition concentrated in a narrow front. This paper looks at the complementary problem of a broad baroclinic zone. The solution is applicable both to the Eady model and to the Phillips two-level quasi-geostrophic model. The reduction in the growth rate relative to an infinitely broad, homogeneous baroclinic mne is inversely proportional to the width of the baroclinic zone, as found in previous studies. The constant of proportionality is expressed in a simplified and more general form, related to the derivative with respect to zonal wave number of the complex phase speed of the homogeneous problem. If the flow is purely baroclinic the maximum growth rate is reduced compared with that of a homogeneous, infinitely broad frontal zone by a factor 1 - (2kmaxr)-1. where kmax is the wave number of the most unstable mode of the homogeneous problem and r is the width of the baroclonic zone. The width, r, is defined in terms of the second meridional derivative of the boundary temperature gradient evaluated at the maximum of the latter. Results in the literature give consistent, though less general, expressions for the growth rate, but various predictions for the structure of the waves. The numerical solutions show that as the jet width is reduced a new type of mode appears in which critical lines at the lid (tropopause) play an important role.

Deformation due to Mechanical and Thermal Sources in a Thermoelastic Body with Voids under Axi-symmetric Distributions

The Laplace and Hankel transforms have been employed to find the general solution of a homogeneous, isotropic, thermoelastic half-space with voids for a plane axi-symmetric problem. The application of a thermoelastic half-space with voids subjected to a normal force and a thermal source acting at the origin has been considered to show the utility of the solution obtained. To obtain the solution in a physical form, a numerical inversion technique has been applied. The results in the form of displacements, stresses, temperature distribution, and change in volume fraction field are computed numerically and illustrated graphically for a magnesium crystal-like material to depict the effects of voids in the theory of coupled thermoelasticity (CT) and uncoupled thermoelasticity (UCT) for an insulated boundary and a temperature gradient boundary.

Thermal transpiration for the linearized Boltzmann equation

AbstractThe phenomena of thermal transpiration due to the boundary temperature gradient is studied on the level of the linearized Boltzmann equation for the hard‐sphere model. We construct such a flow for a highly rarefied gas between two plates and also in a circular pipe. It is shown that the flow velocity parallel to the plates is proportional to the boundary temperature gradient. For a highly rarefied gas, that is, for a sufficiently large Knudsen number κ, the flow velocity between two plates is of the order of log κ, and the flow velocity in a pipe is of finite order. Our analysis is based on certain pointwise estimates of the solutions of the linearized Boltzmann equation. © 2006 Wiley Periodicals, Inc.

Velocity and Temperature Gradient Boundary Layer Formation During a Continuum Drawing in a Polymer Melt Chamber

ABSTRACT This paper presents a boundary layer model for the velocity and temperature gradient on the introduction of a continuum (wire, strip, tube, etc.) in a melt bath of polymer positioned before the plasto-hydrodynamic pressure unit prior to drawing or coating. Results are presented for the boundary layer thicknesses of velocity and temperature at different wire velocities. Also, the friction factor and Nusselt number have been given for polymer melt at different continuum velocities. The velocity and temperature gradient boundary layer thickness are also discussed in relation to the quality of hydrodynamic coating of wire.

Interaction due to Mechanical and Thermal Sources in Thermoelastic Half-Space with Voids

The dynamic response of a homogeneous, isotropic, thermoelastic half-space with voids subjected to time harmonic normal force and thermal source is investigated by applying the Fourier transform. The displacements, stresses, temperature distribution, and change in volume fraction field obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict the voids effect for the theory of coupled thermoelasticity and uncoupled thermoelasticity for an insulated boundary and temperature gradient boundary.