Transverse Temperature Gradient Research Articles

Influence of bottom supporting columns and cooling rate on the surface shape characteristics of sapphire substrates

The manufacturing process of sapphire substrates involves several key steps, including epitaxy, annealing, cutting, and processing. Among these, epitaxy and annealing are particularly crucial. The temperature variances along both the longitudinal and transverse axes within the furnace during the crystallization process play a significant role in determining the crystallization rate and internal structure of sapphire crystals. Furthermore, annealing sapphire serves to alleviate internal stress, enhance crystal structure, optimize physical properties, improve optoelectronic characteristics, enhance surface quality, and increase overall yield. This step is paramount in enhancing the performance and application value of sapphire materials. In order to investigate and optimize the effects of different thermal conductivities of support columns at the base and various annealing procedures on the surface characteristics of sapphire substrates, thereby improving product quality, this study conducted research by utilizing support columns made of different materials and carefully controlling the cooling rate parameters for sapphire. The findings revealed that using graphite as the base support column for the crystal furnace can reduce both the longitudinal and transverse temperature gradients within the furnace, consequently promoting crystal growth and enhancing the quality of sapphire ingots. Additionally, sapphire chips annealed using the rapid one-step annealing program exhibited the highest average warpage and bending rate variation, reaching 2.0 μm, and the average dislocation density was half that of conventionally produced chips, at 108.89 pits/cm2.

Temperature impact on acoustic wave reflection in quasi-collinear acousto-optic devices.

Quasi-collinear geometry is a special configuration of acousto-optic (AO) diffraction that applies the acoustic wave reflection from the AO cell input optical face and provides an extremely large interaction length for achieving abnormally high spectral resolution of AO tunable filters. As a result, it becomes possible to implement the multifrequency diffraction which has found important applications for laser pulse shaping. The operation of quasi-collinear AO devices in the multifrequency diffraction regimen is accompanied by the appearance of the longitudinal and transverse temperature gradients in the crystal, mainly due to the acoustic power absorption. Temperature changes the AO cell material stiffness moduli, affecting the characteristics of the incident and reflected acoustic waves (propagation velocities and walk-off angles), and the reflection condition in general. On the example of paratellurite crystal is shown that the AO cell heating near the reflecting facet leads to a deviation of the reflected acoustic beam propagation direction from that specified during the AO cell manufacturing. The deviation magnitude depends on the reflection geometry choice and, in the paratellurite, may exceed several degrees, which adversely affects the AO diffraction characteristics, reducing the AO interaction efficiency and distorting the transmission function shape. The reflected beam deviation may be compensated by means of choosing the angle between the AO cell reflecting face and the piezoelectric transducer face, taking into account the operating AO device thermal regimen.

Investigation of diabatic imparity involving asymmetric convection in two-dimensional longitudinal fins using lattice Boltzmann solver

This manuscript investigates the effect of diabatic imparity on two-dimensional (2-D) transient fins having naturally obtained non-linear variation of temperature-dependent conductivity. The diabatic imparity arises due to asymmetrical convection coefficient on the surfaces, implemented using different Biot numbers on each respective surface of the fin, which resembles pragmatic industrial applications. The transient solution of 2-D fin has been obtained using a Lattice Boltzmann (LB) solver, firstly, the suitability of 2-D LB formulation is established with the validity of the existing results, and subsequently extending the LB formulation for the present study. The numerical solution is determined under the two types of step-changing boundary conditions at the fin root having (i) heat flow and (ii) temperature. Results have been plotted graphically, and these include instantaneous isotherms, equilibrium isotherms, and threshold iso-temporal lines. Reported results facilitate the fin designer to examine the effect of diabatic imparity on the attainment of steady-state and occurrence of transverse temperature gradient on 2-D transient fin. The reported results provided are pertinent to the pragmatic application and are seldom reported in the literature. The outcomes of the present investigation are eminently informative to practising engineers and will serve as design monograms.

Numerical investigation of MHD mixed-convective flow and heat transfer within immiscible micropolar and nanofluids in a vertical channel

ABSTRACT This paper analyzed the influence of the Brownian motion and thermophoresis on the behavior of microrotation, linear velocity profile, heat transfer, mass diffusion upon a mixed convective flow of two non-miscible nanofluids in a vertical channel in the presence of a transverse magnetic field and temperature gradient. In the OY axis direction, the modified and coupled Navier-Stokes and nanoparticle volume fraction equations are solved using similarity variables. The solution is carried out and highlights non-dimensional numbers and parameters such as Hartmann number (Ha), Prandtl number (Pr), Eckert number (Ec), Reynolds number (Re), and non-analogous Grashof number (Grc) used in cases of mass transfer caused by natural convection and a concentration gradient. Additionally, the Grashof number (Gr) of heat transfer is used as a function of temperature gradients. The material parameter (K), thermophoresis parameter (MT), Brownian motion parameter (MB), etc. are considered. The algorithm of the final equations is plotted using the bvp4c function in @Matlab software, providing insightful graphs that demonstrate motivating effects on nanofluid flow behavior. The ascending and descending curves of velocity profiles are positively influenced by Lorentz force, thermophoretic phenomenon, and Brownian movement, thereby enhancing heat transfer. The results are thoroughly discussed and compared to previous studies.

Numerical prediction of thermal conductivity and thermal expansion coefficient of glass fiber-reinforced polymer hybrid composites filled with hollow spheres

The optimal performance of composites enriched with hollow spheres has been reported in contemporary literature, whereas their thermal properties have received less attention. In this regard, a finite element method (FEM)-based micromechanical model has been developed systematically to investigate the role of intra-matrix embedding of hollow spheres on the thermal conductivity and coefficient of thermal expansion (CTE) of unidirectional fiber-reinforced hybrid composites. In so doing, the concept of representative volume element (RVE) considers microstructures comprising an epoxy matrix, E-glass fiber, and E-glass hollow spheres, assuming perfect bonding (ideal interface) between the components and modified approximate periodic boundary conditions. By computing the longitudinal and transverse temperature gradients generated due to the application of uniform heat flux as well as the geometrical variation in RVE owing to temperature enhancement, thermal conductivity and CTE have been respectively determined. Comprehensive evaluations have been conducted to examine the effects of microstructural-level features, including fiber volume content and orientation, plus volume content and thickness of hollow spheres, on the effective thermal conductivity and CTE of pseudo-porous ternary E-glass/epoxy composites.

In situ experiments in microgravity and phase-field simulations of the lamellar-to-rod transition during eutectic growth

In recent experiments on the solidification of the binary eutectic alloy succinonitrile-(D)camphor carried out on board of the International Space Station (ISS), a transition from rod to lamellar patterns was observed for low growth velocities. The transition was interpreted in terms of a competition between a propagative instability of lamellae and a drift induced by a transverse temperature gradient. Phase-field simulations of a symmetric model alloy support this scenario: for a fixed transverse temperature gradient, the transition from rods to lamellae occurs for a critical composition at fixed velocity, and for a critical velocity at fixed composition. Since the alloy and control parameters used in experiments and simulations are different, our results strongly suggest that this morphological transition is generic for eutectic alloys.

A theory of rheological film condensation

The article provides a theoretical investigation of the laminar film-condensation of shear-thinning fluids onto an isothermal, vertical plate in the presence of gravity, interfacial shear, wall friction, and inertia. The liquid motion occurs toward gravity, overcoming the resistances of interfacial shear, wall friction, and inertia. The liquid motion induces momentum to the adjacent stagnant saturated vapor by interfacial shear. The vapor motion, in turn, influences the liquid film’s heat transfer and fluid dynamics. For film condensation, it is well-known that the film, along the length of the plate, can be grouped in two separate heat transfer regimes, viz. conduction-dominated regime and convection-dominated regime. For the first time, we have identified three distinct fluid dynamic regions across the film (viz. R1, R2, and R3) unique to power-law fluids. R1 is bounded between the condensing surface and the locus of Newtonian shear stress. R2 is bounded between the locus of Newtonian shear stress and the locus of zero shear stress. Beyond R2, R3 is stretched up to the liquid-vapor interface. The transverse temperature gradient is subtly different in these three fluid dynamic regions. We examine flow physics on a non-dimensional platform. The critical role of the power-law index in determining wall-friction and condensate’s mass flow rate and the impact of liquid Prandtl number in achieving the degree of subcooling has been nicely illustrated. We expose various limiting conditions for simplifying the robust mathematical theory. An analytical expression for the liquid’s longitudinal velocity has been derived, neglecting inertia and interfacial shear.

Interaction of a Sparce Particle Stratum with a Constantly Heated Plane in Presence of a Transverse Temperature Gradient

While modelling dispersions in containers or tubes it may be necessary to find distortions brought by the suspended particles in the temperature distribution in a vessel. Essential step of such a calculation is to determine of temperature field emerging when the particles are placed near the plane wall of the vessel. For simplicity one may suppose additionally that the carrying medium is stationary and that the particles are spherical. Solving this problem, the authors replace the plane by a fictitious particle that is mirror-positioned with respect to a given one. This allows to use multipole expansion for representation of the temperature that is a harmonic function in the case discussed. The obtained solution is used to find effective heat conduction coefficient of particles’ stratum placed in a half-space bounded by a plane with constant temperature. To do this, the authors average the temperature in the medium by the particles’ positions and compare the result with the solution of reference problem about temperature distribution in a half-space with a uniform stratum of other thermal conductance. The calculation is provided under the assumption that suspended spheres are placed rarely and therefore interact only with the plane but not with each other. A correction term is obtained that must be included in the expression for heat conduction coefficient if the total medium longitude in the direction orthogonal to the plane is finite.

Temperature gradient of composite PK girder based on monitoring and long-term simulation

Bridge structures exposed to the environment are inevitably affected by the thermal load which is closely related to the type of section. In this study, the temperature field of a composite Pasco-Kennewick (PK) section girder was monitored in situ for the first time. Meanwhile, a refined finite-element model (FEM) of the temperature field was established and verified with measured temperatures. The temperature distribution and variation characteristics were analyzed using measured temperatures. On this basis, the simplified profiles of vertical temperature gradient (VTG) and transverse temperature gradient (TTG) were proposed. The representative values of temperature differences with a 100-year return period were predicted by extreme value analysis (EVA) with the samples of temperature differences obtained through 23-year numerical simulation. Finally, comparisons were made between the temperature gradients of composite PK section and the recommendations in current specifications. The results show that the vertical temperature distributions and variations on different webs have apparent differences. Meanwhile, remarkable transverse temperature differences exist on the top plate and bottom plate. Five VTGs and four TTGs are proposed with totally different simplified profiles. The representative values of positive temperature differences in TTGs are larger than those in VTGs, as well as the absolute values of negative temperature differences. The proposed temperature gradients are significantly distinct from the recommendations in current specifications. These temperature gradients are expected to improve the stipulation about the temperature action of bridges.

The Multi-Scale Model Method for U-Ribs Temperature-Induced Stress Analysis in Long-Span Cable-Stayed Bridges through Monitoring Data

Temperature is one of the important factors that affect the fatigue failure of the welds in orthotropic steel desks (OSD) between U-ribs and bridge decks. In this study, a new analysis method for temperature-induced stress in U-ribs is proposed based on multi-scale finite element (FE) models and monitoring data First, the long-term temperature data of a long-span cable-stayed bridge is processed. This research reveals that a vertical temperature gradient is observed rather than a transverse temperature gradient on the long-span steel box girder bridge with tuyere components. There is a linear relationship between temperature and temperature-induced displacement, taking into account the time delay effect (approximately one hour). Then, a multi-scale FE model is established using the substructure method to condense each segment of the steel girder into a super-element, and the overall bridge temperature-induced displacement and temperature-induced stress of the local U-rib on the OSD are analyzed. The agreement between the calculated temperature-induced stresses and measured values demonstrates the effectiveness of the multi-scale modeling strategy. This approach provides a valuable reference for the evaluation and management of bridge safety. Finally, based on the multi-scale FE model, the temperature-induced strain distribution of components on the OSD is studied. This research reveals that the deflection of the girder continually changes with the temperature variation, and the temperature-induced strain of the girder exhibits a variation range of approximately 100 με.

Investigation on Effect of Reflective Coating on Temperature Field of CRTS Ⅱ Slab Ballastless Track under Sunlight

The internal temperature variation of ballastless track is very complicated under the effect of a sunlit environment, and there are serious transverse and vertical temperature gradients, which will cause cracking and deformation of the structure. In this paper, an ANSYS temperature effect analysis model for ballastless track, considering box girder structure, is established based on the environmental information of the bridge and the characteristics of the structural system. The model considers the influence of solar radiation intensity, wind speed, air temperature, geographical location, bridge orientation, material parameters, and other factors on the boundary conditions, and can meet the needs of the daylight temperature response analysis and calculation of any complex bridge structure. On this basis, the effect and applicability of a solar reflective coating on ballastless track cooling are studied. The results showed that the calculated results of the finite element model agree well with the measured results. Under the high-temperature conditions in summer, sunlight and ambient temperature mainly have significant effects on the temperature and temperature gradient of the track slab, and the maximum vertical temperature gradient reaches 74.48 °C/m. The reflective coating can significantly reduce the track slab’s temperature and vertical temperature gradient, with a maximum temperature gradient reduction of 34%. The transverse temperature gradient of the track slab can be reduced by up to 54% by further application of the side reflective coating. This study can promote the application of reflective coatings on high-speed railway track structures.

The impact of technological parameters of the torch to physical and chemical properties of a gas-thermal burner for spraying ultra-high molecular weight polyethylene

The values of the heat flux density, transverse and longitudinal temperature gradients of the gas-thermal burner torch, the type of reaction during the combustion in various modes (reducing, neutral, oxidizing) depending on the mass fractions of the fuel and oxidizer burning have been determined in this paper. The significant role of the torch temperature as one of the most important parameters determining the quality of polymer coatings obtained by the gas-thermal method has been established. A spatial model of a gas-thermal burner has been designed, which allows to obtain thermal modes at specified technological parameters. A physical model of the interactions “torch-polymer particle”, “thermal jet – base” has been developed. The necessary density of the torch heat flux for the complete melting of ultrahigh molecular weight polyethylene (UHMWPE) particles not exceeding the temperature threshold of destruction has been determined. The required rate of introduction the UHMWPE powders into the burner flame has been also determined. Based on the calculations of the “torch-polymer particle interaction”, the optimal geometry of the torch, the particles trajectory in the torch and the spraying distances have been determined.

Abnormal Seebeck Effect in Vertically Stacked 2D/2D PtSe2 /PtSe2 Homostructure.

When a thermoelectric (TE) material is deposited with a secondary TE material, the total Seebeck coefficient of the stacked layer is generally represented by a parallel conductor model. Accordingly, when TE material layers of the same thickness are stacked vertically, the total Seebeck coefficient in the transverse direction may change in a single layer. Here, an abnormal Seebeck effect in a stacked two-dimensional (2D) PtSe2 /PtSe2 homostructure film, i.e., an extra in-plane Seebeck voltage is produced by wet-transfer stacking at the interface between the PtSe2 layers under a transverse temperature gradient is reported. This abnormal Seebeck effect is referred to as the interfacial Seebeck effect in stacked PtSe2 /PtSe2 homostructures. This effect is attributed to the carrier-interface interaction, and has independent characteristics in relation to carrier concentration. It is confirmed that the in-plane Seebeck coefficient increases as the number of stacked PtSe2 layers increase and observed a high Seebeck coefficient exceeding ≈188 µV K-1 at 300 K in a four-layer-stacked PtSe2 /PtSe2 homostructure.

CONV-3D Code-Aided Calculation of the Free-Convective Flow Parameters of Lead–Bismuth Alloy in a Cavity with a Transverse Temperature Gradient

CONV-3D Code-Aided Calculation of the Free-Convective Flow Parameters of Lead–Bismuth Alloy in a Cavity with a Transverse Temperature Gradient

CFD simulation aided glass quality and energy efficiency analysis of an oxy-fuel glass melting furnace with electric boosting

• Inexpensive coupled CFD simulations of glass furnace with verified numerical models. • Link between specific power input and glass quality was established and quantified. • Space utilisation increased when specific heat input over free glass surface increased. • Space utilisation increased when pull rate was reduced or fuel mass flow increased. Determining glass quality has been a focal point of CFD studies of glass furnaces for several decades. Previous research identified the utilisation of glass tank space by inhomogeneities as a crucial quantity for the scrutinization of glass quality. However, the majority of previous CFD based parametric studies were conducted on idealized glass tank models, which neglected the influence of the turbulent gas phase in the combustion chamber on the heat transfer. Consequently, not all of the findings are universally applicable in practical settings. Hence, the present work aims at closing this research gap by introducing two improvements over the current state-of-the-art in a parametric study by: 1) Employing a verified, computationally inexpensive, coupled numerical model in the complete CFD simulation of a glass melting furnace and 2) Establishing and quantifying the link between variations of the specific power input and common glass quality indicators. It was shown that due to the cross-fired configuration of the burners, increasing the specific power input over the free glass surface resulted in higher transversal velocities and temperature gradients, which favoured the development of helical flow in the melt and thus increased the critical residence time and by extension, the glass quality.

Evaluation of Heat Transfer Rates through Transparent Dividing Structures

In this paper, heat transfer and airflow in the gap between the panes of a central part of a double-glazed window were investigated using mathematical modeling. It has been shown that the cyclical airflow regime, in the form of ascending and descending boundary layers, loses stability and changes to a vortex regime under certain conditions depending on the gap width, transverse temperature gradient, inclination angle and window height, as in Rayleigh–Bernard convection cells. The study made it possible to determine the critical values of the Rayleigh number (Ra) at which the air flow regime in the gap between the panes of a window changes (in the range of values 6.07 × 103 < Ra < 6.7 × 103). As a result of the modeling, the values of the thermal resistance of a central part of double-glazed window were determined as a function of the width of the gap between the panes, the angle of inclination and the transverse temperature gradient.

Ferromagnetic nematics: A macroscopic two-fluid description.

We present the macroscopic dynamic description of a ferromagnetic nematic, where the nematic part and the magnetic part can move relative to each other. The relative velocity that describes such movements can be a slowly relaxing variable. Its couplings to the nematic and the magnetic degrees of freedom are particularly interesting since the symmetry properties (behavior under spatial inversion and time reversal) of the three vectorial quantities involved are all different. As a consequence, a number of new crosscouplings involving the relative velocity exist. Some of them are discussed in more detail. First, we demonstrate that transverse temperature gradients generate transverse relative velocities and, vice versa, that transverse relative velocities give rise to temperature gradients. Second, we show that a simple shear flow in the relative velocity with the preferred direction in the shear plane can lead in a stationary situation to a tilt of the magnetization.

Non-isothermal effects in the slippage condition and absolute viscosity for an electroosmotic flow

In this work, we have developed a novel asymptotic analysis using perturbation techniques for an electroosmotic flow in a rectangular microchannel, considering that the absolute viscosity η is a function of temperature; a situation that affects also the slip condition at the walls of the microchannel, u=−sη∂u∂n. The physical importance of this temperature dependence is based on the presence of the applied external electric field on the electrolyte solution, which originates the Joule heating effect that disturbances the isothermal hydrodynamic behavior. The above leads to a significant increase of the volumetric flow rate for this non-isothermal condition in comparison to the purely isothermal electroosmotic flow. This result is simultaneously controlled by the heat losses to the ambient and the slip effect: the lower the presence of the heat dissipation mechanism on the outer walls of the microchannel and the higher the sliding condition, the higher the values of the volumetric flow rate. The above trend differs substantially from the isothermal case and finds its justification in the recognition of the presence of the Joule heating effect that induces significant longitudinal and transverse temperature gradients along the microchannel. Considering the proper limitations of the asymptotic analysis, we compare the present asymptotic results with a full numerical solution of the governing equations, which are composed of the continuity, momentum, and energy equations for the electrolyte flow, together with the Poisson–Boltzmann.

Seebeck effect in nanomagnets

We present a theory of the Seebeck effect in nanomagnets with dimensions smaller than the spin diffusion length, showing that the spin accumulation generated by a temperature gradient strongly affects the thermopower. We also identify a correction arising from the transverse temperature gradient induced by the anomalous Ettingshausen effect and an induced spin-heat accumulation gradient. The relevance of these effects for nanoscale magnets is illustrated by ab initio calculations on dilute magnetic alloys.

Coexistence of rod-like and lamellar eutectic growth patterns

We present the first observations of a large-scale coexistence between rod-like and lamellar eutectic growth patterns during directional solidification of a eutectic alloy. In situ experiments with real-time optical monitoring were carried out under microgravity onboard the International Space Station (ISS). We used the transparent succinonitrile-d,camphor eutectic alloy that ordinarily forms rod-like patterns. At low growth velocity, short lamellae stabilized at the contact line with a sample glass wall. In the presence of a controlled transverse temperature gradient, the coupled-growth pattern experienced a global drift along an inclined isotherm, and a stable lamellar domain spread over the solidification front. The propagative nature of the lamellar-to-rod transition was evidenced. The advance of the lamellar/rod domain boundary was determined by a slowly amplifying varicose instability of the lamellae. On a large scale, the domain boundary underwent a dynamic faceting.