Temperature Gradient Parameter Research Articles

Generalized mean state of the isothermal Darcy–Benard problem and its instability onset

Thermally-driven natural convection is theoretically explored in the present work within a porous layer with respect to the Darcy’s law. The usual non circulating basic cellular flow between two infinitely long horizontal Darcy porous plates leads to generalized basic state considering the isothermal boundary conditions leading to the Hadley flow configuration. Such a motion is governed by a circulatory flow together with a temperature both varying along the horizontal axis. Hence, besides the buoyancy Rayleigh parameter, yet another parameter appears dominating the evolution of basic cellular circulation and thermal progress. Instability onset of this basic state is targeted based on the linear stability analysis of small normal modes. The resulting 3D instability system of equations is treated numerically and the stationary modes leading to convective neutral stability are determined. The found eigenvalues are also justified to be those deviating from the well-known no-flow Darcy porous solution through an asymptotic perturbation method in the special circumstances. The bounds of neutral stability curves in regard to the longitudinal, oblique and transverse modes are thoroughly investigated and it is shown that longitudinal modes are always the most unstable ones, while the transverse and oblique modes having finite encapsulated zone of instability can undergo a complete stability after a threshold value of horizontal temperature gradient parameter.

Generation of O-Mode in the Presence of Ion-Cyclotron Drift Wave Turbulence in a Nonuniform Plasma

This study aims to investigate the effect of ion-cyclotron drift wave turbulence on the generation of ordinary mode (O-mode) in the presence of density and temperature gradients. For this, a Vlasov plasma is considered where a resonant, and non-resonant modes are considered to be present in the system. Here, the non-resonant mode is a perturbation caused by O-mode in a quasi-steady state of plasma, which is characterised by the presence of low frequency ion-cyclotron resonant mode waves. The interaction between these waves is studied by the Vlasov-Maxwell set of equations and a modified Maxwellian-type distribution function for particles that includes the external force field and associated density and temperature gradient parameters . The study analyses the growth rate of electromagnetic O-mode at the expense of ion-cyclotron drift wave energy and the associated impact of the density and temperature gradient. This model uses the linear response theory on weakly turbulent plasma, evaluates the responses due to turbulent and perturbed fields, and obtains the nonlinear dispersion relation for O-mode.

Statistical analysis and Neural Network Modeling of functionally graded porous nanobeams vibration in an elastic medium by considering the surface effects

The natural frequency of a clamped–clamped functionally graded porous (FGP) nanobeam is predicted in this study. Material distribution is considered based on monotonous, symmetric, and non-symmetric patterns in the thickness direction. This paper deals with governing equations of nanobeams based on third-order shear deformation beam theory in conjunction with nonlocal strain gradient theory (NSGT) and surface effects. Artificial neural network (ANN) is utilized to predict the effect of eight parameters including temperature gradient, residual surface stress, porosity distribution pattern, porosity parameter, nonlocal and material length scale parameters, and elastic and shear coefficients of Pasternak foundation on the fundamental frequency of FGP nanobeam. Different training methods are selected to simulate input and output dependency. Results show that the dependency of the natural frequency is inverse to the temperature gradient and nonlocal parameter in the sense that increasing these factors will decrease the natural frequency. Also, increasing the material length scale parameter grows the effect of the nonlocal parameter. Residual surface stress, material length scale, and Pasternak foundation parameters have a direct effect on the output and among them; the material length scale parameter has a more noticeable effect. Finally, it was found that by increasing the porosity parameter value, the diversity of natural frequency levels up drastically

Parametric Stability Analysis of a Spring Attached, Pre-Twisted, Rotating Sandwich Beam with Tip Mass and Viscoelastic Support

This paper inspects the influence of a spring attachment provided on the top elastic layer on the stability of a pre-twisted, rotating sandwich beam having viscoelastic supports at the root under the impact of a periodically varying axial load. The spring is deployed on the beam to achieve more strength to weight ratio without compromising the stability. The beam is exponentially tapered, and a tip mass is at the free end to represent the rotating members in various types of machinery as closely as possible. The ruling equations and inter-related boundary conditions are attained by applying Hamilton’s principle. To obtain the solution, a matrix equation was developed through the assumed-mode variational method. The resulting matrix equation was converted to a coupled Hill’s equation of parametric vibration through the modal matrix corresponding to the free vibration problem. Finally, static and dynamic stability graphs were obtained for several system parameters such as position and length of the attached spring on the top elastic layer, the mass of the spring attachment, stiffness of the spring attachment, angle of pre-twist, tip mass, taper parameter, temperature gradient parameter, setting angle, viscoelastic spring stiffness, etc. to analyze their impact on the system’s stability. Saito and Otomi conditions were used to obtain dynamic stability plots. Greater stability is achieved due to the spring attachment on the top of the top elastic layer.

The growth and characterization of six inch lithium niobate crystals with high homogeneity

On a self-designed automatic diameter control system, large diameter (6 inch) LiNbO3 crystals without cracks are successfully grown by choosing a suitable temperature gradient, starting composition, and growth parameters with the Czochralski method.

Stability Study of a Sandwich Beam with Asymmetric and Non-uniform Configuration Supported Viscoelastically Under Variable Temperature Grade

The end conditions, temperature gradient and geometric parameters affect the system stability. This research work concerns with the parametric instability study of a non-uniform asymmetric sandwich beam supported viscoelastically at the ends acted upon by a harmonic axial load and a variable temperature grade which is more appropriate along with a constant temperature grade. Hamilton’s energy principle is used to develop the equations of motion and associated end conditions. Then the non-dimensional form of the equation of motion is obtained. Galerkin’s process is used to find a set of Hill’s equations. The parametric instability regions are acquired by means of Saito-Otomi conditions. The consequences of taper parameter, uniform as well as variable temperature grade, shear parameter, spring parameters and spring loss factors on the instability regions are examined and represented by a number of plots. The results reveal that rise in the values of thermal gradient for bottom layer and shear parameter, make the beam more stable against harmonic load. Increase in the values of taper parameters and thermal gradient for top layer reduce the flexural rigidity of the system, hence worsen the system stability. The dynamic instability of the system reduces with increase in the values of spring loss factors and spring parameters.

Influence of transverse temperature gradient on the propagation of triple flames in porous channels

We present in this paper a numerical simulation to the problem of triple flame propagation in a porous-walls channel in the presence of a temperature gradient across the channel. The problem has been formulated using the thermo-diffusive approximation and then solved numerically using finite elements method. The study showed that temperature gradient plays a crucial role on the existence and propagation of triple flames. More precisely, the effect of temperature gradient on the flame propagation was found to: (i) cause the flame to exist only for a limited range of values of the temperature gradient parameter, (ii) establish multiplicity of solutions each of them characterizes unique combustion regimes, (iii) modifies the flame shape from the usual triple flame shape when the temperature gradient is large, and finally (iv) enhance the reactivity of the underlying mixture, but on the other hand will have serious implications on the safety of the combustion chamber.

Asymptotic analysis to the effect of temperature gradient on the propagation of triple flames

We study asymptotically in this paper the influence of the temperature gradient across the mixing layer on the propagation triple flames formed inside a porous wall channel. The study begins by formulating the problem mathematically using the thermo-diffusive model and then presents a thorough asymptotic analysis of the problem in the limit of large activation energy and thin flames. Analytical formulae for the local burning speed, the flame shape and the propagation speed in terms of the temperature gradient parameter have been derived. It was shown that varying the feed temperatures can significantly enhance the burning of the reactants up to a critical threshold, beyond which no solutions can be obtained. In addition, the study showed that increasing the temperature at the boundaries will modify the usual triple structure of the flame by inverting the upper premixed branch and extending it to the boundary, which may have great implications on the safety of the adopted combustion chambers.

Wind Regimes above and below a Temperate Deciduous Forest Canopy in Complex Terrain: Interactions between Slope and Valley Winds

The thermally driven wind over mountainous terrains challenges the estimation of CO2 exchange between forests and the atmosphere when using the eddy covariance technique. In this study, the wind regimes were investigated in a temperate deciduous forested valley at the Maoershan site, Northeast China. The wind direction above the canopy was preferentially up-valley in the daytime and down-valley in the nighttime, corresponding to the diurnal patterns of above-canopy temperature gradient and stability parameter. In both leaf-on and -off nighttime, a down-valley flow with a maximum velocity of 1~3 m∙s−1 was often developed at 42 m above the ground (2.3-fold of the canopy height). However, the below-canopy prevailing wind was down-slope in the night, contrast to the below-canopy temperature lapse and unstable conditions. This substantial directional shear illustrated shallow slope winds were superimposed on larger-scale valley winds. As a consequence, the valley-wind component becomes stronger with increasing height, indicating a clear confluence of drainage flow to the valley center. In the daytime, the below-canopy wind was predominated down-slope due to the temperature inversion and stable conditions in the leaf-on season, and was mainly up-valley or down-slope in the leaf-off season. The isolation of momentum flux and radiation by the dense canopy played a key role in the formation of the below-canopy unaligned wind and inverse stability. Significant lateral kinematic momentum fluxes were detected due to the directional shear. These findings suggested a significant interaction between slope and valley winds at this site. The frequent vertical convergence / divergence above the canopy and horizontal divergence/convergence below the canopy in the nighttime / daytime is likely to induce significant advections of trace gases and energy flux.

Control of solid–liquid interface morphology and radial composition distribution: TbDyFe single crystal growth

Optical zone melting method was adopted for the crystal growth of TbDyFe giant magnetostrictive alloys. Effects of zone-melting length and growth velocity on the quenched solid–liquid interface bending direction, curvature and corresponding radial composition distribution were investigated both experimentally and theoretically. By increasing the zone-melting length, the solid–liquid interface morphology was evolved from convex to flat and then to concave. In the case of convex solid–liquid interface, the curvature of the interface was decreased by increasing the growth velocity. When the initial interface was flat, changing growth velocity had no effect on the interface morphology under our experimental conditions. Accordingly, quite different radial composition distributions were monitored. A 〈110〉 axial oriented twinned-single crystal of TbDyFe alloy without radial composition segregation was obtained through controlling the solid–liquid interface morphology. Solid–liquid interface curvature functions were proposed with the parameters of zone-melting length, growth velocity, temperature gradient and other thermal physical parameters. Furthermore, functions of corresponding radial composition distribution were also given. The theoretical analysis shows that, the curvature of solid–liquid interface and the rate of radial composition segregation are determined by zone melting length, growth velocity and temperature gradient. Theoretical analysis results matched well with the experiments.

Analysis of Vertical Turbulent Heat Flux Limit in Stable Conditions with a Local Equilibrium, Turbulence Closure Model

Assuming that the vertical turbulent heat flux vanishes at extremely stable conditions, one should expect its maximal absolute value to occur somewhere at moderate stability, between a neutral and extremely stable equilibrium. Consequently, in some situations duality of solutions may be encountered (e.g. two different values of temperature difference associated with the same values of heat flux and wind speed). A quantitative analysis of this feature with a local equilibrium Reynolds-stress model is presented. The fixed-wind / fixed-shear maximum has been identified both in the bulk and in single-point flux–gradient relationships (that is, in the vertical temperature gradient and wind-shear parameter domain). The value of the Richardson number corresponding to this maximum is derived from the model equations. To study the possible feedback in strongly stable conditions, weak and intense cooling scenarios have been simulated with a one-dimensional numerical, high-resolution atmospheric boundary-layer model. Despite the rapid cooling, flow decoupling at the surface has not been observed; instead, a stability-limited heat flux is maintained, with a gradual increase of the Richardson number towards the top of the turbulent layer, with some signs of oscillatory behaviour at intermediate heights. Vertical changes of wind shear and the Brunt–Väisälä frequency display a remarkably non-monotonic character, with some signs of a gradually developing instability.

Stability of narrow-gap Taylor–Dean flow with radial heating: Stationary critical modes

A linear stability analysis for the Taylor–Dean flow, a viscous flow between concentric horizontal cylinders with a constant azimuthal pressure gradient, keeping the cylinders at different temperatures, when the inner cylinder is rotating and outer one is stationary has been implemented. The analysis is made under the assumption that the gap spacing between the cylinders is small compared to the mean radius. A parametric study covering wide ranges of β, a parameter characterizing the ratio of representative pumping and rotation velocities and N, the parameter characterizing the direction of temperature gradient is conducted. The eigenvalue problem is solved by differential transform method using unit disturbance scheme along with shooting technique. Emphasis is given to the occurrence of critical stability for the onset of instability by finding the intersection of the two neutral curves for the inner and outer part in a range of values of the radial temperature gradient parameter N,−1.25<N<0.75. We find that the existence of such critical point of stability is realizable near N=−0.995. It is found that with the introduction of radial heating, the discontinuity in critical Taylor number is not seen for N (=−0.75,−1.25). The most stable state occurs for β=βmax (=−3.62,−3.66,−3.95,−4.2) at which maximum of critical Taylor number occurs corresponding to N (=0.25,0,−0.75,−1.25) and can be concluded that for N<0, the most stable state occurs, when βmax<−3.666 (the value of βmax near which the maximum Taylor number occurs, when N=0).

Effect of radial temperature gradient on the stability of Taylor–Dean flow between two arbitrarily spaced concentric rotating cylinders

The effect of a radial temperature gradient on the stability of Taylor–Dean flow of an incompressible viscous fluid between two arbitrarily spaced concentric rotating circular cylinders driven by a constant azimuthal pressure gradient is studied. Here the ratio of representative pumping and rotation velocities β is varied from −6.1613 to 1.00 and both positive and negative values of the temperature gradient parameter N are considered, where N depends on the temperature differences T2−T1 between the outer and inner cylinders. The linearized stability equations form an eigenvalue problem which is solved by using a classical Runge–Kutta scheme combined with a shooting technique, termed unit disturbance method. It is found that as the gap width between the cylinders increases, the critical Taylor number progressively increases for given values of β and N. It is also found that for given values of η (the ratio of the radii of inner and outer cylinders) and β, the flow becomes more and more unstable with increase in N(>0). In the present work, emphasis is given on the point as to whether the two neutral stability curves cross at some point for given value of N for which the flow is completely stable.

Thermophoresis of colloids by mesoscale simulations

The motion of a colloid induced by a temperature gradient is simulated by means of multiparticle collision dynamics, a mesoscale simulation technique. Two algorithms to quantify the thermophoretic behavior are employed and contrasted. The validity of the methods is verified as a function of the temperature gradient, system size, and algorithm parameters. The variation of the solvent–colloid interaction from attractive to purely repulsive interestingly results in the change of the colloid behavior from thermophobic to thermophilic.

Variations of microhardness with solidification parameters and electrical resistivity with temperature for Al–Cu–Ag eutectic alloy

Al–Cu–Ag eutectic alloy was directionally solidified upwards with different growth rates (1.83–498.25 μm/s) at a constant temperature gradient (8.79 K/mm) and with different temperature gradients (3.99–8.79 K/mm) at a constant growth rate (8.30 μm/s) by using a Bridgman type directional solidification apparatus. The dependence of microhardness (HV) on the growth rate (V), temperature gradient (G) and microstructure parameter (λ) were found to be HV = k 1 V 0.10, HV = k 2 G 0.13 and HV = k 3 λ −0.22, respectively. The electrical resistivity of the Al–Cu–Ag eutectic cast alloy increases linearly with the temperature in the range of 300–780 K. The enthalpy of fusion and specific heat change during melting for same alloy were also determined to be 223.8 J/g, and 0.433 J/g K, respectively by a differential scanning calorimeter from heating curve during the transformation from eutectic solid to eutectic liquid.

An uncountable number of solutions for a BVP governing Marangoni convection

This paper investigates a boundary value problem (BVP) governing Marangoni convection over a flat surface. The BVP involves a temperature gradient parameter k > − 1 . Previous numerical and analytical studies report the existence of one solution for each value of k . Here we show that the nature of the solutions varies greatly depending on the value of k . For each − 1 < k < − 1 / 2 we prove that an uncountable number of solutions to the BVP exist. For − 1 / 2 ≤ k < 0 a unique solution exists. For k ≥ 0 we prove the existence of a solution but, based on numerical integration of the differential equation, conjecture the existence of precisely two solutions when k > 0 .

Compressed ion temperature gradient turbulence in diverted tokamak edge

It is found from a heat-flux-driven full-f gyrokinetic particle simulation that there is ion temperature gradient (ITG) turbulence across an entire L-mode-like edge density pedestal in a diverted tokamak plasma in which the ion temperature gradient is mild without a pedestal structure, hence the normalized ion temperature gradient parameter ηi=(d log Ti/dr)/(d log n/dr) varies strongly from high (&amp;gt;4 at density pedestal top/shoulder) to low (&amp;lt;2 in the density slope) values. Variation of density and ηi is in the same scale as the turbulence correlation length, compressing the turbulence in the density slope region. The resulting ion thermal flux is on the order of experimentally inferred values. The present study strongly suggests that a localized estimate of the ITG-driven χi will not be valid due to the nonlocal dynamics of the compressed turbulence in an L-mode-type density slope. While the thermal transport and the temperature profile saturate quickly, the E×B rotation shows a longer time damping during the turbulence. In addition, a radially in-out mean potential variation is observed.

Optical diffractometry

Interference of light has numerous metrological applications because the optical path difference (OPD) can be varied at will between the interfering waves in the interferometers. We show how one can desirably change the optical path difference in diffraction. This leads to many novel and interesting metrological applications including high-precision measurements of displacement, phase change, refractive index profile, temperature gradient, diffusion coefficient, and coherence parameters, to name only a few. The subject fundamentally differs from interferometry in the sense that in the latter the measurement criterion is the change in intensity or fringe location, while in the former the criterion is the change in the visibility of fringes with an already known intensity profile. The visibility can vary from zero to one as the OPD changes by a half-wave. Therefore, measurements with the accuracy of a few nanometers are quite feasible. Also, the possibility of changing the OPD in diffraction allows us to use Fresnel diffraction in Fourier spectrometry, to enhance or suppress diffracted fields, and to build phase singularities that have many novel and useful applications.

Effect of pressure work on free convection flow along a vertical circular cone with suction and variable surface temperature

AbstractFree convection laminar flow from a vertical circular cone maintained a variable surface temperature with suction and pressure work effects has been investigated. The governing boundary layer equations are transformed into a non‐dimensional form and the resulting nonlinear system of partial differential equations are reduced to local non‐similarity equations. The governing non‐similarity equations are then solved numerically by implicit finite difference method together with Keller box scheme. Numerical results are presented in terms of velocity and temperature profiles of the fluid as well as the local skin‐friction coefficients and the local heat transfer rate for different values of Prandtl number Pr, suction parameter ξ, temperature gradient parameter n and the pressure work parameter ∈. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Sea-surface temperature gradients across blue whale and sea turtle foraging trajectories off the Baja California Peninsula, Mexico

Sea-surface temperature (SST) fronts are integral to pelagic ecology in the North Pacific Ocean, so it is necessary to understand their character and distribution, and the way these features influence the behavior of endangered and highly migratory species. Here, telemetry data from sixteen satellite-tagged blue whales (Balaenoptera musculus) and sea turtles (Caretta caretta, Chelonia mydas, and Lepidochelys olivacea) are employed to characterize ‘biologically relevant’ SST fronts off Baja California Sur. High residence times are used to identify presumed foraging areas, and SST gradients are calculated across advanced very high resolution radiometer (AVHRR) images of these regions. The resulting values are compared to classic definitions of SST fronts in the oceanographic literature. We find subtle changes in surface temperature (between 0.01 and 0.101C/km) across the foraging trajectories, near the lowest end of the oceanographic scale (between 0.03 and 0.31C/km), suggesting that edge-detection algorithms using gradient thresholds 40.101C/km may overlook pelagic habitats in tropical waters. We use this information to sensitize our edge-detection algorithm, and to identify persistent concentrations of subtle SST fronts in the Northeast Pacific Ocean between 2002 and 2004. The lower-gradient threshold increases the number of fronts detected, revealing more potential habitats in different places than we find with a higher-gradient threshold. This is the expected result, but it confirms that pelagic habitat can be overlooked, and that the temperature gradient parameter is an important one. r 2006 Elsevier Ltd. All rights reserved.