Model Of Thermal Convection Research Articles

Onset of Plate Motion in the Presence of Chemical Heterogeneities in the Mantle and the Effect of Mantle Temperature

AbstractChemical heterogeneities of various origins have been observed in the Earth's mantle. Their assumed higher density acts on the style of mantle convection and therefore, as tectonic plates form the highly viscous upper boundary layer of mantle convection, the onset of surface motion is also affected by chemical heterogeneities. We perform 2D basally heated thermochemical mantle convection models which initially include layers of dense material at different mantle depths. In comparison to purely thermal convection models, the onset of first plate motion is delayed. This delay is even more pronounced, the deeper the location of dense material, the larger its volume and the higher its density. Additionally, we varied the starting temperature of our models. In an initially hot mantle, a strong temperature‐dependent viscosity contrast between the mantle and cold surface leads to a cold, highly viscous plate (stagnant lid). For an initially cold mantle, rising plumes first need to transport basal heat upwards to create a sufficient viscosity contrast. Consequently, the formation and subsequent breaking of the stagnant lid is delayed. Considering a hotter mantle after Earth's magma ocean phase, we find that plate motion can occur within approximately the first 0.5 Gyr of solid‐state convection if no chemical structures are present or for dense material situated at the surface. Deep chemical heterogeneities delay the onset by at least one order of magnitude. Furthermore, the early surface motion will have been more erratic than todays stable plate motion, probably with a few single subduction events.

Towards stochastic subgrid‐scale modeling of turbulent thermal convection in an under‐resolved off‐lattice Boltzmann method

AbstractA characteristic‐based Off‐Lattice Boltzmann Method (OLBM) and a stochastic One‐Dimensional Turbulence (ODT) model is utilized for numerical simulation of turbulent thermal convection. Standalone ODT results for low‐order statistics are compared with those from various eddy‐viscosity‐based subgrid‐scale models utilized in Large‐Eddy Simulations (LES) with OLBM. The predictive capabilities of both approaches are discussed by comparison with available reference Direct Numerical Simulation (DNS) results. All turbulence models are able to predicted the mean temperature, but fail to fully capture fluctuations. While the OLBM aims to represent large‐scale structures, it misses some constitutional small‐scale fluctuations. By contrast, the reduced‐order ODT model captures small‐scale fluctuations in the vicinity of the wall, but cannot resolve the organized bulk flow. Here, the modeling capabilities of both OLBM and ODT as standalone tools are discussed. On this basis, a strategy for the incorporation of ODT as wall model in OLBM is suggested.

Dynamics of the (2+1)$$ \left(2+1\right) $$‐dimensional coupled cubic–quintic complex Ginzburg–Landau model for convecting binary fluid: Analytical investigations and multiple‐soliton solutions

The ‐dimensional coupled cubic–quintic complex Ginzburg–Landau equations ( ‐DCC‐QCGLEs) can simulate a variety of binary fluid thermal convection characteristics, containing complex parameters. The analysis of pattern formation in chaotic and nonlinear dynamical systems can benefit greatly from the use of this thermal convection model. The primary goal of this study is to find analytical solutions for some recent advances that have been made for Rayleigh–Bénard convection by applying the ‐DCC‐QCGLEs model for slowly varying spatio‐temporal amplitudes of the wave motion. In addition, novel traveling solitary wave solutions for the model equation are derived using a very useful method to investigate how complex physical coefficients affect the profiles of propagating waves. Furthermore, we introduce the WTC‐Kruskal algorithm of the Painlevé methodology to examine the integrability of the ‐DCC‐QCGLEs and the truncated Painlevé expansion is used to extract the Bäcklund transform, from which new solitary solutions can be acquired. The results also demonstrated a good agreement with previous works and were more significant and accurate in two and three dimensions of the proposed model. Finally, the computational results indicate that the effects of the physical parameters of the considered equations can be demonstrated by utilizing 2D and 3D graphics for different values of these parameters.

Oxygen-Driven Enhancement of the Electron Correlation in Hexagonal Iron at Earth's Inner Core Conditions.

Earth's inner core (IC) consists of mainly iron with some light elements. Understanding its structure and related physical properties has been elusive as a result of its required extremely high pressure and temperature conditions. The phase of iron, elastic anisotropy, and density-velocity deficit at the IC have long been questions of great interest. Here, we find that the electron correlation effect is enhanced by oxygen and modifies several important features, including the stability of iron oxides. Oxygen atoms energetically stabilize hexagonal-structured iron at IC conditions and induce elastic anisotropy. Electrical resistivity is much enhanced in comparison to pure hexagonal close-packed (hcp) iron as a result of the enhanced electron correlation effect, supporting the conventional thermal convection model. Moreover, our calculated seismic velocity shows a quantitative match with geologically observed preliminary reference Earth model (PREM) data. We suggest that oxygen is the essential light element to understand and model Earth's IC.

Diagenetic studies of the Eagle Ford and Indidura Formations in the Sabinas basin: Implications for source rock maturation

We analyzed the dynamics of interacting fluids within the Cenomanian-Turonian source rocks associated with hydrocarbon generation. Diagenetic alterations, authigenic minerals, isotopic data (δ13C and δ18O) of the matrix and carbonated cement, fluid inclusions, and fluorescence of hydrocarbons present were examined. Three thermal episodes related to diagenetic cements were defined, but only one is associated with gas production with temperatures of 99° and 168 °C. The isotopic data of the cements and segregations of calcite indicate that their generation is associated with the production of CO2 derived from organic matter. Therefore, they must have been formed during the interaction of hot fluids, organic acid, and meteoric waters. Due to the increased compaction and deepening of the succession, these fluids migrated through the dissolution, re-crystallization, and fracture zones, with a mainly lateral direction until reaching the large faults. For this, we can observe how the hottest fluids are expelled closer to the limits of the basin. The presence of light and intermediate hydrocarbons in permeable zones indicates that the Eagle Ford and Indidura Formations are also acting as reservoir rock due to the fracture system that allowed fluid circulation. Finally, a thermal convection model is proposed in the Sabinas basin with the microthermometric data of fluid inclusions, observing the wet gas and dry gas production zones through stratigraphy.

Thermal convection in a Brinkman–Darcy–Kelvin–Voigt fluid with a generalized Maxwell–Cattaneo law

We investigate thoroughly a model for thermal convection of a class of viscoelastic fluids in a porous medium of Brinkman–Darcy type. The saturating fluids are of Kelvin–Voigt nature. The equations governing the temperature field arise from Maxwell–Cattaneo theory, although we include Guyer–Krumhansl terms, and we investigate the possibility of employing an objective derivative for the heat flux. The critical Rayleigh number for linear instability is calculated for both stationary and oscillatory convection. In addition a nonlinear stability analysis is carried out exactly.

Increasing model vertical resolution may not necessarily lead to improved atmospheric predictability.

The widely accepted existence of an inherent limit of atmospheric predictability is usually attributed to weather's sensitive dependence on initial conditions. This signature feature of chaos was first discovered in the Lorenz system, initially derived as a simplified model of thermal convection. In a recent study of a high-dimensional generalization of the Lorenz system, it was reported that the predictability of its chaotic solutions exhibits a non-monotonic dimensional dependence. Since raising the dimension of the Lorenz system is analogous to refining the model vertical resolution when viewed as a thermal convection model, it is questioned whether this non-monotonicity is also found in numerical weather prediction models. Predictability in the sense of sensitive dependence on initial conditions can be measured based on deviation time, that is, the time of threshold-exceeding deviations between the solutions with minute differences in initial conditions. Through ensemble experiments involving both the high-dimensional generalizations of the Lorenz system and real-case simulations by a numerical weather prediction model, this study demonstrates that predictability can depend non-monotonically on model vertical resolution. Further analysis shows that the spatial distribution of deviation time strongly contributes to this non-monotonicity. It is suggested that chaos, or sensitive dependence on initial conditions, leads to non-monotonic dependence on model vertical resolution of deviation time and, by extension, atmospheric predictability.

The tidal–thermal evolution of the Pluto–Charon system

The existence of subsurface oceans on the satellites of the giant planets and Trans-Neptunian objects has been predicted for some time. Liquid oceans on icy worlds, if present, exert a considerable influence on the dynamics of the ice–ocean system and, because of the astrobiological potential, represent an important objective for future missions to the outer solar system. The Pluto–Charon system is representative of an icy moon orbiting a dwarf planet that is believed to have formed from the remnants of a giant impact. The evolution of icy moons is primarily controlled by the mode and efficiency of heat transfer through the outer ice shell, which is influenced by the presence of impurities, by tidal dissipation in the ice shell, and by the radioactive element budget in the silicate core. Previous studies on the evolution of the Pluto–Charon system generally considered either only the thermal or the tidal evolution, and in the cases where both were considered, the important effect of the presence of impurities in the liquid oceans was not addressed. Here, we consider the joint tidal–thermal evolution of the Pluto–Charon system by combining a comprehensive tidal model that incorporates a viscoelastic description of the tidal response with a parameterized thermal convection model developed for icy worlds. This approach enables an extensive analysis of the conditions required for the formation and maintenance of subsurface liquid oceans up to the present. Our results show that because of relatively fast circularization and synchronization of the orbits of Pluto and Charon, tidal heating is only important during the early stages of evolution (<1 Myr). As part of our study, we test the sensitivity of our results to a number of parameters that pertain to the orbital and thermal history. In all the studied cases, oceans on Pluto are always predicted to remain liquid to the present, ranging in thickness from 40 km to 150-km, whereas oceans on Charon, while in-place for approximately 4 Gyr, have solidified. This is supported by New Horizons observations of primarily extensional faults on Pluto and both extensional and compressional faults on Charon.

Thermal convection with generalized friction

A model for thermal convection with generalized friction is investigated. It is shown that the linear instability threshold is the same as the global stability one. In addition, decay of the energy in the L^2 norm is shown for the perturbation velocity and temperature fields. However, due to the presence of the generalized friction we establish exponential decay in the L^{beta +1} norm for the perturbation temperature, where beta >1.

Irreversibilities in natural convection inside a right-angled trapezoidal cavity with sinusoidal wall temperature

Analysis on natural convective heat transfer in different engineering systems allows optimization of the technical apparatus. For this purpose, numerical simulation of the fluid flow and heat transport within the system is combined with study of entropy generation. The latter is very important considering the Gouy–Stodola theorem of thermodynamics. The present research deals with the mathematical modeling of thermal convection and entropy generation in a right-angled trapezoidal cavity under the influence of sinusoidal vertical wall temperature distribution. Control Oberbeck–Galerkin finite element technique has solved Boussinesq equations formulated using the non-dimensional primitive variables. Analyses of flow structures, thermal and entropy generation patterns for different values of the Rayleigh number, and parameters of non-uniform wall temperature were performed. It was found that a rise in the sinusoidal wall temperature amplitude increases the average Nusselt and Bejan numbers and average entropy generation. Moreover, growth in the non-uniform wall temperature wave number decreases the energy transport strength and Bejan number.

The Effect of Electrical Discharge Machining Total Heat Generated on White Layer Thickness (WLT) and Fatigue Life for Die Steel

The present paper concerns with studying the high complexity nature of the EDM multiple discharge analysis transformed into a feasible solvable mathematical model for the die steel workpiece type AISI D2, the copper and graphite materials electrodes, and the kerosene dielectric by setting the Transient Thermal and the Multiphysics analyses domain loads models using the ANSYS 15.0 finite element analysis. Two load steps modeled the entering setting time analysis, six sub-periods setting time cycle, four heating, and two cooling periods, six transient temperature values, and four transient thermal convection models. The radius spark (discharge channel), the total number of discharges sparks, the total heat power generation, the absorbed heat flux fractions by the electrodes, the workpieces and kerosene fluid dielectric, the heat-affected zones (HAZ), the hard white recast layer thickness (WLT) and properties, the workpiece fatigue safety factor and life after EDM machining were determined and simulated. The thermal model errors compared with theoretical calculations and a modeled predicted equation were also deduced and verified. The experimental results evinced that the maximum total heat flux generated using the graphite material electrodes is (2.619E+009 W/m2) which is higher than when using copper material electrodes by (82.4%), while the minimum value of the white layer thickness (WLT) after EDM machining using graphite tool electrodes is (8.34 μm), which it gives an improvement comparing with using of copper tool electrodes by (40.0%). The macrographic and microstructure evaluation manifest that the discharge spark craters sizes when using graphite tool electrodes reached their sizes. The maximum fatigue stresses and fatigue safety factor when using copper tool electrodes are (240 MPa) and (0.89) which is higher by a value of (3.35%) and (3.45%) comparing with the using of graphite electrodes, respectively.

An accurate transient model for temperature fluctuation on localized shear band in serrated chip formation

The temperature fluctuation process on localized shear band is an important foundation of the chip formation mechanism in mesoscopic scale of time (700-70ms) and dimension (65-500um). An accurate transient temperature fluctuation modeling of localized shear band is proposed by using the classic method of moving heat source and thermal convection in mesoscopic scale. Where, chip geometry, time coefficient of the coupling effect from relative chip segment, temperature rise from different heat sources and thermal convection model for chip segmentation process are developed, respectively. A novel measuring method are applied for thermal distribution in shear band and its evolution in chip generation progression. The given experimental and numerical results can show that the proposed temperature model can get the efficient predictions of temperature and physical phenomena at various chip segmentation stage. Physical phenomena in chip formation process, such as instable chip flow, crack generated and propagation, from the viewpoint of temperature fluctuation and its instable evolution, and cutting force are addressed and analyzed. The innovative model can determine the temperature fluctuation and evolution, area of maximum temperature of shear band in chip segmentation process in mesoscale of time and dimension.

Model for thermal convection with uniform volumetric energy sources

Abstract

Instability thresholds for thermal convection in a Kelvin\u2013Voigt fluid of variable order

We present numerical techniques for calculating instability thresholds in a model for thermal convection in a complex viscoelastic fluid of Kelvin–Voigt type. The theory presented is valid for various orders of an exponential fading memory term, and the strategy for obtaining the neutral curves and instability thresholds is discussed in the general case. Specific numerical results are presented for a fluid of order zero, also known as a Navier–Stokes–Voigt fluid, and fluids of order 1 and 2. For the latter cases it is shown that oscillatory convection may occur, and the nature of the stationary and oscillatory convection branches is investigated in detail, including where the transition from one to the other takes place.

Effects of density-affecting scalar on the onset of chaos in a simplified model of thermal convection: a nonlinear dynamical perspective

To explore how density-affecting scalar influences the onset of chaos in a simplified model of thermal convection, we consider three versions of a physically extended Lorenz system obtained from incorporating additional physical ingredients such as rotation and density-affecting scalar. The three versions of the extended Lorenz system correspond to the cases when the density-affecting scalar has positive, neutral, and negative impacts on buoyancy. In general, compared to the case when the density-affecting scalar has a positive (neutral) impact on buoyancy, the case when the density-affecting scalar has a neutral (negative) impact on buoyancy leads to a higher critical Rayleigh parameter, a sign of delayed onset of chaos. For an appropriate choice of parameters that lead to chaotic solutions in all three cases, it is shown that the chaotic attractors for the three cases can exhibit a variety of different characteristics, such as taking on the shape of the classic Lorenz attractor, sharing the phase space with stable point attractors, and taking an unusual shape that is distinguished from the Lorenz attractor. The different characteristics in chaotic attractors lead to qualitative differences in the behaviour exhibited by the corresponding flow and temperature patterns reconstructed from the numerical solutions. Further analysis of this simplified model offering a nonlinear dynamical perspective on the thermal convection problem is expected to serve as an avenue for gaining new insights into this and related problems.

Thermoelectrohydrodynamic convection in parallel plate capacitors under dielectric heating conditions

A theoretical model of thermal convection induced by dielectric heating is developed via further exploitation of the analogy between gravity-driven thermal convection and convection driven by an electrohydrodynamic effect. The model is applied to a horizontal layer of dielectric fluid to determine the conditions of convection generation by the linear stability theory. The competition between gravity and the electrohydrodynamic effect under dielectric heating gives rise to different flow patterns depending on the Rayleigh number.

Heat transport bounds for a truncated model of Rayleigh–Bénard convection via polynomial optimization

Upper bounds on time-averaged heat transport are obtained for an eight-mode Galerkin truncation of Rayleigh’s 1916 model of natural thermal convection. Bounds for the ODE model—an extension of Lorenz’s three-ODE system—are derived by constructing auxiliary functions that satisfy sufficient conditions wherein certain polynomial expressions must be nonnegative. Such conditions are enforced by requiring the polynomial expressions to admit sum-of-squares representations, allowing the resulting bounds to be minimized using semidefinite programming. Sharp or nearly sharp bounds on mean heat transport are computed numerically for numerous values of the model parameters: the Rayleigh and Prandtl numbers and the domain aspect ratio. In all cases where the Rayleigh number is small enough for the ODE model to be quantitatively close to the PDE model, mean heat transport is maximized by steady states. In some cases at larger Rayleigh number, time-periodic states maximize heat transport in the truncated model. Analytical parameter-dependent bounds are derived using quadratic auxiliary functions, and they are sharp for sufficiently small Rayleigh numbers.

Modeling of buoyancy-driven thermal convection in immersed granular beds

For the first time, Eulerian three-dimensional transient modeling of thermal convection in immersed granular beds (IGB) has been developed. The modeling accounts for the destabilization of the IGB and the granular boundary upper layer deformation induced by thermal heating element. As observed in the recent experiments, the developed 3D CFD model predicts well the local phenomena: destabilization onset, particles removal or ejection, and the dynamic granular boundary upper layer deformation. The model predicts with good accuracy the two destabilization times td,onset, and td,total as function of the IGB initial height hi. Innovatively, a new critical Rayleigh number Racr* was introduced as function of a locally measured critical temperature Tcr at t=tcr>td,onset. The critical time tcr corresponds to a critical temperature drop observed inside the IGB near the heating element that was locally measured. The CFD model predicts correctly the thermal phase stability diagram, based on Racr* versus hi, as observed experimentally.

Scaling Laws for Regional Stratification at the Top of Earth's Core

AbstractSeismic and geomagnetic observations have been used to argue both for and against a global stratified layer at the top of Earth's outer core. Recently, we used numerical models of turbulent thermal convection to show that imposed lateral variations in core‐mantle boundary (CMB) heat flow can give rise to regional lenses of stratified fluid at the top of the core while the bulk of the core remains actively convecting. Here, we develop theoretical scaling laws to extrapolate the properties of regional stratified lenses measured in simulations to the conditions of Earth's core. We estimate that regional stratified lenses in Earth's core have thicknesses of up to a few hundred kilometres and Brunt‐Väisälä frequencies of hours, consistent with independent observational constraints. The location, thickness, and strength of the stratified regions would change over geological time scales in response to the slowly evolving CMB heat flux heterogeneity imposed by mantle convection.

Nonlinear Stability for Thermal Convection in a Brinkman Porous Material with Viscous Dissipation

We investigate nonlinear stability in a model for thermal convection in a saturated porous material using Brinkman theory, taking into account viscous dissipation effects. There are (at least) two models for viscous dissipation available, and we include a derivation of one of these by assuming that the flow in the porous medium may be described by a theory for a mixture of an elastic solid and a linearly viscous fluid. A fully nonlinear stability result is provided when either of the viscous dissipation functions is taken into account, and it is shown that from the nonlinear energy stability viewpoint both models are, in a sense, equivalent.