Numerical Convection Models Research Articles

Marginal stability analyses for thermochemical convection and its implications for the dynamics of continental lithosphere and core–mantle boundary regions

SUMMARY Significant compositional differences may exist in the lithospheric mantle and above the core–mantle boundary (CMB) relative to the ambient mantle. The intrinsic density differences may affect the development of thermal boundary layer (TBL) instabilities associated with lithospheric delamination and formation of thermochemical plumes. In this study, we explored the instability of two-layer thermochemical fluid using two different techniques: marginal stability analysis with a propagator-matrix method and finite element modelling. We investigated both the instabilities in lithospheric mantle (i.e. lithospheric instability) and the mantle above the CMB (i.e. plume-forming instability) using a background temperature Tbg(z) with the TBL. For lithospheric instability, we found that two-layer fluid with free-slip boundary conditions mainly undergoes the same three different convective modes (i.e. two oscillatory convection modes and one layered convection regime) as that with no-slip boundary conditions reported in Jaupart et al. However, with free-slip boundary conditions, the transitions between these convection modes occur at larger values of buoyancy number B. Free-slip boundary conditions lead to smaller critical Rayleigh number Rac, but larger convective wavelength and oscillation frequency ωc, compared with those with no-slip boundary conditions. Our numerical modelling results demonstrate that Rac and ωc predicted from the classical marginal stability analyses using Tbg(z) with TBL temperature may have significant errors when the oscillatory period is comparable with or larger than the timescale of lithospheric thermal diffusion that causes Tbg(z) to vary with time significantly. In this case, using a more gently sloped background temperature profile ignoring the TBL temperature, the stability analysis predicts more accurate stability conditions, thus presenting an effective remedy to the stability analysis. For plume-forming instability, because of the reduced viscosity in the hot and compositionally dense bottom layer, the transition to the layered convection occurs at significantly smaller B values, and in the oscillatory convection regime, Rac is larger but ωc is smaller, compared with those for lithospheric instability. Finally, our study provides a successful benchmark of numerical models of thermochemical convection by comparing Rac and ωc from numerical models with those from the marginal stability analysis.

Numerical Modeling of Natural and Mixed Convection in a Confined Space

Numerical Modeling of Natural and Mixed Convection in a Confined Space

Numerical Modeling of Non-Boussinesq Natural Convection in a Square Cavity Containing a Porous Layer

Numerical simulations were conducted to study the fluid flow and heat transfer through a partially filled square enclosure with a horizontal porous layer at the bottom. The vertical walls of the enclosure were subjected to uniform heating and cooling at specified temperatures TH and TC, respectively. The problem formulation was based on the Darcy–Brinkman model, which took into account density variation using the Mach number law approximation and incorporated variable properties. Based on the developed code, a parametric study of fluid flow and heat transfer inside the cavity was carried out to examine the effects of temperature difference, medium permeability, and Darcy number. Additionally, the variation of the Nusselt number on the hot and cold walls was provided to demonstrate the overall nature of heat transfer within the enclosure. The results of this study highlight that fluid flow and heat transfer are influenced by the temperature difference between the vertical walls and the characteristic parameters of the porous layer.

Numerical modeling and experimental validation of air-side forced convection on a Wire-on-tube condenser for a domestic refrigerator

In this study, the effects of various parameters on the air-side performance of a condenser used in a domestic refrigerator were investigated numerically and experimentally. A new condenser design with streamlined eye and kammtail tube shapes was studied to delay flow separation. The kammtail form was utilized in a wire-and-tube heat exchanger for the first time in this work instead of traditional round or elliptical geometry. Different design parameters were studied for the outer tube height (3, 3.5, 4, 4.5, and 5 mm), aspect ratio of the tube (1.5, 2, and 2.5), tube pitch (20 and 15 mm), tube arrangement (inline and staggered), and tube shapes (eye, kammtail, and ellipse forms) to improve the air-side performance. The model was validated using experimental data based on a performance test setup and wind tunnel measurements conducted at different air velocities. The impact of tube shape and tube dimensions on the convection coefficient and pressure drop were found to be dominant due to delayed flow separation and reduction in the recirculation area. The results showed that, for a similar heat-transfer rate, the total tube surface area was reduced by 7%, the convection coefficient was increased by 9.4%, and the static pressure drop was decreased by 27% with the new Kamm tail-form design of 3 × 6 mm compared to the respective values of the original condenser. In addition, for a similar air-side performance, decreasing the tube pitch from 20 to 15 mm resulted in subsequent decreases of up to 30% in the heat exchanger volume. When the tube arrangement was changed from inline to staggered, the convective coefficient increased by 23% and the pressure decreased by 14%. The numerical results were in good agreement with the experimental results, showing errors of less than 10% for air pressure drop and less than 9% for heat-transfer capacity.

Numerical Modeling of Natural and Mixed Convection in a Confined Space

Numerical Modeling of Natural and Mixed Convection in a Confined Space

Comparison of Two Numerical Models of Convection in the Earth’s Mantle

Comparison of Two Numerical Models of Convection in the Earth’s Mantle

Numerical modeling of magnetohydrodynamic buoyancy-driven convection for enhanced energy applications

In the realm of thermal management for electronic systems, the efficacy of heat dissipation serves as a major predictor of the reliability and operational lifespan of electronic components. Simultaneously, within the realm of geothermal energy utilization, where harnessing the Earth’s inherent heat reservoirs is employed for power generation and direct heating applications, an intricate comprehension of temperature gradients and the dynamics governing heat transfer stands as an imperative prerequisite for optimizing the extraction of thermal energy. This work offers a complete mathematical model aimed at understanding the principles governing energy transfer inside naturally convected flows subjected to the impact of an external magnetic field. The analytical inspection involves a broad parametric study of the flow system, comprising variations in buoyancy-driven factors, as well as the magnetic field parameter, indicated as the Hartmann number (Ha), ranging from 0 to 50. This multifaceted study unveils the profound impact of magnetic fields on critical aspects of the flow, including isotherm alignment, velocity distributions, thereby paving the way for the development of advanced cooling systems poised to deliver elevated energy efficiency and enhanced performance in electronic devices. The computational analysis digs into the complicated temperature distributions, velocity profiles, and vorticity patterns. It is found that increment of the external magnetic force limits the variations in fluid’s horizontal and vertical velocities. Convective heat transfer is decreased with increasing Hartmann number at cold and hot sections of the fluid chamber. While for Rayleigh number this behavior is reversed.

Numerical Modelling of Forced Convection of Nanofluids in Smooth, Round Tubes: A Review

A comprehensive review of published works dealing with numerical modelling of forced convection heat transfer and hydrodynamics of nanofluids is presented. Due to the extensive literature, the review is limited to straight, smooth, circular tubes, as this is the basic geometry in shell-and-tube exchangers. Works on numerical modelling of forced convection in tubes are presented chronologically in the first part of the article. Particular attention was paid to the method of the solution of governing equations, geometry of the heating section, and boundary conditions assumed. Influence of nanoparticles on heat transfer and flow resistance are discussed. Basic information is summarized in tabular form, separately for single-phase approach and two-phase models. The second part of the article contains the correlation equations proposed in the presented papers for the calculation of the Nusselt (Nu) number or heat transfer coefficient, separately for laminar and turbulent flow. Details of the type of nanofluids, the concentration of nanoparticles, and the Reynolds (Re) number range are also presented. Finally, advantages and disadvantages of individual numerical approaches are discussed.

Numerical modeling of mixed convection near a vertical heat source in saturated granular soils

Accurate design of energy geostructures such as energy piles requires an exact prediction of soil thermal responses close to the embedded heat sources in the ground. In saturated soil, both heat conduction and heat convection facilitate heat transfer in the soil medium. Conventional analyses of heat transfer in saturated porous medium classified heat convection into two categories: (i) natural convection that could happen in the hydrostatic condition and (ii) forced convection that occurs due to the groundwater flow in the soil medium. This paper demonstrates that, in the presence of groundwater flow, the natural convection in the form of buoyancy-driven flow plays a prominent role in temperature distribution through saturated soil as well as the forced convection. A finite element analysis is performed to study the effects of groundwater velocity and soil permeability on the behavior of a fluid-saturated porous medium (soil). The results confirm that neglecting the natural convection can lead to inaccurate results. Furthermore, a novel expression is defined to estimate the importance of natural convection in heat transfer mechanisms in the soil medium.

Numerical modeling of solute convection in the system of two porous layers with different permeabilities

The numerical simulation of the dynamics of a liquid with solute of high concentration in two horizontal layers of a porous medium with different permeability coefficients is carried out. The dynamics of the solute is modeled within the framework of a nonlinear MIM model that takes into account the adhesion and separation process at the skeleton of a porous medium. The modeling was carried out in a two-dimensional setting. The mobile (moving together with the carrier fluid) and immobile (deposited on the skeleton) phases are modeled by the finite volume method with adaptive mesh refinement algorithm. At each point in space, functions of volumetric saturation are set, and a kinematic equation is solved that describes the dynamics of adhesion and separation. The effective permeability of a porous medium depends on the saturation function of the immobile phase and is calculated using the Kozeny-Karman formula. The obtained numerical data are compared with the results of a linear analysis of stability, and the nonlinear regimes of concentration convection and the distribution of impurities at high supercriticalities are studied. In the case of high ratio of permeability coefficients of upper and lower layers, convection occurs locally in a more permeable sublayer, even with a decrease in its thickness. With an increase in supercriticality the penetration of the convective flow into the poorly permeable sublayer and the transition from local convection to large-scale convection are observed.

Numerical modeling of magnetohydrodynamic thermosolutal free convection of power law fluids in a staggered porous enclosure

In this study, the influence of a magnetic field on thermosolutal free convective flow inside a staggered porous enclosure, filled with non-Newtonian power-law fluids is investigated using the Galerkin finite element method. The computational model has been validated against available data from the literature. Results indicate that the augmentation of Hartmann number (Ha) causes heat and mass transport to decrease significantly. However, the magnetic field has a greater influence on mass transfer in comparison with heat transfer. The maximum local Nu and Sh numbers are decreased respectively by 55% and 43% at Ha = 75. This reduction becomes more significant for Hartmann number values higher than 25. However, the increase of Darcy number reduces the influence of the magnetic field. In the presence or absence of magnetic field, the alteration of power law index provides different trends for the prediction of the convective flow intensity. The increase in Lewis (Le) number has a smaller effect on the heat transfer rate compared to the mass transfer rate. Increase in Le augments mass transfer rate by 230% but decreases heat transfer rate by 37%. Further, the augmentation of the buoyancy ratio causes a significant increase in the heat and mass transfer rates.

Particle resolved numerical modeling of unsteady forced convection of nanofluid around a porous cuboid with sinusoidal inlet velocity

Abstract In this research, the laminar, incompressible, unsteady oscillatory flow and convective heat transfer of nanofluid around a porous cuboid were studied two-dimensionally using particle resolved calculations. Several cuboids of different sizes and porosities and with a constant temperature were subjected to a nanofluid flow with a sinusoidal velocity profile. The effects of the Reynolds number (Re = 100–900), the volume fraction of nanoparticles, the aspect ratio of the porous cuboid, the Darcy number and the amplitude and frequency of the inlet velocity on the flow field and heat transfer were investigated. To evaluate the system’s optimal performance, performance evaluation criteria (PEC) were also investigated. The results showed that increasing the Reynolds number improved thermal performance. Increasing the volume fraction of nanoparticles increased the Nusselt number; however, the pressure drop coefficient increased more strongly. The heat transfer and pressure drop coefficient increased in line with the growth of the porous cuboid aspect ratio. When the Darcy number was increased, the Nusselt number first increased and then decreased and the pressure drop coefficient continuously decreased. A higher amplitude of the inlet velocity profile augmented the heat transfer and pressure drop coefficient. An increase in the amplitude and frequency of the inlet velocity profile widened the range of drag and lift coefficients. Furthermore, flow at different inlet velocity frequencies (f * = 0–10) behaved differently; as a result, the maximum rate of heat transfer and pressure drop was obtained at f *=5. However, considering the ratio of the Nusselt number to the pressure drop coefficient and PEC parameter, the optimum frequency was f *=9.

Scaling laws for stagnant-lid convection with a buoyant crust

SUMMARY Stagnant-lid convection, where subduction and surface plate motion is absent, is common among the rocky planets and moons in our solar system, and likely among rocky exoplanets as well. How stagnant-lid planets thermally evolve is an important issue, dictating not just their interior evolution but also the evolution of their atmospheres via volcanic degassing. On stagnant-lid planets, the crust is not recycled by subduction and can potentially grow thick enough to significantly impact convection beneath the stagnant lid. We perform numerical models of stagnant-lid convection to determine new scaling laws for convective heat flux that specifically account for the presence of a buoyant crustal layer. We systematically vary the crustal layer thickness, crustal layer density, Rayleigh number and Frank–Kamenetskii parameter for viscosity to map out system behaviour and determine the new scaling laws. We find two end-member regimes of behaviour: a ‘thin crust limit’, where convection is largely unaffected by the presence of the crust, and the thickness of the lithosphere is approximately the same as it would be if the crust were absent; and a ‘thick crust limit’, where the crustal thickness itself determines the lithospheric thickness and heat flux. Scaling laws for both limits are developed and fit the numerical model results well. Applying these scaling laws to rocky stagnant-lid planets, we find that the crustal thickness needed for convection to enter the thick crust limit decreases with increasing mantle temperature and decreasing mantle reference viscosity. Moreover, if crustal thickness is limited by the formation of dense eclogite, and foundering of this dense lower crust, then smaller planets are more likely to enter the thick crust limit because their crusts can grow thicker before reaching the pressure where eclogite forms. When convection is in the thick crust limit, mantle heat flux is suppressed. As a result, mantle temperatures can be elevated by 100 s of degrees K for up to a few Gyr in comparison to a planet with a thin crust. Whether convection enters the thick crust limit during a planet’s thermal evolution also depends on the initial mantle temperature, so a thick, buoyant crust additionally acts to preserve the influence of initial conditions on stagnant-lid planets for far longer than previous thermal evolution models, which ignore the effects of a thick crust, have found.

Numerical modeling of free convection in a partially heated triangular enclosure with chamfer

Two-dimensional numerical modelling of water natural convection inside a chamfered triangular cavity, that is being partially heated from below has been investigated in this paper. The walls of the cavity are considered isothermally isolated except a source part of heat which is inserted at the bottom wall while the inclined wall is considered as cold wall. A COMSOL Multiphysics 5.5 has been used to solve the numerical solutions. This paper considered some variables such as Rayleigh number (Ra = 103 to 106), heating length ratio (HL= 0.2, 0.4, and 0.5) and the ratio of the chamfer’s radius (R= 0.1, 0.2, and 0.25) while all other physical parameters are considered constant such as the length of the cold wall and the adiabatic wall. The results have been validated with previous published work in order to ensure the accuracy of the current coding. The main results observed an increase in streamlines and isotherms with the rise of Rayleigh (Ra) number and the rise of heating length ratio; additionally, the average Nusselt number (Nuavg) value increases with the rise of the Ra number and the length of the heating source. For example, average Nusselt number increased from 2.0443 at Ra=103 to 7.2793 at Ra= 106 for (R=0.25 and HL = 0.5).

Artificial intelligence prediction of natural convection of heat in an oscillating cavity filled by CuO nanofluid

BackgroundIn the last five years, a new generation of advanced numerical methods was developed to reduce computational costs and improve the prediction process. The combination of Artificial Intelligence and traditional computational methods is the best sample of this generation. Employing this method can expand the horizon of numerical modeling. This method is also suitable for complex processes such as natural convection and oscillating heat transfer. This case study tries to peruse the effects of variable boundary conditions such as magnetic field, angle, and nanofluids volume fraction on the heat transfer. Also, the impact of oscillation has been studied. MethodsTo accomplish these aims, numerical modeling of natural convection based on Boussinesq approximation was used. Techniques from machine learning were employed to develop a predictive tool that utilizes the data generated by computational analysis of the problem. The Ra and Ha were considered in the ranges of 103<Ra<106 and 0<Ha<40, respectively. Oscillation frequencies between 20 and 50 Hz and amplitudes of 0.5, 1, and 2 mm were studied. FindingsThe result showed that Nu increased in initial steps and then decreased at a constant Ha by increasing the rotation angle. It appeared that the amplitude of oscillation has a pronounced effect on the heat transfer rate. The results show that the Ha could affect streamlines of fluid. By increasing Ha=0 to Ha=52, the maximum velocity point in the close enclosure moved 14% closer to the hot side.

Retraction notice to “Numerical modelling of free convection in a symmetrical cone using MRT LB model combined with experimental properties of TiO2-water” [Phys. B Condens. Matter 114 (2019) 113633

Retraction notice to “Numerical modelling of free convection in a symmetrical cone using MRT LB model combined with experimental properties of TiO2-water” [Phys. B Condens. Matter 114 (2019) 113633

Tectonic depressions on the East-European and Siberian platforms: numerical modeling of convection beneath the Eurasian continent

In modern concepts, the upper mantle of the Earth is a highly viscous incompressible liquid, and its flow is described using the Navier – Stokes equations in the Oberbeck – Boussinesq and geodynamic approximations. Convective flows in the upper mantle play a decisive role in the kinematics of lithospheric plates and the geological history of continental regions. Mathematical modeling is a basic method for studying convective processes in the mantle. Our paper presents a numerical model of convection, which is based on the implicit artificial compressibility method. This model is tested in detail by comparing our calculation results with the results of a well-known international test. It is demonstrated that the Fedorenko grids sequence method is highly efficient and reduces the computing time almost by a factor of eight. The numerical model is generalized in order to state the problem in a spherical system of coordinates. It is used to analyse the distribution of convective flows in the upper mantle underneath the Eurasian continent. The analysis shows that the thickness and geometrical parameters of the lithospheric blocks are the factors of significant influence on the distribution of convective flows in the upper mantle. The resulting structure of convective flows is manifested in the surface topography of large platform areas wherein the lithosphere thickness is increased. Thus, the locations of extended downward convection flows under the East European and Siberian platforms are clearly comparable to syneclises observed in the study area.

Simulation of Thermal Radiation and Turbulent Free Convection in an Enclosure with a Glass Wall and a Local Heater

In this study, a numerical modelling of thermal radiation and turbulent thermogravitational convection in a large-scale chamber containing a thermally-generating element is conducted. The lower border of the cabinet is maintained under adiabatic conditions, while on the other walls the convective boundary conditions (Robin boundary condition) are used. The managing equations with corresponding restrictions are transformed using the stream function–vorticity formulation and then solved by employing a finite difference method. The influence of both the height and wall emissivity of the heated source on fluid motion and the heat transmission in a large-scale chamber is investigated. Our results of the calculations on non-uniform grids with algebraic transformation are in excellent agreement with other available experimental and numerical outcomes for turbulent thermal convection in enclosures. The computations indicate that the average total Nusselt number is enhanced up to 2 times with an increase in the heater height. The results show that the surface emissivity of the heat source has a great influence on the total thermal transference coefficient. Furthermore, a growth of the heater surface emissivity has no significant effect on the flow structure.

Timescale of Short‐Term Subduction Episodicity in Convection Models With Grain Damage: Applications to Archean Tectonics

AbstractThe style of subduction that prevailed on the early Earth, or even whether subduction was prevalent at all, is an important question in the evolution of Earth's crust, mantle, and surface environment. Here, two‐dimensional numerical convection models, that include grain size evolution to generate weak plate boundaries, reveal a clear transition in subduction behavior with increasing internal heating rate. Sustained subduction with a coherent slab gives way to a style where slabs periodically detach and sink rapidly into the deep mantle, with increasing internal heating rate. In this latter, “drip‐like” subduction regime, repeating cycles of slab growth by subduction, followed by necking and detachment of the lower portion of the slab, are seen. These cycles are termed “slab detachment cycles,” and similar behavior has been seen in regional scale subduction models of the early Earth. Fourier analysis is used to constrain the timescale of slab detachment cycles, and a simple scaling law for this timescale is developed. Applying the scaling law to the early Earth indicates that slab detachment cycles can occur on timescales of &lt;10 Myr, even as low as &lt;5 Myr if the lithosphere is thick and mantle temperature is &gt;1900 K. These cycles may thus be capable of explaining repeating sequences of rocks with “arc” and “non‐arc” signatures seen in some Archean cratons. The drip‐like subduction regime could also have significant implications for the generation of the tonalite‐trondhjemite‐granodiorite (TTG) suite of rocks and exhumation of high pressure metamorphic rocks, two important features of the early Earth geologic record.

On numerical modeling of natural convection based on the OpenFOAM solver

This work considers numerical modelling of natural incompressible convection problems in the gravity field in the Boussinesq approximation using OpenFOAM. A mathematical model of natural convection in the gravity field, using Boussinesq approximation, was considered. The built-in solver was identified and modified. The exact solution, theoretical data and experiment were used to verify the solver. A numerical study of natural convection in a horizontal liquid layer was performed. Natural convection in a fluid layer between coaxial cylinders was considered.