Convective Flow Patterns Research Articles

Numerical analysis of free convection under the influence of radiation and inclined MHD in a triangular cavity filled with hybrid nanofluid and a porous fin

This study presents a novel investigation into the thermal behavior of a hybrid nanofluid (MgO − Ag − H2O) in natural convection around a porous fin in a triangular enclosure under the influence of radiation and magnetohydrodynamic effects. The research uniquely combines these complex phenomena, addressing a significant gap in the literature. This configuration has potential applications in advanced solar thermal collectors, electronic cooling systems for high-power devices, and compact heat exchangers in various industries. The main objectives are to understand how various parameters influence heat transfer and fluid flow behavior and to optimize the design for enhanced thermal performance. The study considers a range of variables including Rayleigh number (103 − − 106), Hartmann number (0 – 50), Aspect ratio (0.3 – 0.6), radiation parameters (Rd = 1 − − 5, λ = 1 − 5), and volume concentration (0- 0.05), which have been numerically analyzed using the finite element method (FEM). The findings reveal that increasing the Darcy number (Da) enhances heat transfer at low Rayleigh numbers (Ra = 103,104). However, at higher Ra (Ra = 106), the impact of Da becomes more complex, with a critical Da beyond which heat transfer efficiency decreases due to an increase in flow resistance. The nanoparticle volume concentration plays a vital role, as higher concentrations lead to improved heat transfer efficiency, especially at higher Ra, through enhanced thermal conductivity and thermal dispersion. The length of the porous fin greatly impacts fluid flow patterns and heat transfer rates, with longer fins creating more complex flow patterns, promoting enhanced heat transfer and stronger thermal plumes. Thermal radiation, represented by the radiation parameters (Rd and λ), significantly influences both the heat transfer rate and the convective flow patterns within the enclosure. This study also incorporates a comprehensive entropy generation analysis, providing novel insights into system irreversibilities and optimization potential. The entropy analysis reveals the complex interplay between various parameters and their impact on system efficiency, offering valuable guidance for designing high-performance thermal management systems.

Numerical study of granulation in anelastic thermal convection in spherical shells

The present work investigates granulation or convective flow patterns in density-stratified (or anelastic) convection in spherical shells. The density-stratified thermal convection is typically present in astrophysical systems (such as solar convection); motivated by this, we performed a series of three-dimensional anelastic convection simulations in a spherical shell geometry using an in-house developed hybrid solver. We explored the effect of Rayleigh number and density scale height on the convective flow patterns. The granulation (or cell-like structures) are more prominent at higher density scale height and Rayleigh number. The granulation is further characterized by kinetic energy and helicity spectra. Our results support the argument that the convective flow patterns (or granulation) emerge due to inverse cascade owing to the presence of density stratification. Convective patterns (or granulation) are identified based on length scales, time scales, and flow velocity. The length scale of granules is further verified using a solar granulation model. Our analysis suggests the existence of inverse cascade and supergranulation on the spherical surface due to density-stratified thermal convection in spherical shells.

Formation of convective roll patterns over a longitudinal throughflow in an active inhomogeneous porous medium with weak clogging

The convective stability of a plane-parallel longitudinal throughflow in a system consisting of two porous sublayers with distinct permeability is studied taking into account the weak pore clogging effect and given a finite difference in concentration between the upper and lower boundaries of the system. A system of differential equations for convection is derived within the framework of the continuum approach and the nonlinear MIM model. A linear stability analysis of the basic longitudinal flow is carried out. The boundary value problem is solved using the numerical technique for constructing a fundamental system of solutions. The neutral stability curves of the basic flow with respect to the disturbances in the form of rolls with different wavelength are obtained. For the absence of pore clogging, the convective stability maps of the critical solutal Rayleigh-Darcy number versus the permeability ratio for the initial uncontaminated sublayers, as well as the plots of the critical disturbance frequency and wave number versus the permeability ratio for some values of the Peclet number, are constructed. It is shown that these results have symmetry with respect to the solution for equal initial permeability of sublayers. The clogging effect associated with the solute adsorption and desorption in a porous medium is studied in the two-layered systems with the values 0.1 and 10 of the ratio of initial permeabilities of the sublayers; convection localization occurs in distinct sublayers. It was found that clogging increases the stability of the longitudinal basic flow relative to solutal inhomogeneity and breaks the symmetry of solutions with respect to the case when the two-layered system is reduced to a single layer with the same filtration properties of the porous medium throughout its volume. The influence of sorption effects on the critical parameters of oscillatory convection is investigated by plotting the critical solutal Rayleigh-Darcy number, disturbance frequency and wave number against the adsorption coefficient at fixed values of the desorption coefficient. The isolines of the stream function are constructed to analyze convective flow patterns. It was established that there is a weak relationship between the typical size of local convective roll patterns and the clogging parameters. It is shown that the sorption processes, which can lead to clogging, have a significant impact on the velocity of convective rolls moving along the two-layered system at a slight variation in their sizes.

Differential Rotation in Convecting Spherical Shells with Non-Uniform Viscosity and Entropy Diffusivity

Contemporary three-dimensional physics-based simulations of the solar convection zone disagree with observations. They feature differential rotation substantially different from the true rotation inferred by solar helioseismology and exhibit a conveyor belt of convective “Busse” columns not found in observations. To help unravel this so-called “convection conundrum”, we use a three-dimensional pseudospectral simulation code to investigate how radially non-uniform viscosity and entropy diffusivity affect differential rotation and convective flow patterns in density-stratified rotating spherical fluid shells. We find that radial non-uniformity in fluid properties enhances polar convection, which, in turn, induces non-negligible lateral entropy gradients that lead to large deviations from differential rotation geostrophy due to thermal wind balance. We report simulations wherein this mechanism maintains differential rotation patterns very similar to the true solar profile outside the tangent cylinder, although discrepancies remain at high latitudes. This is significant because differential rotation plays a key role in sustaining solar-like cyclic dipolar dynamos.

Heat transfer measurements in an inclined low aspect ratio Rayleigh–Bénard convection cell under feedback control

We report experimental results on the inclined Rayleigh–Bénard convection of a moderate aspect ratio convection cell using a high Prandtl aqueous solution of glycerol. The main goal of the present work is to measure continuously the transition from a convective condition into a purely conduction regime by a smooth quasi-static variation of the tilt angle of the convection cell with respect to the gravity vector in 180° at Rayleigh numbers just above of convection onset. Flow circulation inside the convection cell is indirectly detected by temperature sensors located at the bounding active plates. Changes in the temporal evolution of the heat transfer curve appear directly related to flow transitions between characteristic flow patterns from transversal rolls evolving into an unicellular single roll convective pattern and then a conductive state. For small tilt angles 6°≤γ≤20° time signal fluctuations on both the Nusselt number and temperature readings were observed. Flow visualizations and PIV measurements provided a complementary view of the convective flow pattern being associated to transitions in the Nusselt number evolution with the tilt angle of the cell. For small tilt angle transitions, we observed a loss of rolls process followed by a reorganization of the flow which might be the responsible of the Nusselt unsteadiness.

Evaporation-induced convective transport in confined saline droplets

Here, we report on the convection pattern, inside a confined saline droplet sandwiched between two hydrophobic substrates, before crystallization (prenucleation) and at the onset of crystallization (postnucleation). Crystallization occurs inside a saline droplet due to evaporation-induced supersaturation of the droplet. The hydrophobic nature of the substrates leads to the crystallization at a single nucleation site at the triple contact line of the droplet or in the interior of the droplet. The flow field in the prenucleation and the postnucleation stages is attributed to the density gradient established inside the droplet during evaporation and subsequent crystallization. A stark contrast in the convective flow patterns and the flow strength is observed between the two stages of evaporation. While the prenucleation regime is marked by an axisymmetric toroidal vortex pattern, the symmetry breaks in the postnucleation regime. Once the nucleation of crystal initiates, a recirculating flow field directed upward from the location of nucleation, and a 3–4-fold increase in the magnitude of flow velocity is observed. This increase in flow strength is attributed to the large difference in the local concentration arising because of nucleation. In addition, prior to nucleation, the change in the magnitude of maximum velocity is marginal (~10%) over an evaporation time of ~15 min. In contrast, the flow strength reduces appreciably with evaporation time (~ 45% over 15 min) in the postnucleation stage due to the growth of the crystal that in turn lowers the solutal concentration inside the droplet. We present a numerical model to determine the flow field inside the droplet in the postnucleation regime by introducing a sink term, accounting for crystallization-induced-depletion of solute, in the species transport equation and show that it agrees well with the experimental observation.

Finite element analysis on the hydrothermal pattern of radiative natural convective nanofluid flow inside a square enclosure having nonuniform heated walls

AbstractThe present article enlightens us on the hydrothermal pattern of a steady incompressible laminar natural convective nanofluid flow inside a heated square chamber. The square enclosure is filled with water‐based spherical‐shaped ferrous (Fe3O4) nanoparticles. Magnetic effect and thermal radiation are presumed within the flow. The left‐sided vertical wall and one bottom wall of the chamber are nonuniformly and uniformly heated, while the remaining right‐sided vertical wall is isothermally cooled at a constant temperature and the upper wall is insulated. A detailed analysis is conducted to exhibit that how nonuniform and uniform heated walls influence flow within the square chamber. The leading dimensional equations are made into a dimensionless form using apposite similarity variables and the Galerkin finite element technique is executed to solve those equations. The grid independence test and a parallel comparison with existing literature are presented to verify the validity of the outcomes. The streamlines, isotherms, temperature, velocities, and average Nusselt number are depicted through several graphs for several parametric values of Rayleigh number, Hartmann number, thermal radiation, and nanoparticle volume fraction. The outcomes showed that increasing nanoparticle concentration and Rayleigh number lead to improve the Nusselt number, while heat transport is reduced for Hartmann number and radiation parameter. The uniformly heated walls convey better heat transport as compared to nonuniformly heated walls.

Hilbert transform revisited – Proper orthogonal decomposition applied to analytical signals of flow fields

The modes delivered by proper orthogonal decomposition (POD) are uncorrelated as per definition; but interestingly, they are not necessarily independent in terms of spatio-temporal flow-pattern dynamics. For instance, periodic structures that travel as waves through a series of snapshots often consist of pairs of modes with harmonic functions shifted 90 degree in phase and/or a spatial offset by a quarter of the spatial wave length of the convective flow pattern. Identification of such pairs, however, largely builds upon experience, visual inspection and/or the analysis of the reconstructed coefficients in cyclograms (Lissajous figures). This effort becomes even more challenging if measurement noise or other spurious information contaminates the raw data under consideration. One possibility to automatically pair corresponding patterns with common POD algorithms is the immediate application of the POD method to complex data (see Pfeffer et al., 1990). As outlined by Horel (1984), the Hilbert transform is a well-known and straight forward means to obtain the required extension of the original signal with an appropriate 90 degrees phase shift, which is independent of the fundamental frequencies. The complex extension of the original (real) signal Xi and its (discrete) Hilbert transform HT{Xi} as the imaginary part Xi +iHT{Xi} with the imaginary unit i is commonly known as the so-called analytical signal.

Steady Marangoni instabilities in variable-viscosity liquid layer in the presence of insoluble surfactant

The ability to control the complex convective flow patterns is important and one of the factors that alter the dynamics of the surface tension is surface-active agents or surfactants. Surfactants affect the surface tension at the free upper surface by producing tangential stress. This study theoretically examines the onset of steady instabilities in a thin nondeformable and deformable variable-viscosity liquid layer in the presence of insoluble surfactant. The surface tension at the free surface is assumed to be linearly dependent on temperature and concentration gradients. The dynamic viscosity is assumed to be exponentially dependent on temperature. The stability problems are governed by the systems of nonlinear partial differential equations consisting of continuity, momentum and energy equations. Linear stability analysis consisting of scaling, perturbation of infinitesimal disturbances and superposition in normal modes are used to transform the system of partial differential equations into system of ordinary differential equations. The exact analytical solutions are derived and the marginal curves are illustrated to show effects of some controlling parameters particularly the variable viscosity and elasticity parameter. Viscosity variation and elasticity parameter of surfactant act as destabilizer while the Biot number and Lewis number stabilize. For deformable surface, convection sets in at long wavelength for liquid with variable viscosity but convection occurs at short wavelength for constant viscosity liquid.

Data-based model reduction for phase change problems with convective heat transfer

Latent heat thermal energy storages (LHTES) exploit the high energy density of phase change material (PCM). The typically low thermal conductivity of PCM limits the charging and discharging rates and poses considerable challenges for dynamic storage operation. To operate LHTES efficiently and to exploit their full potential, new methods are required to obtain accurate and fast models for state of charge estimation and control tasks. In LHTES the heat transfer in low viscosity PCM is driven by conduction and also significantly by convective transport. In previous works, various high-precision models have been developed which employ finite element, difference and volume methods to solve the coupled Navier–Stokes and energy equations, but they incur large computational effort. In the present work, a novel, high-fidelity model reduction technique is proposed to achieve real-time capability while preserving high model accuracy. The idea is to short-cut the laborious solution of the Navier–Stokes equations by an efficiently parametrized, data-based model which approximates the stream function of the typical convection flow pattern by singular value decomposition. To account for the complexity of the solution-dependent flow domain, a suitable transformation method is proposed. The efficiency and accuracy of the proposed reduction method is demonstrated in typical operating modes.

Azimuthal instability of the radial thermocapillary flow around a hot bead trapped at the water–air interface

We investigate the radial thermocapillary flow driven by a laser-heated microbead in partial wetting at the water–air interface. Particular attention is paid to the evolution of the convective flow patterns surrounding the hot sphere as the latter is increasingly heated. The flow morphology is nearly axisymmetric at low laser power (P). Increasing P leads to symmetry breaking with the onset of counter-rotating vortex pairs. The boundary condition at the interface, close to no-slip in the low-P regime, turns about stress-free between the vortex pairs in the high-P regime. These observations strongly support the view that surface-active impurities are inevitably adsorbed on the water surface where they form an elastic layer. The onset of vortex pairs is the signature of a hydrodynamic instability in the layer response to the centrifugal forced flow. Interestingly, our study paves the way for the design of active colloids capable of achieving high-speed self-propulsion via vortex pair generation at a liquid interface.

Experimental and numerical investigation of saltwater intrusion dynamics on sloping sandy beach under static seaside boundary condition

Two-dimensional sandbox experiments were conducted to investigate the variable-density circulation and flow patterns in sloping beach configurations. The experiments provide new benchmark results for validating the sandbox models based on quantitative and qualitative measurements. Previous studies have considered density dependent flow in porous media, vertical beach face saltwater boundary, and multilayered hydrogeology ignoring a sloping beach face, which is a much more common phenomenon in real world. The present study considers sloping beach face under both homogeneous and low-permeability strata configurations. The geohydraulic processes encountered were quantified through pore-water pressure measurements and image analysis techniques. Moreover, validations were performed with numerical simulations (FEFLOW). A simple image analysis procedure is proposed with respect to two-dimensional laboratory scale benchmark experiments. Experimental results provided a detailed circulation flow path within and outside the saltwater wedge with sloping beach face. Fingering effect in porous media was also observed for both the experiments during initial time periods. Stability analysis shows the existence of a stationary convective flow pattern followed by gravitational instabilities under the quasi-steady state condition.

Numerical study on the uncertainty reduction for thermal power estimation of an open pool research reactor with natural convection core cooling

In this study, the calorimetric method is used to study the thermal power estimation in an open pool research reactor during power operation under natural convection core cooling. The pool temperature measuring points are used as a key factor to minimize the uncertainty of the thermal power of the research reactor. The Computational Fluid Dynamics (CFD) technique is used to analyze the natural convection flow pattern in the reactor pool. The results show how the natural convection flow pattern influences the uncertainty of the thermal power estimation in terms of the flow stabilization and how the optimal temperature measuring point can be chosen. This paper shows that an appropriate thermal power estimation with a low uncertainty can be obtained based on the temperature measurement in the lower section of the reactor pool with the proper time criteria in view of the temperature propagation.

Suppression of photothermal convection using silicon carbide substrates for optofluidics experiments

Photothermal convection on glass substrate has been a major obstacle for optofluidic measurement at elavated optical power. Here we demonstrate a strategy to suppress the photothermal convection by using silicon carbide substrates of high thermal conductivity for optimal heat sinking. We measure and compare the photothermal convection flow pattern and confirm that the photothermal convection on gold coated silicon carbide substrate is indeed much smaller than that on gold coated glass substrate. We further demonstrate the undisrupted optical acceleration using silicon carbon as optical window and stable plasmonic optical trapping. This technique is generally applicable to reduce photothermal heating and plasmonic optical tweezers based on patterned plasmonic nanostructures.

On the application of neural networks for temperature field measurements using thermochromic liquid crystals

This study presents an investigation regarding the applicability of neural networks for temperature measurements using thermochromic liquid crystals (TLCs) and discusses advantages as well as disadvantages of common calibration approaches. For the characterization of the measurement technique, the dependency of the color of the TLCs on the temperature as well as on the observation angle and, therefore, on the position within the field of view of a color camera is analyzed in detail. In order to consider the influence of the position within the field of view on the color, neural networks are applied for the calibration of the temperature measurements. In particular, the focus of this study is on analysis of the error of temperature measurement for different network configurations as well as training methods, yielding a mean absolute deviation and a mean standard deviation in the range of 0.1 K for instantaneous measurements. On the basis of a comparison of this standard deviation to that of two further calibration approaches, it is shown that neural networks are suited for temperature measurements via the color of TLCs. Finally, the applicability of this measurement technique is illustrated at an exemplary temperature measurement in a horizontal plane of a Rayleigh–Bénard cell with large aspect ratio, which clearly shows the emergence of convective flow patterns by means of the temperature field.Graphic abstract

Convective Transport through Porous Layers

Convective motions are a multi-physics phenomenon, in which flow and transport processes interact in a two-way coupling. The density of the fluid depends on the value of transport variable and this back-coupling leads to non-linear behaviour. For the classical constellation of a closed fluid container heated from below convective motions appear, when a critical threshold for the Rayleigh number is exceeded. The heat transfer due to convection is much higher than in the case of pure conduction. Here systems of three layers are examined in detail. Using numerical CFD modelling it is shown that in layered systems different convective flow patterns appear than in the single layer case. The number and constellation of convection cells characterize steady flow patterns. Using a parametric sweep over the relevant parameter range of layer Rayleigh numbers and layer thicknesses we determine diagrams that show the excess heat or mass transfer of the dominant convection patterns, measured by the Nusselt- or Sherwood numbers.

Appraising conjugate heat transfer, heatlines visualization and entropy generation of Ag-MgO/H2O hybrid nanofluid in a partitioned medium

Purpose This paper aims to perform the lattice Boltzmann simulation of conjugate natural convection heat transfer, heat flow visualization via heatlines approach and entropy generation in a partitioned medium filled with Ag-MgO (15-85%)/water. Design/methodology/approach The lattice Boltzmann method (LBM) is used to predict the dynamic and thermal behaviors. Experimental correlations for dynamic viscosity and thermal conductivity versus solid volume fraction are used. The study is conducted for the ranges of Rayleigh number 103 ≤ Ra ≤ 106, the partitioner thickness 0.01 ≤ δ ≤ 0.9, its position 0.15 ≤ Xs ≤ 0.85 and the hybrid nano-suspensions volume fraction 0% ≤ ϕ ≤ 2%. Findings The effects of varying of controlling parameters on the convective flow patterns, temperature contours, heat transfers, the heatlines and the entropy generation are presented. It has been found that the maximum rate of heat transfer enhancement occurs for low Ra numbers (103) and is close to 13.52%. The solid thickness d and its horizontal position Xs have a substantial influence on the heat transfer rate, flow structure, heatline, total entropy generation and Bejan number. Besides, the maximum heat transfer is detected for high Ra and δ ≈ 1 and the percentage of augmentation is equal to 65.55% for ϕ = 2%. According to the horizontal position, the heat transfer remains invariant for Ra = 103 and takes a maximum value near the active walls for Ra ≥ 104. The total entropy generation increases with Ra and decreases with ϕ for Ra = 106. The increase of ϕ from 0 to 2% leads to a reduction in close to 40.76%. For this value of Ra, the entropy is the maximum for δ = 0.4 and Xs = 0.35 and Xs = 0.65%. Moreover, as the Ra increases the Bejan number undergoes a decrease. The Bejan number is the maximum for Ra = 103 independently to δ and Xs. The superior thermal performance manifests at low Ra and high value of δ independently to the positions of the conducting body. Originality/value The originality of this paper is to analyze the hybrid nano-additive effects on the two-dimensional conjugate natural convection in a partitioned medium using the LBM. The experimental correlations used for the effective thermal conductivity and dynamic viscosity give credibility to our study. Different approaches such as heatlines and entropy generation are used.

Experimental and numerical study of the natural convection in dispersed systems in a heated rectangular cell

In this work, we study the appearance and development of convective flows in a dispersed medium by the experimental methods and mathematical modeling. An experimental study of the dynamics of thermoconvective flows is carried out in a specially designed cell, which is a rectangular vertical cavity with the possibility of heating the walls. A series of experiments were carried out at different temperature gradients. Various modes of convective flow have been obtained. To simulate the dynamics of convective flows in a rectangular cavity, a mathematical model based on the equations of thermal convection in the diffusion approximation has been created. Convective flow patterns for a dispersed medium have been obtained. Numerical calculations coincide with the experimental results. Numerical simulation of the problem allows us to estimate the distribution of velocities, temperature, and concentration of the dispersed phase inside the cell during the formation of convective flows and the established convection regime.

Unstable Density-Driven Flow in Fractured Porous Media: The Fractured Elder Problem

The Elder problem is one of the well-known examples of an unstable density-driven flow (DDF) and solute transport in porous media. The goal of this research is to investigate the influence of fracture networks on this benchmark problem due to the great importance of the fractured heterogeneity effect on unstable DDF. For this aim, the fractured Elder problem is solved using COMSOL Multiphysics, which is a finite element method simulator. Uniform and orthogonal fracture networks are embedded to analyze free convective flow and development of unstable salt plumes. The results indicate that the mesh sensitivity of the fractured Elder problem is greater than the homogeneous case. Furthermore, it has been shown that in the fractured cases, the onset of instability and free convection occur with lower critical Rayleigh number, which means that fracture networks have a destabilizing effect. Also, we examined the structural properties of fracture networks that control convective flow patterns, and the simulation results show that the strength of convection and instability at the beginning of the intrusion is proportional to the aperture size of the fractures. Moreover, the increase of the fracture’s density leads different modes of transient convective modes, until a specific fracture density after which the transient convective modes become similar to the homogenous case.

Hybrid Simulations of Magnetodisc Transport Driven by the Rayleigh‐Taylor Instability

AbstractPlasma transport in the rapidly rotating giant magnetospheres is thought to involve a centrifugally driven flux tube interchange instability, similar to the Rayleigh‐Taylor (RT) instability. In three dimensions, the convective flow patterns associated with the RT instability can produce strong guide field reconnection, allowing plasma mass to move radially outward while conserving magnetic flux (Ma et al., 2016, https://doi.org/10.1002/2015JA022122). We present a set of hybrid (kinetic ion/fluid electron) plasma simulations of the RT instability using high plasma beta conditions appropriate for the inner and middle magnetosphere at Jupiter and Saturn. A density gradient, combined with a centrifugal force, provide appropriate RT onset conditions. Pressure balance requires only a temperature gradient as the magnetic pressure is constant. Pressure balance is achieved with a temperature gradient in a fixed magnetic field. The three‐dimensional simulation domain represents a local volume of the magnetodisc resonant cavity. Simulated RT growth rates compare favorably with linear theory, where the fundamental mode of the resonant cavity determines the largest (stabilizing) parallel wavelength. We suggest that the perpendicular scale of RT structures is determined by the fundamental mode, which limits growth due to magnetic tension. Finally, we investigated strong guide field magnetic reconnection and diffusive processes as plausible mechanisms to facilitate kinetic‐scale radial transport.