Low Rayleigh Numbers Research Articles

Limiting regimes of turbulent horizontal convection. Part 1. Intermediate and low Prandtl numbers

We report the existence of two new limiting turbulent regimes in horizontal convection (HC) using direct numerical simulations at intermediate to low Prandtl numbers. In our simulations, the flow is driven by a step-wise buoyancy profile imposed at the surface, with free-slip, no-flux conditions along all other boundaries, except along the spanwise direction, where periodicity is assumed. The flow is shown to transition to turbulence in the plume and the core, modifying the rate of heat and momentum transport. These transitions set a sequence of scaling laws that combine theoretical arguments from Shishkina, Grossmann and Lohse (SGL) and Hughes, Griffiths, Mullarney and Peterson (HGMP). The parameter range extends through Rayleigh numbers in the range [ $6.4\times 10^5, 1.92\times 10^{15}$ ] and Prandtl numbers in the range [ $2\times 10^{-3},2$ ]. At low Prandtl numbers and intermediate Rayleigh numbers, a core-driven regime is shown to follow a Nusselt-number scaling with $Ra^{1/6}Pr^{7/24}$ . For Rayleigh numbers larger than $10^{14}$ , the Nusselt number scales with $Ra^{0.225}Pr^{0.417}$ . For these particular regimes, the Reynolds number is found to scale as $Ra^{2/5}Pr^{-3/5}$ for the low-Prandtl-number regime and $Ra^{1/3}Pr^{1}$ for Rayleigh numbers larger than $10^{14}$ . These results embed the HGMP model in the SGL theory and extend the known regime diagram of HC at high Rayleigh numbers. In particular, we show that HC and Rayleigh–Bénard share similar turbulent characteristics at low Prandtl numbers, where HC is shown to be ruled by its core dynamics and turbulent boundary layers. This new scenario confirms that fully turbulent HC enhances the transport of heat and momentum with respect to previously reported regimes at high Rayleigh numbers. This work provides new insights into the applicability of HC for geophysical flows such as overturning circulations found in the atmosphere, the oceans, and flows near the Earth's inner core.

Numerical Investigation of Effect Partially Corrugated Heated Wall on Behaviour Natural Convection Heat Transfer in A Square Enclosure

For fluid flow and heat transfer with engineering industrial applications important methods called natural convection are used. The current numerical study focuses on the effect of changing the heating positions of the corrugated left wall on heat transfer by natural convection with laminar flow in a closed square two-dimensional cavity filled with air as a working fluid. The code of a commercial program (COMSOL Multiphysics 6.0) was used to solve the mathematical equations governing fluid flow represented by continuity, momentum, and conservation of thermal energy. The right wall is exposed to a cold temperature, the other walls are thermally insulated. The effect of partial heating of the left corrugated wall and the Rayleigh number on the process of heat transfer by free convection was studied. At different Rayleigh numbers, flow field patterns and temperature distribution lines appear. The average Nusselt number, the average air temperature, and the flow field are slightly affected by low Rayleigh numbers, while with high Rayleigh numbers, these parameters are significantly and noticeably affected and behave differently by changing the heating sites. Numerical results show negligible effects of wall heating sites at low Rayleigh numbers and significant effects at high Rayleigh numbers. Also, the Nusselt number increases progressively with increasing Rayleigh number, so the heat transfer process gets improved.

Double-reflection symmetry of thermal convection for Rayleigh number up to 1010

The Rayleigh–Bénard convection system exhibits certain known symmetries at low Rayleigh numbers that are broken as the Rayleigh number increases. In this study, we investigate the statistical symmetry of Rayleigh–Bénard convection at moderately high Rayleigh numbers through direct numerical simulations. The simulations are conducted for a fluid confined within two-dimensional walls, with an aspect ratio of unity and a fixed Prandtl number. Although elliptical large-scale circulations break both left-right and top-down reflection symmetries, we observe the emergence of a restored double-reflection symmetry. This symmetry is evident in the velocity and temperature fields, as well as in the variations of mean velocity and temperature profiles along the streamwise direction and the characteristics of the kinetic and thermal boundary layers. For Rayleigh numbers ranging between 107 and 1010, our results demonstrate a remarkable data collapse under this double-reflection transformation.

Thermal performance of nanofluid natural convection magneto-hydrodynamics within a chamber equipped with a hot block

In this study, flow and free convection thermal performance within a chamber in the presence of a permanent magnetic field are simulated. Boussinesq approximation and the Lorentz force equation are used for the density variation in free convection, and the magnetic field, respectively. The steady-state, two-dimensional, and incompressible governing equations are simulated using the Semi-Implicit Method for Pressure Linked Equations (SIMPLE). The present study is simulated for different Rayleigh numbers (Ra) corresponding to the situation where the conduction mechanism was predominant (Ra = 100) and the convection heat transfer was predominant (Ra = 105). Also, different intensities of the magnetic field (0 ≤ Ha ≤ 40) and different directions of the magnetic field along with the effects of three different nanoparticles Ag, Cu, and Al2O3 are given. The present study showed that in the case of the dominant convection mechanism, the presence of the magnetohydrodynamics (MHD) condition decreases the Nusselt number (Nu). However, if the conduction is predominant, the applied magnetic field improves the average Nu number. The optimum state for the magnetic field strength was found in the low Rayleigh number. The presence of nanoparticles also intensifies the magnetic field effects. In the high Rayleigh number, the heat transfer rate reduces by 13.5% with the increase of the Hartmann number.

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.

Natural convection heat transfer in an eccentric annulus filled with hybrid nanofluid under the influence of thermal radiation and heat generation/absorption

This investigation aims to scrutinize the flow and heat transfer characteristics of a hybrid nanofluid composed of Ag-MgO within an eccentric annular space, where the inner circular wall is held at a constant elevated temperature and the outer circular wall is uniformly cooled. Natural convection in such eccentric annular enclosures, with thermal radiation and the effects of heat generation/absorption taken into consideration, plays a vital role in various engineering applications, including solar collectors, nuclear reactors, thermal storage systems, and heat exchangers. The resolution of the fundamental governing equations was executed employing the Gauss-Seidel approach, with the inclusion of a sub-relaxation process, all within the framework of the finite volume method. The impact of the Rayleigh number, radiation number, volume fraction as well as heat generation/absorption coefficient on thermal transfer, flow, and temperature distributions were investigated. It was observed that for low Rayleigh numbers, radiation influences enhance flow stability and improve the conductive heat transfer mode. Conversely, at high Rayleigh numbers, radiation intensifies convective heat exchange. The growth of the Rayleigh number diminishes the impact of heat generation and reinforces the radiation heat transfer process, while heat absorption exhibits the opposite effect. From Nr = 1 onwards, the average Nusselt number values are no longer influenced by an increase in nanoparticle volumetric fraction, and they are solely linked to the radiation number.

Applying a momentum-based variable formulation in the SIMPLE algorithm to numerically solve thermo-buoyant turbulent flow in enclosures

Natural or buoyant convection flow is an exemplary heat transfer phenomenon, with growing applications in various industries. This article develops a new algorithm, which models and solves the buoyancy-driven turbulent flows in enclosures more accurately than the past similar solvers. A careful literature review shows that the past existing approaches have mostly had serious limitations to apply their algorithms to buoyancy-driven flows with high temperature differences magnitude because of employing the classical Boussinesq approximation. As the novelty of this study, it benefits from a momentum-based variable approach in the context of the semi-implicit method for the pressure linked equations (SIMPLE) algorithm, which lets it accurately solve the strong compressible buoyant flows with high temperature differences. The algorithm is applied to both the Navier-Stokes and the accompanied turbulent flow governing equations using OpenFOAM 4.1 as the platform. To validate the developed algorithm, the current results are compared with experimental data in both square and tall cavities considering low (8.6 × 105), high (1.43 × 106), and very high (1.58 × 109) Rayleigh numbers. As the major contribution of this work, it improves the accuracy of the thermo-buoyant turbulent flow prediction at both low and high Rayleigh numbers. All test cases are carried out employing two different turbulence models of k-ω and k-ε. Furthermore, comparing the results of the present non-Boussinesq algorithm and those of the past developed methods with the experimental data, it is shown that the present algorithm provides a more accurate prediction for the temperature field, that is, <10% differences with the experimental data. Moreover, the present maximum velocity results surpass the solution of the past numerical methods and show <3% differences with the experimental data.

The Lattice Boltzmann Simulation of Free Convection Heat Transfer of a Carbon-Nanotube Nanofluid in a Triangular Cavity with a Solar Heater

In this paper, the flow and free convection heat transfer of a multi-walled carbon nanotube/water nanofluid in a triangular cavity with a solar heater is studied using the lattice Boltzmann method. The side walls of the cavity are cold and the bottom wall is partially heated by a solar heater, which have a non-uniform temperature distribution. It is assumed that the heating energy is provided by an absorber that is directly exposed to sunlight. Because of the limited variations of density, the Boussinesq approximation is used, which causes the coupling of hydrodynamic and thermal fields. For velocity and temperature distribution functions, a lattice Boltzmann model with two dimensions and nine directions is adopted. The effect of parameters, such as the Rayleigh number, the volume fraction of nanoparticles, and the position of solar heater, on the flow and heat fields is studied. The results show that, for all Rayleigh numbers studied, the Nusselt number increases as nanoparticles volume fraction increases. The addition of 4% nanoparticles causes the average Nusselt number to increase about 11% at low (Ra = 103) and moderate (Ra = 104) Rayleigh numbers and 217% at the high Rayleigh number (Ra = 105). Furthermore, it is shown that for a fixed Rayleigh number, heat transfer can be optimized by adjusting solar heater’s position. This study can provide a useful insight for utilizing solar heaters with non-uniform temperature distribution in triangular cavities.

Oscillatory instability of magneto-convection during the melting of non-Newtonian ferromagnetic nano-enhanced phase change materials at low Rayleigh number

This work complements mechanism of the oscillatory instability of magneto-convection in the process of melting heat transfer controlled by magnetic field at low Rayleigh number (Ra), aiming to provide a theoretical basis for improving the stability of energy storage system and melting manufacturing process. A latent heat storage cavity unit exposed in uniform magnetic field is designed to reveal the magnetic-controlled heat transfer in solid–liquid phase change process. The volume average method is used to describe porous media composite nano-enhanced phase change materials in latent heat unit. Special attentions are paid to the key parameters of Magnetic number (Mn) and Ra, and coupling flow heat transfer mechanism of magnetic force and natural convection effect is numerically studied. The evolution stages of different flow patterns are divided according to the Kelvin force, vorticity, velocity, flow field and isotherm distributions of characteristic points. Main results show that the magnetic field-modulated phase change process at low Ra can be divided into three stages, of which the second stage is characterized by periodic oscillations. Increasing Mn at fixed Ra accelerates the second stage of oscillatory convection heat transfer coming earlier and promotes melting. When Mn increase to 5 × 106, the full melting time is reduced to the greatest extent, resulting in 11.6 % reduction in heat storage but 17.4 % increase in heat storage efficiency. Three mechanisms of magnetic forced convection coupled with natural convection are found during the increase of Ra: synergistic (Ra < 2 × 103), antagonistic (2 × 103≤ Ra < 1 × 104), and natural convection-dominated (Ra = 1 × 104). Finally, the mode distribution map of Ra-Mn regulation is obtained, in which the unstable transformation mechanism of steady-state, periodic oscillation and chaotic oscillation heat transfer in the melting process under the control of magnetic field is described.

Rayleigh–Bénard Convection With Multiple Solutions in Trapezoidal Closed Cavities

Abstract Rayleigh–Bénard convection (RBC) in symmetric trapezoidal closed cavities with cavity angle ϕ=70°−110°, filled with air, is studied using numerical simulations where inclined side walls are adiabatic. In contrast to rectangular cavities, where no flow exists below a threshold value, there is a weak convection even at a low Rayleigh number (Ra) due to the fact that there is a component of thermal gradient in the horizontal direction in these cavities. Interestingly, these cavities show sudden and significant jumps in the convection, similar to square cavities (Rac = 2585.02 for ϕ=90°), as Ra increases beyond a critical value (Rac). It is noted here that these Rac represent symmetry-breaking pitchfork bifurcations. These bifurcations are seen in both acute (Rac = 8000 for ϕ=70°) and obtuse (Rac = 2300 for ϕ=110°) angle trapezoidal cavities. Moreover, it is observed that multiple steady-state solutions (MSSS) exist as Ra is further increased. A forward and backward continuation approach for numerical simulations is used to track the co-existence of MSSS. These steady-states have co-existing one-roll and two-roll convective patterns beyond another threshold value of Ra. Here, two types of critical Ra have been identified for different cavity angles; one shows the sudden jump in the convection, and the other is the one beyond which MSSS co-exist. Furthermore, a codimension two bifurcation analysis is carried out with Ra and ϕ as two parameters. The bifurcation analysis divides the parameter space into different regions based on the multiplicity of the solutions.

Influence of magnetic field on dynamic behavior of double-diffusive convection

Double-diffusive convection under an external magnetic field has several industrial applications, and how the magnetic field affects flow and heat and mass transfer is a research focus. This paper studies the dynamical behavior of two-dimensional double-diffusive convection in a uniform magnetic field is investigated using a high-accuracy numerical method. The effects of the magnetic field strength on the flow and on the heat and mass transfer are analyzed, and the process of flow transition in the presence of a magnetic field is studied. The results show that, as the strength of the magnetic field increases, the flow is gradually inhibited, and most of the heat transfer occurs through conduction. For a fixed magnetic field strength, the temperature-dominated flow changes from periodic to chaotic, and finally back to periodic, as the orientation of the magnetic field increases. Two types of periodic flow occur in the transition route, namely, a simple periodic flow with an integer multiple of the fundamental frequency and a complex periodic flow with multiple lower-frequency subharmonic waves. In the presence of a strong magnetic field, the effect of the magnetic field orientation on the flow is significant. At high Rayleigh numbers and a fixed magnetic field strength, the heat transfer efficiency of a vertical magnetic field surpasses that of a horizontal magnetic field by approximately 50% when temperature is dominant, achieving a mass transfer efficiency of about 100%. In cases when concentration is dominant, the heat transfer efficiency of a vertical magnetic field is 20% higher than that of a horizontal magnetic field, and the mass transfer efficiency is approximately 60% higher for the vertical magnetic field compared to the horizontal magnetic field. The flow transitions from chaotic or periodic to steady as the Prandtl number increases. The solution branch bifurcates at certain Prandtl numbers, and hysteresis appears when Prandtl number is equal to 0.023. For low Rayleigh numbers, the heat and mass transfer efficiencies increase monotonically with increasing Prandtl number under a weak magnetic field but remain constant for various Prandtl numbers under a strong magnetic field.

Investigation of Fractal Fins towards Heat Transfer Properties in Thermal Storage System

To augment heat transfer in energy storage systems, fin inclusion is frequently adopted. This study critically examines various fin arrangements by employing a dimensionless parameter calculation method. Metrics of comparison include total melting time, dynamic temperature behavior, liquid fraction, and a unit performance indicator. The findings reveal that at Prandtl and Stefan numbers of unity, a Rayleigh number of 104 demarcates the boundary between convective and conductive heat transfer, thus determining the dominant heat transfer mode. By reorienting the internal fins within a four-fin structure, we observed improved transfer performance at low Rayleigh numbers (Ra ≤ 104); the liquid fraction approached unity with rising Rayleigh numbers. When assessing the unit performance metric, the reoriented four-fin structure manifested superior attributes in comparison to alternative configurations for Ra ≤ 5 × 104. However, at higher Rayleigh numbers, complex fin structures impede heat convection, and the two-fin structure makes the more effective configuration.

Enhancing the convective heat transfer in vertical and horizontal rectangular enclosures using nanofluids: The crucial role of aspect ratio

This study extensively examines double-diffusive natural convection of a water nanofluid containing Al2O3 nanoparticles in both horizontal and vertical rectangular enclosures subjected to uniform thermal and solutal fluxes along the horizontal direction. The key contribution of this research is to emphasize the significance of aspect ratio as a critical factor for enhancing heat transfer. Neglecting this factor could have substantial implications for the advancement and practical application of nanotechnology in heat transfer. The study also examines the impact of other relevant parameters namely nanoparticle concentration, thermal Rayleigh number, and three distinct models to calculate effective viscosity and thermal conductivity. A comparison among these models highlights a notable disparity between models based on experimental data (model II and III) and that based on theoretical assumptions (model I). It was revealed that the thermal Rayleigh number manifests a notable impact on both heat and mass transfers, especially for horizontal enclosures, and an augmentation in the aspect ratio improves the convective heat and mass transfers. However, for lower Rayleigh numbers, the aspect ratio effect diminishes. The incorporation of nanoparticles might deteriorate up to 21% or enhance up to 12% heat transfer according to the dominant transfer mode, we obtain the enhancement in conduction and deterioration in convection. Model I gives higher Nusselt and Sherwood numbers, followed by models II and III, but model I showed a peculiar behavior compared to models II and III. A critical aspect ratio is identified which defines the regions where nanofluid enhances heat transfer compared with clear water.

The Influence of linear Heating on Free Convection in a Cylindrical Enclosure

The current study aims to numerically investigate free convection airflow within a horizontal cylinder with a linearly heated side wall. The computation of heat transfer and fluid flow structure has been carried out using the finite element software COMSOL Multiphysics. The influence of the heat source position on fluid flow and heat transfer is inspected. Special attention is paid to the effect of Rayleigh number and the heater position on energy efficiency within the cavity. The results indicate that the best heat transfer performance is achieved for low Rayleigh numbers and when the active wall is centered in the vicinity of 90°.

The appearance of oscillatory flows within a horizontal packed bed partly heated from below

We report on a numerical investigation of the unsteady mixed convective flow in a channel through a horizontal porous layer under localised isothermal heating from below to probe the oscillatory flow and thermal characteristics. The study was carried out for water flow within a plane channel containing stainless steel spherical particles. For this study, the channel height/particle diameter ratio was H/d=100 and the porosity was ɛ=0.35. The effects of the imposed pressure-driven flow characterised by the Péclet number (0.1≤Pe≤1000), and heating represented by the Rayleigh number (105≤Ra≤2×107), are investigated. The results reveal that for low Péclet numbers, steady free convective flows are dominant, while for high Péclet numbers, steady forced convective flows dominate. Importantly, no oscillatory flows are found to develop in the free and forced convection regimes. However, for moderate Péclet numbers, oscillatory mixed convective flows occur with different periodic, quasi-periodic, and chaotic flow behaviours. In addition, for low Rayleigh numbers, Ra≤106, the Nusselt number is not influenced by the Péclet number for Pe≤1. Nevertheless, for high Rayleigh numbers, Ra≥2×106, it is observed that there always exists a critical Péclet number for which the Nusselt number is a minimum. The effects of the Péclet and Rayleigh numbers on the local and average temperature disparity between the fluid and solid phases are then investigated.

Hydrothermal and entropy generation analyses of natural convection of nano-encapsulated phase change materials suspension in a cavity subjected to the localized heating

Being heated electronic components significantly reduces their efficiency, and thus requiring high-efficient cooling strategies to keep such devices operating at an optimal temperature level. The present study is devoted to investigating the cooling performance of water-based nano-encapsulated phase change materials (NePCMs) suspension in the presence of a heat source with uniform temperature. The nano-sized PCM capsules are constructed by n-nonadecane as the core and polyurethane for the protective shell. The n-nonadecane is capable of absorbing/releasing a significant quantity of latent heat in the process of its phase transition, which is actually beneficial for improving the heat transfer performance. The home developed FORTRAN program based on the finite volume method (FVM) combined with the artificial compressibility algorithm is employed to solve the nonlinear coupled equations for fluid flow and heat transfer. The influences of the Rayleigh number (103≤Ra≤105), the Stefan number (0.1≤Ste≤0.9), the volume fraction of the nano-capsules (0≤ϕ≤0.04), and the heating position (0.25≤a≤0.75) on the hydrothermal behavior and entropy generation are explored. The findings reveal that there exists a capsule loading interval wherein the heat transfer enhancement can be achieved, but beyond that range, the deterioration of cooling performance may occur. Moreover, the contribution of suspending NePCMs to the heat transfer improvement is greatly more noticeable at low Rayleigh number, and particularly for the arrangement of upper heating. The average Nusselt number decreases with the increment of the Stefan number, and the variation approximately follows an exponential change for all considered Rayleigh numbers and heating positions. Concerning the entropy generation, it is essentially contributed by the heat transfer irreversibility, and the region with high irreversibility is always located around the intersection of the heated surface and the insulated vertical wall. This research can provide theoretical guidance for cooling the electronic components by utilizing the NePCMs suspension.

Simulation investigation of the oscillatory motion of two elliptic obstacles located within a quarter-circle cavity filled with Cu-Al2O3/water hybrid nanofluid

This study investigates the consequences of introducing a pair of oscillating elliptical obstacles on the natural convection and entropy generation within a quarter-circle cavity that is filled with a water-based hybrid nanofluid. The Galerkin Finite Element Method was utilized to perform numerical simulations on a 2-dimensional cavity, where the outer wall was set to a low temperature and the inner wall was kept at a high temperature, while the other walls were adiabatic. The hybrid nanofluid containing Cu-Al2O3 nanoparticles was used. The impact of changes in the values of dimensionless parameters, such as the Rayleigh number, heated wall length, oscillation frequency, oscillation amplitude, and oscillation period, on the flow and heat transfer within the cavity was examined. Results showed that an increase in the length of the hot source resulted in a decrease in heat transfer rate and that increasing the Rayleigh number led to a significant increase in total entropy generation and heat transfer irreversibility. A drop in the average Bejan number was noted as the Rayleigh number increased, demonstrating the prevalence of entropy caused by fluid friction. The effect of changing the amplitude had a higher impact on the average Nusselt number compared to the frequency value. At low Rayleigh numbers, the average Nusselt number was higher when the elliptical obstacles oscillated in the same direction, while the opposite trend was observed at higher Rayleigh numbers.

Weakly nonlinear bifurcation behaviour at the onset of instability in horizontal convection using an advective buoyancy approximation

Horizontal free convection is studied under an extended buoyancy approximation constructed to capture centrifugal effects in strongly rotating regions within buoyancy driven flows. Under this approximation, the Gay-Lussac parameter (Ga) arises in the momentum equation to characterise non-Boussinesq behaviour. The scaling of average Nusselt numbers (Nuavg) are determined, as is its dependence on Ga. Increasing Ga is found to decrease Nuavg when convection dominates the flow, while no influence is detected in the low Rayleigh number regime dominated by conduction. The influence of Ga on the onset of the time-dependent regime is investigated and the critical Rayleigh number corresponding to different Ga are determined. Results demonstrate that increasing Ga stabilises the flow, delaying transition to the time-dependent regime. An Orr–Sommerfeld type stability analysis is performed to determine the local stability at different horizontal stations. A zone of convective instability is first detected, growing from the hot end of the enclosure, at Rayleigh numbers three orders of magnitude lower than the predicted global stability threshold at the maximum investigated Ga value. Ga is found to play a key role in determining the preferred orientation of instability roll structures, with increasing Ga being accompanied by a bias toward transverse-roll instabilities over longitudinal rolls. The Stuart—Landau model is used to reveal that the non-linear characteristics of this unsteady transition are consistent with a supercritical Hopf bifurcation.

Natural Convective Nanofluid Flows Immersed in Oscillating Magnetic Fields Simulated by a Sub-Continuous Lattice Boltzmann Model

Abstract Natural convective nanofluid flows immersed in oscillating magnetic fields are simulated with a sub-continuous nondimensional lattice Boltzmann model. The effective electrical conductivity model is built including coupled effects of nanoparticle concentrations and two Knudsen numbers. Effects of directions, frequencies, and strength amplitudes of the magnetic fields are studied in wide ranges of Hartmann numbers (0.1≤Haf,L≤600) and Rayleigh numbers (103≤Raf,L≤107). To achieve higher values of cycle averaged Nusselt numbers Nu¯̂f,L, optimal magnetic directions are along or opposite from the gravity directions. Effects of the magnetic frequency f˜B are negligible, in the conduction dominating lower Rayleigh number regime of Raf,L&amp;lt;104. In the convection dominating regime, Nu¯̂f,L increase with Raf,L in orders of Raf,L0.48 and Raf,L0.45 for vertical and horizontal magnetic directions, respectively, and maximum values of Nu¯̂f,L appear at the optimal magnetic frequency of f˜B=1/5cs*MaL(L/UL) for all magnetic directions. With Raf,L as high as 106, the oscillating amplitudes of the transient wall mean Nusselt numbers Nu¯f,L increase with increasing Haf,L, but the cycle averaged Nusselt numbers Nu¯̂f,L decrease from 9.35 to 1.42 with increasing Haf,L in the transient regime of 5≤Haf,L≤500. Meanwhile, heat transfer patterns transit back from convection to conduction dominating patterns with increasing Haf,L, as illustrated by transient streamlines and isotherms.

Wall slip effects in Rayleigh–Bénard convection of viscoplastic materials

PurposeAccording to the research, viscoplastic fluids are sensitive to slipping. The purpose of this study is to determine whether slip affects the Rayleigh–Bénard convection of viscoplastic fluids in cavities and, if so, under what conditions.Design/methodology/approachThe wall slip was evaluated using a model created for viscoplastic (Bingham) fluids. The coupled conservation equations were solved numerically using the finite element method. Simulations were performed for various parameters: the Rayleigh number, yield number, slip yield number and friction number.FindingsWall slip determines two essential yield stresses: a specific yield stress value beyond which wall slippage is impossible (S_Yc); and a maximum yield stress beyond which convective flow is impossible (Y_c). At low Rayleigh numbers, Y_c is smaller than S_Yc. Hence, the flow attained a stable (conduction) condition before achieving the no-slip condition. However, for more significant Rayleigh numbers Y_c exceeded S_Yc. Thus, the flow will slip at low yield numbers while remaining no-slip at high yield numbers. The possibility of slipping on the wall increases the buoyancy force, facilitating the onset of Rayleigh–Bénard convection.Originality/valueAn essential aspect of this study lies in its comprehensive examination of the effect of slippage on the natural convection flow of viscoplastic materials within a cavity, which has not been previously investigated. This research contributes to a new understanding of the viscoplastic fluid behavior resulting from slipping.