Range Of Rayleigh Numbers Research Articles

Statistics of thermal plumes and dissipation rates in turbulent Rayleigh-Bénard convection in a cubic cell

We investigate the statistics of dissipation rates in turbulent Rayleigh-Bénard convection inside a cubic cell for air (Pr=0.7) in the Rayleigh number range 2×106≤Ra≤109 using direct numerical simulations. Based upon the product of the vertical velocity and the temperature fluctuation (v′θ′), the entire cell volume is decomposed into plume and background dominated regions. Different cutoff values (Ct=0−10% of the global maximum of v′θ′) are used to demarcate these regions, and for all Ct, the volume fraction of the plume dominated region (v′θ′>Ct) decreases with the increase in Ra, while that of the background (v′θ′≤Ct) increases. The contribution of both the regions to the thermal dissipation rate decreases with Rayleigh number with a power-law behaviour. At Ct=0, the thermal dissipation rates from the plume and background approach the global scaling for higher Rayleigh numbers (Ra≥108). For lower cutoffs, the plume contributions scale with Reynolds number as predicted by the Grossmann-Lohse theory, while significant deviations are observed in the background counterpart. We observe that the probability density functions (PDF) of the thermal dissipation rates depart considerably from a log-normal distribution, while for viscous dissipation the PDFs approach log-normality at higher Rayleigh numbers.

Effect of fibrous porous material on natural convection heat transfer from a horizontal circular cylinder located in a square enclosure

A numerical simulation study was carried out to investigate a steady two-dimensional laminar natural convective heat transfer from a uniformly heated inner circular cylinder placed inside an air-filled square enclosure with a porous material. The enclosure’s side and upper walls were isothermal, while the bottom wall was adiabatic. All the numerical calculations were performed in the range of Rayleigh numbers between 103 and 107. The material porosity (ε), the solid to fluid thermal conductivity ratio (kr), and Darcy number in the present study were 1.0, 0.5, and 0.01, respectively. The results showed that for Rayleigh numbers that are less than 106, the isotherms are almost parallel inside the three cold walls except for the corners of the adiabatic bottom wall. The rates of vertical velocity are higher than the horizontal velocity, especially at higher Grashof numbers. Also, the use of fibrous porous material with low thermal conductivity relative to the fluid thermal conductivity reduces the values of average Nusselt number, in addition to reducing the horizontal and vertical velocities along the horizontal axis.

Numerical Study of MHD Natural Convection in Trapezoidal Enclosure Filled With (50%MgO-50%Ag/Water) Hybrid Nanofluid: Heated Sinusoidal from Below

Numerical simulation of MHD free convection in a two-dimensional trapezoidal cavity of a hybrid nanofluid has been carried out in this research. The cavity is heated sinusoidal from the bottom wall, and the inclined walls are cooled while the top wall is isolated. The hybrid nanofluid (MgO-Ag/water) has been used as a working fluid. The numerical simulation has been validated with past papers and met a good agreement. The considered parameters are a range of Rayleigh number (Ra= 103 to 106), Hartmann number (Ha= 0 to 60) and volume fraction (f= 0 to 0.02). The results are presented as isotherms, stream functions, local and average Nusselt numbers, from which it is observed that the strength of the stream functions and isotherms increases with the increase of the Ra and ϕ while the increase in Hartmann number reduce the circulation of the flow and increases the isotherms strength. Also, the Nusselt number is increases with Ra and ϕ while it decreases with Ha.

Thermal state of a conical antenna cooled by means of nanofluid saturated porous media

Thermal state of a conical antenna used for big data transfer was determined in this work. Its cooling is provided through porous media saturated with water-based copper nanofluid (NF) whose volume fraction varies in the 0% (pure water) [Formula: see text] range. Otherwise, the ratio between the thermal conductivity of the highly porous material and that of the fluid base (water) varies between 4 and 41.2. The solution is obtained by means of 3D numerical approach based on the volume control method using the SIMPLE algorithm in the large [Formula: see text]–[Formula: see text] Rayleigh number range. The average temperature of the antenna can be determined with the correlation proposed in this work for any combination of the thermal conductivity ratio, volume fraction and Rayleigh number. This new and original correlation makes it possible to determine the optimal values of these three influencing parameters to ensure the correct antenna’s operation.

Natural convection with water-copper nanofluid around a finned vertical cylindrical electronic component

PurposeThe purpose of this study is to quantify the free convective heat transfer around a vertical cylindrical electronic component equipped with vertical fins representing an antenna, contained in a closed cavity maintained isothermal. Its cooling is provided via a water-based copper nanofluid whose volume fraction varies between 0% and 10%. Its effective viscosity and thermal conductivity are determined with the Brinkman and Maxwell models.Design/methodology/approachThe governing equation system has been solved by means of the volume control method based on the SIMPLE algorithm.FindingsA Nusselt-Rayleigh correlation valid in the 3.32 × 105 – 6.74 × 107 Rayleigh number range is proposed. It allows the thermal sizing of the considered system used in high power electronics to ensure their correct operation in the worst conditions.Originality/valueThe proposed correlations are original and unpublished.

Numerical investigation of nanoparticles slip mechanisms impact on the natural convection heat transfer characteristics of nanofluids in an enclosure

This study intends to give qualitative results toward the understanding of different slip mechanisms impact on the natural heat transfer performance of nanofluids. The slip mechanisms considered in this study are Brownian diffusion, thermophoretic diffusion, and sedimentation. This study compares three different Eulerian nanofluid models; Single-phase, two-phase, and a third model that consists of incorporating the three slip mechanisms in a two-phase drift-flux. These slip mechanisms are found to have different impacts depending on the nanoparticle concentration, where this effect ranges from negligible to dominant. It has been reported experimentally in the literature that, with high nanoparticle volume fraction the heat transfer deteriorates. Admittingly, classical nanofluid models are known to underpredict this impairment. To address this discrepancy, this study focuses on the effect of thermophoretic diffusion and sedimentation outcome as these two mechanisms turn out to be influencing players in the resulting heat transfer rate using the two-phase model. In particular, the necessity to account for the sedimentation contribution toward qualitative modeling of the heat transfer is highlighted. To this end, correlations relating the thermophoretic and sedimentation coefficients to the nanofluid concentration and Rayleigh number are proposed in this study. Numerical experiments are presented to show the effectiveness of the proposed two-phase model in approaching the experimental data, for the full range of Rayleigh number in the laminar flow regime and for nanoparticles concentration of (0% to 3%), with great satisfaction.

Development of unsteady natural convection in a square cavity under large temperature difference

To investigate how the nonuniform fluid density distribution caused by large temperature variations affects the development of unsteady natural convection, we perform a series of direct numerical simulations of two-dimensional compressible natural convection in an air-filled square cavity. The cavity has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The simulations are done using a kinetic approach based on a modeled Boltzmann equation, from which the fully compressible Navier–Stokes–Fourier equations are recovered. No Boussinesq approximation or low Mach number approximation is made. An extra source term is introduced to adjust the fluid Prandtl number. Simulations are performed for a range of Rayleigh numbers (107−109) with a fixed dimensionless temperature difference of ε=0.6 to determine the critical Rayleigh number and study the development of unsteady flow. To illustrate the instability mechanism, instantaneous fluctuation field, time trace of temperature, and velocity at selected monitoring points, the spectrum and other statistics are presented and discussed. As expected, significant differences are observed between the instability of compressible natural convection and the Boussinesq-type natural convection. With a large temperature difference, the transition to unsteady flow is asymmetric for the flows near the hot wall and cold wall. For the Rayleigh number range we studied, the cold wall region is dominated by low-frequency impact instability of the boundary thermal jet at the bottom corner. For the hot wall region, besides the upper corner impact instability, a boundary layer instability featuring high-frequency oscillations is observed.

Numerical simulation of thermal management during natural convection in a porous triangular cavity containing air and hot obstacles

A numerical study is presented of laminar viscous magnetohydrodynamic natural convection flow in a triangular-shaped porous enclosure filled with electrically conducting air and containing two hot obstacles. The mathematical model is formulated in terms of dimensional partial differential equations. The pressure gradient term is eliminated by using the vorticity–stream (\(\omega - \psi\)) function approach. The emerging dimensionless governing equations are employed by the regular finite difference scheme along with thermofluidic boundary conditions. The efficiency of the obtained computed results for isotherms and streamlines is validated via comparison with previously published work. The impact of physical parameters on streamlines and temperature contours for an extensive range of Rayleigh number (Ra = 103–105), Hartmann magnetohydrodynamic number (Ha = 5–30), Darcy parameter (Da = 0.0001–0.1) for fixed Prandtl number (Pr = 0.71) is considered. Numerical results are also presented for local and average Nusselt numbers along the hot base wall. Interesting features of the thermofluid behaviour are revealed. At lower Rayleigh number, the isotherms are generally parallel to the inclined wall and only distorted substantially near the obstacles at the left vertical adiabatic wall; however, with increasing Rayleigh number, this distortion is magnified in the core zone and simultaneously warmer zones expand towards the inclined cold wall. The simulations are relevant to magnetic materials processing and hybrid magnetic fuel cells.

A low-Rayleigh transition into chaos for natural convection inside a horizontal annulus at Prandtl number 0.1

Instabilities in the flow of natural convection in a horizontal annulus of radius ratio 2 filled with fluid of Prandtl number 0.1 are investigated numerically. The investigation largely focuses on the very small range of Rayleigh numbers between 3,500 and 5,000 in which the equivalent thermal conductivity increases suddenly. Since this instability is quite uncommon and only occurs in a narrow range of Rayleigh numbers, previous studies have not concentrated on the mechanism behind it. However, the present numerical simulation with very fine increments in Rayleigh number reveals that the jump in equivalent conductivity is caused by a transition into chaos, and this transition is akin to the typical Ruelle-Takens-Newhouse and Pomeau-Manneville scenarios. As well, it is more interesting that the flow escapes out of chaos and re-stabilizes at around the Rayleigh number of 4,800; it follows a reverse Pomeau-Manneville route. The progressions in the oscillatory pattern, power spectral density, and trajectories of equivalent conductivity in 2D and 3D phase spaces are plotted against the Rayleigh number in detail.

Study on forcing schemes in the thermal lattice Boltzmann method for simulation of natural convection flow problems

AbstractThe present study addresses the effect of various schemes for applying an external force term on the accuracy and performance of the thermal lattice Boltzmann method (LBM) for simulation of free convection problems. Herein, the forcing schemes of Luo, shifted velocity method, Guo, and exact difference method are applied by considering three velocity discrete models of D2Q4, D2Q5, and D2Q9. The accuracy and performance of these schemes are evaluated with the simulation of three natural convection problems, namely, free convection in a closed cavity, in a square enclosure with a hot obstacle inside, and the Rayleigh‐Benard problem. The obtained results based on the present thermal LBM with different forcing schemes and velocity discrete models are compared with the existing experimental and numerical data in the literature. This comparison study indicates that imposing all employed forcing schemes leads to similar performance for the simulation of free convection problems studied at the middle range of Rayleigh numbers. It is found that the Luo forcing scheme is simple for implementation in comparison with the other three forcing schemes and provides the results with acceptable accuracy at moderate Rayleigh numbers. At higher Rayleigh numbers, however, the Guo scheme is not only numerically stable but a more precise forcing scheme in comparison with the other three methods. It is illustrated that employing the discrete velocity model of D2Q4 has more appropriate numerical stability along with less computational cost in comparison with two other discrete velocity models for simulation of natural convection heat transfer.

MHD Double-Diffusive Natural Convection in a Closed Space Filled with Liquid Metal: Mesoscopic Analysis

In this paper, the lattice Boltzmann approach is carried out to study the double-diffusive natural convection in a space encapsulating liquid metal is presented. The Uniform magnetic field is applied horizontally at the square domain and an insulated rectangular block is kept stationary at the center of the cavity. The linear increment of temperature and concentration is used at the left wall and cold temperature is applied at the right wall. Horizontal walls are adiabatic conditions. Horizontal walls are adiabatic conditions. The numerical analysis is performed at the range of Rayleigh number (103 ≤ Ra ≤ 105), Lewis number (2 ≤ Le ≤ 10), buoyancy ratio (-2 ≤ N ≤ 2), Hartmann number (0 ≤ Ha ≤ 50) with Prandtl number (Pr) = 0.054. Results show that the increase in Ra tends to maximize heat and mass transfer rate while increasing Ha, decreases the same. The rise in Le diminishes heat transfer marginally but increasing the mass transfer significantly. The effect of N differs with different operating conditions, in general, the rate of heat and mass transfer is found to decrease with a decrease of N value.

Scale law analysis of the curved boundary layer evolving around a horizontal cylinder at Pr > 1

The convective boundary layer flow on the external surface of an isothermally heated horizontal cylinder is investigated in this study. Numerical simulations are first carried out for a wide range of flow parameters, i.e., Rayleigh and Prandtl numbers, and scale relations quantifying the boundary layer flow are then determined from the simulation data. The numerical results suggest that the curved boundary layer experiences an initial growth state, a transitional state, and a developed state, which are essentially identical to the extensively studied flat boundary layers. Scale relations quantifying the local flow variables are obtained, and the proposed scale laws indicate that during the initial growth, the present curved boundary layer flow follows a two-dimensional growth rather than the well-known one-dimensional startup of flat boundary layers. It is further demonstrated that the characteristic velocity of the boundary layer flow maximizes at π/2, but its thickness is circumferential location independent. In the steady state, however, the maximum streamwise velocity of the boundary layer shifts to approximately 7π/9 and the thickness consistently increases with the circumferential location. It is also shown that the thickness of the inner viscous boundary layer could be obtained by properly considering the Prandtl number effect, i.e., by the term (1 + Pr−1/2)−1. The proposed scale relations could reasonably describe the curved boundary layer flow, and all regression constants are above 0.99.

Porous materials saturated with water-copper nanofluid for heat transfer improvement between vertical concentric cones

Water-Copper nanofluid saturated porous materials are used to improve cooling of a conical electronic component contained in another concentric cavity of the same shape maintained at low temperature. Ratio between thermal conductivity of the solid matrix of the porous materials and that of the base fluid (water) varies between 4 and 41.2 while the nanofluid's volume fraction varies between 0% (pure water) and 10%. Free convective heat transfer was determined by means of a numerical approach based on the volume control method using the SIMPLE algorithm. Results show improvement of heat transfer as thermal conductivity ratio, nanoparticles concentration and Rayleigh number increase. Improvement was quantified through specific functions. New correlation is proposed to determine the average Nusselt number for any combination of the thermal conductivity ratio and nanofluid volume fraction in the 3.32x105-6.74x107 Rayleigh number range.

Optimization of Inclination Angle of Cavity and Characteristics of Attached Fins on the Absorber for Performance Enhancement of Solar Collectors

This research investigation was undertaken in ANDUAT, Kumarganj, Ayodhya, Uttar Pradesh, India to study the numerical optimization of natural convection heat suppression in a solar flat plate collector with straight fins. Optimal characteristics of an array of thin fins attached on the absorber plat were obtained by Particle Swarm Optimization algorithm (PSOA). Free convection considered dominant in the cavity. Governing equations contained continuity; momentum and energy are discretized by finite volume method. The medium is considered incompressible, whose free convection is dominant and Boussinesq approximation is applied. A simplified model of real systems is applied with free convection. Free convection problem is solved by SIMPLER algorithm. Two confined cavities with aspect ratios 30 and 60 are considered as flat plate solar collectors. The results indicate that significant reduction on the free convection heat loss can be obtained from solar flat plate collector by using plate fins, and an optimal plate fins configuration exit for minimal natural convection heat loss for a given range of Rayleigh number. Reduction of up to a maximum of 25% at 0 inclination angle was observed in aspect ratio 30. Results showed PSOA is able to obtain characteristics of attached adiabatic fins on the absorber plate also it can obtain optimal inclination angle of cavity to decrease heat losses from solar collectors. The results obtained provide a novel approach for improving design of flat plate solar collectors for optimal performance.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

Effects of Prandtl number in two-dimensional turbulent convection* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11961160719, 11702128, 91752201, and 11772362), the Shenzhen Fundamental Research Program (Grant No. JCYJ20190807160413162), the Fundamental Research Funds for the Central Universities (Sun Yat-sen University under Grant No. 19lgzd15), and the Department of Science and Technology of Guangdong Province, China (Grant

We report a numerical study of the Prandtl-number (Pr) effects in two-dimensional turbulent Rayleigh–Bénard convection. The simulations were conducted in a square box over the Pr range from 0.25 to 100 and over the Rayleigh number (Ra) range from 107 to 1010. We find that both the strength and the stability of the large-scale flow decrease with the increasing of Pr, and the flow pattern becomes plume-dominated at high Pr. The evolution in flow pattern is quantified by the Reynolds number (Re), with the Ra and the Pr scaling exponents varying from 0.54 to 0.67 and –0.87 to –0.93, respectively. It is further found that the non-dimensional heat flux at small Ra diverges strongly for different Pr, but their difference becomes marginal as Ra increases. For the thermal boundary layer, the spatially averaged thicknesses for all the Pr numbers can be described by δθ ∼ Ra −0.30 approximately, but the local values vary a lot for different Pr, which become more uniform with Pr increasing.

Significance of near-wall dynamics in enhancement of heat flux for roughness aided turbulent Rayleigh–Bénard convection

We report a numerical investigation of the effect of multiscale roughness on heat flux (Nu) and near-wall dynamics in turbulent Rayleigh–Bénard convection of air in a cell of aspect ratio 2 in the Rayleigh number (Ra) range 106≤Ra≤4.64×109. We observe that despite the same wetted area, taller roughness yields higher heat flux owing to a multiple roll state. Based on the number of roughness peaks penetrating the thermal boundary layer, three regimes are identified. In regime I, heat flux drops marginally as only 50% of the peaks emerge uncovered, followed by a nearly unaltered Nu in regime II. A sudden increase in Nu in regime III is noted with more than 65% penetrating peaks. In contrast to the previous observation, heat flux continues to increase even when all the peaks exceed the boundary layer. Transformation of two large-scale rolls into smaller multiple rolls favors better access to the trapped fluid in the roughness throat leading to greater mixing. A significant improvement in the mixing of fluid inside the cavities is found due to the cascade of secondary vortices, which is connected to the improved heat flux in the tallest roughness setup. A thin thermal boundary layer that envelopes the rough surface at higher Ra supports the enhanced inter-mixing of fluid inside the cavities. Greater perturbation of the thermal boundary layer for the smaller roughness setup shows consistent connection with the enhanced Nu(Ra) scaling.

Experimental Investigation of Free Convection Heat Transfer from Horizontal Cylinder to Nanofluids

The results of free convection heat transfer investigation from a horizontal, uniformly heated tube immersed in a nanofluid are presented. Experiments were performed with five base fluids, i.e., ethylene glycol (EG), distilled water (W) and the mixtures of EG and water with the ratios of 60/40, 50/50, 40/60 by volume, so the Rayleigh (Ra) number range was 3 × 104 ≤ Ra ≤ 1.3 × 106 and the Prandtl (Pr) number varied from 4.4 to 176. Alumina (Al2O3) nanoparticles were tested at the mass concentrations of 0.01, 0.1 and 1%. Enhancement as well as deterioration of heat transfer performance compared to the base fluids were detected depending on the composition of the nanofluid. Based on the experimental results obtained, a correlation equation that describes the dependence of the average Nusselt (Nu) number on the Ra number, Pr number and concentration of nanoparticles is proposed.

Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Bénard convection in a square cavity by direct numerical simulations. The Rayleigh number range is 1 × 108 ≤ Ra ≤ 1 × 1013, and the Prandtl number is selected as Pr = 0.7 and Pr = 4.3. It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns. In the thermal boundary layer, the normalized fluctuation θ rms/θ rms,max is independent of Ra and a power law relation is identified, i.e., θ rms/θ rms,max∼ (z / δ)0.99 ± 0.01, where z / δ is a dimensionless distance to the boundary (δ is the thickness of thermal boundary layer). Out of the boundary layer, when Ra ≤ 5 × 109, the profiles of θ rms/θ rms,max descend, then ascend, and finally drop dramatically as z/δ increases. While for Ra ≥ 1 × 1010, the profiles continuously decrease and finally overlap with each other. The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls. Besides, there is a critical value of Ra indicating the transition, beyond which the fluctuation 〈 θ rms〉 V has a power law dependence on Ra, given by 〈 θ rms〉 V ∼ Ra −0.14 ± 0.01.

The comparative investigation of three approaches to modeling the natural convection heat transfer: A case studyon conical cavity filled with Al2O3 nanoparticles

The cornerstone of a new method to modeling nanofluids is particle movement. There are three primary forms of nanofluid simulation. The single-phase modeling with nanofluid properties (SPU), the multiphase fluid with discrete particle (MDP) and the discrete element method with particle (DEMP). In this study, by comparing three approaches to modeling the natural convection heat transfer in nanofluid, this method's (discrete element method with particle) ability was examined to predict properties and processes, such as heat transfer and friction factor. With a high range of Rayleigh numbers (0 ≤ Ra ≤ 100, 000), this method tries to model the natural convection process in a conical cavity filled with Al2O3 nanofluid and nanoparticles. For modeling the MDP and thermophoresis effect (DEMP), a unique code with a novel grid generation algorithm was developed. The results demonstrated that the initial conditions determined the accuracy of the three methods for modeling the final parameters of natural convection within the conical cavity, the accuracy of the used equations, the procedure through which the boundary conditions were applied and the Rayleigh number. Accordingly, the DEMP and MDP methods were recommended for low Rayleigh numbers and those beyond 5500, respectively.