Low Rayleigh Numbers Research Articles

Impact of Linear Heating Profiles on Nanofluidic Convection in Enclosure

The present study demonstrates the influence of non-uniform heating on the nanofluidic thermal convection in an enclosure by keeping the mean temperature of heating constant. The non-uniform heating is applied by varying the slope of the linear temperature profile from 0° to 60° at an interval of 15°. The investigation is executed numerically following the finite volume discretization technique. Two different cases are taken into consideration: Case A for linearly increasing temperatures and Case B for linearly decreasing temperatures. The flow structures and heat transfer characteristics are studied for the Rayleigh number from 103 to 106 and the copper-water nanoparticle concentrations from 0 to 0.04, utilizing the streamlines, isotherms, and heatlines. The results reveal that the mean Nusselt number monotonically increases with a rise in slope for all linearly increasing temperature profiles. For the decreasing profiles (Case B), the Nusselt number decreases with a rise in the temperature slope for the lower Rayleigh number (103 and 104); however, a marginal increment is observed at the maximum profile angle for the higher Rayleigh number (105 and 106). This study provides findings helpful for designing thermal devices with the efficient utilization of heating sources.

Study on the melting process of oxide layer of micrometer-sized aluminum particles using Lattice Boltzmann method

The study of the oxide layer in aluminum-oxygen combustion is crucial for the subsequent reaction. In this article, a 2-D lattice Boltzmann model is established and the effects of different Rayleigh number, oxide thickness, Ste number, and porosity on melting speed and melting time are studied based on the enthalpy method. The results demonstrate that a low Rayleigh number has no noticeable impact on the melting process. However, a rise in the Rayleigh number can obviously advance the melting process when the Rayleigh number exceeds 105. The melting speed slows down and the melting time prolongs as the oxide thickness increases, but the effect of thickness on melting speed decreases progressively with increasing thickness. In contrast, rising Stefan number can promote the melting process, and the effect is more pronounced at lower Stefan number. High porosity is beneficial to the development of natural convection and is able to significantly boost the melting process.

Simulation of heat transfer in a nanoparticle enhanced phase change material to design battery thermal management systems: A lattice Boltzmann method study

BackgroundIn the present paper, the natural convection of phase change material (PCM) in a T-shaped cavity is investigated by the lattice Boltzmann method (LBM). In recent years, LBM has become a powerful method for computational modeling of a broad variety of complex fluid flow concerns, including the simulation of the melting process in PCMs. MethodsThe enclosure contains CuO nanoparticles and two constant temperature heat sources on the sidewalls of the cavity. The obtained results are presented in different Rayleigh numbers (Ra=103–105), cavity angles (θ = 0 − 90), the volume fraction of nanoparticles (ϕ = 0 − 0.03), and aspect ratios. Results show that the PCM melting speed is lower for low Rayleigh numbers compared to when the number is equal to 105 by 50%. To alter melting time in a specific Ra number, adding nanoparticles, changing cavity slope, and aspect ratio are investigated. Results show that the melting rate is little affected by the addition of nanoparticles but, generally adding nanoparticles delays PCM melting. Significant findingsRaising the distance between the battery and the top of the cavity is known to delay melting by 70% when the distance ratio increase from H1/H = 0.25 to 075, whereas increasing or lowering the distance between the batteries does not affect the melting time. Such a study can be used to design battery thermal management systems (BTMS).

Hydrothermal impact of multiwall carbon nanotube diameter in a conventional square cavity

This study aimed to computationally examine the effect of the average diameter of multiwall carbon nanotubes (MWCNTs) on the hydrothermal properties of a square cavity. A conventional square cavity filled with MWCNT–water was used for the experiment. The left and right walls of the cavity are maintained as hot and cold respectively, whereas the top and bottom walls were assumed to be adiabatic. Mathematical models were developed using the Navier–Stokes equations by applying the thermophysical properties of the MWCNT–water nanofluid. A newly proposed correlation between the effective thermal conductivity and the diameter of carbon nanotube was utilized to analyze the impact of the average diameter on the natural convection of nanofluid inside the cavity. The governing equations were non-dimensionalized using suitable variables and then solved using the Galerkin finite element technique. The combined effects of the Rayleigh number (103<Ra<106) and the average diameter of the MWCNTs (10 nm to 30 nm) on the streamlines, isolines, velocity, local Nusselt number, and mean Nusselt number were examined in detail. It is found that the flow and heat transfer rate inside the cavity can be effectively controlled by increasing the average diameter of MWCNTs at higher Rayleigh numbers compared to lower Rayleigh number. A larger MWCNT diameter dominated the impact of the buoyancy force inside the square cavity.

Experimental study on subcooled pool boiling of FC-72 on a flat plate in normal and microgravity

A series of experimental studies on the heat transfer characteristics of pool boiling were conducted aboard the Chinese satellite SJ-10 in April 2016. Ground comparative experiments under the same conditions were carried out using the same apparatus. FC-72 was used as the working fluid containing non-condensable gas. The total quasi-stable-state acceleration aboard satellite SJ-10 during its in-orbit flight is approximately 2 × 10−6 g0. The integrated microheater fabricated by the microelectromechanical system (MEMS) technique was used to investigate the boiling characteristics. The boiling surface of the integrated microheater is on top of a flat plate quartz glass wafer substrate 2 mm thick, heated by a serpentine Pt thin film (main heater) below the substrate. The effective area of the boiling surface in direct contact with FC-72 is 5.5 mm in diameter. Ten temperature sensors are located around the boiling surface center and uniformly distributed in the circumferential direction. The experimental results show that single-phase convection could still be maintained under lower Rayleigh number conditions, showing consistency with the predictions based on the available correlations. The generated bubble volume determines the boiling state. At high liquid subcooling, the bubbles formed after the liquid vaporizes are relatively small, and steam condensation at the bubble cap promotes the phase change efficiency, which maintains nucleate boiling in microgravity. When subcooling is low, bubbles are larger and cover most of the heating surface, nucleate boiling is difficult to maintain, and the boiling becomes transition boiling. High liquid subcooling improves the heat transfer efficiency, thereby contributing to maintaining the progress of nucleate boiling in microgravity. However, boiling is less affected by liquid subcooling on the ground than in microgravity. A comparison of pool boiling curves between microgravity and normal gravity experiments indicates that nucleate boiling curves under the same subcooling partially overlap, while the heat flux corresponding to the initiation of the nucleate state is lower than that on the ground. In microgravity, lower liquid subcooling and higher heating power will result in larger bubble volumes and easier complete coverage of the heating surface, resulting in an easier transition from nucleate boiling to film boiling.

The Effect of Vibrating Inner Cylinder on Natural Convective Heat Transfer in Concentric and Eccentric Horizontal Cylindrical Annuli

In this study, natural heat convection caused by centric and vertically eccentric long horizontal cylinders under the influence of vibration is experimentally investigated. The internal wall of the annulus is heated and kept at a constant heat flux, while the outside wall is cooled and maintained at a constant temperature. The vibration frequency impacts the annular convection heat transfer process and the effects of the Rayleigh number, heat flow, and eccentricity. This work employed a moderate, laminar-ranging Rayleigh number from (5×104 to 6.48×106), while the eccentricity range is varied from (-0.667, 0, and+0.667). The investigation is carried out at five different frequencies (0, 2, 5, 10, 15, and 20 Hz); therefore, it was decided to compare the case under the same circumstances in both the absence and presence of vibration. The present results' verification worked exceptionally well in concordance with previous studies. When heat fluxes are considered, the study demonstrates that the temperature difference along the gap (radial difference) between the two cylinders significantly decreases for negative as opposed to positive eccentricities for each Rayleigh number. For different eccentricities, it was discovered that the temperature difference decreased as the Rayleigh number increased. Along with these reductions, the temperature difference was promoted as the vibration frequency increased, which is significant at (20 Hz) within the range considered for controlling parameters. It was also observed that the decrease in temperature difference is higher for the negative eccentric position than for the centric and positive positions. At vertical positive eccentricity at a low Rayleigh number, the gain in vibrational average Nusselt number caused by applying vibration had a minimum value of 22.50601475%, While at the higher value of the Rayleigh number, the maximum increase in negative vertical eccentricity was 86.66933125%. However, the gain in the average Nusselt number depends on the position of the heated inner cylinder, the Rayleigh number, and the vibrational frequency.

Natural convection of Cu-[formula omitted] nanofluid inside hexagonal enclosure fitted with a square cavity with a non-uniformly heated wall(s)

Numerical simulations are undertaken to investigate the flow of fluids and heat transfer through a nanofluid inside a hexagonal enclosure fitted with a square cavity and characterized by buoyancy-driven fluid motion. A periodic hot temperature Th and cold temperature Tc respectively, with Th > Tc is maintained on the parallel walls of the cavity on a regular basis. The Galerkin finite element method discretizes the equations in two dimensions. Stabilized solutions are obtained by using an upwind scheme. Based on the developed code, a parametric study of fluid flow and heat transfer inside the cavity is conducted to study the effects of the Rayleigh number. As the Rayleigh number and nanoparticle volume fraction increase from 101to106, the Nusselt number increases as well. Additionally, the bottom-middle and middle locations of the thermally active parts have the highest average Nusselt numbers for the high and low Rayleigh numbers. The novelty and originality of the proposed work lie in the exploration of a unique hexagonal cavity geometry, the parametric study involving varying Rayleigh numbers and nanoparticle volume fractions, and the utilization of numerical simulations with advanced computational techniques. These contributions enhance the understanding of nanofluid behavior and provide valuable insights for optimizing heat transfer systems in various applications.

Effect of natural convection hybrid nanofluid flow on the migration and deposition of MWCNT-Fe[formula omitted]O[formula omitted] in a square enclosure

In the present study, the migration and deposition of multi-walled carbon nanotube (MWCNT)-Fe3O4 nanocomposite particles in a square enclosure for natural convection hybrid nanofluid flow are analysed numerically using the Eulerian–Lagrangian model with one-way coupling. The governing equations are solved by the finite volume method and Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The location and velocity of 3000 selected composite particles in the host nanofluid are obtained by employing the Lagrangian approach. The influences of Rayleigh number and nanoparticle volume fraction on the thermal and flow behaviours of the system are presented. It is observed that the increasing volume fraction leads to a rise in the average Nusselt number at low Rayleigh numbers, while the case of ϕ=0.1% is the optimum volume fraction of nanoparticle in terms of heat transfer enhancement and strength of flow structure at Ra≥104. The simulations of Lagrangian particle tracking demonstrate that the minimum deposition rate of composite particles with dp=0.5 μm is obtained for a given Rayleigh number. The number of deposited large composite particles for the case of ϕ=0.1% is slightly more than for ϕ=0.3%, while the deposition rate of ultra-fine composite particles gets a higher value in the case of ϕ=0.3%. Moreover, the thermophoresis force plays a more significant role in small particle deposition than the Brownian random force.

Darcy number influence on natural convection around porous cylinders in an enclosure using Darcy- Brinkman-Forchheimer model: LBM study

We evaluated numerically the combined impact of Darcy and Rayleigh number changes on natural convection around two vertically arranged hot porous cylinders of different diameters in a square enclosure. Numerical simulations are conducted by implementing lattice Boltzmann technique using the D2Q9 model. The Darcy-Brinkman-Forchheimer equations for porous medium are solved with a single-domain approach. The influence of Darcy number (10−6≤Da≤ 10−2) on rate of heat transfer from cylinders is described for 104≤Ra≤ 106 by altering the cylinder diameter from 0.1 to 0.4L. With increment of cylinder size, Ra and Da, heat transfer rates are found to improve. At Ra = 106, the highest enhancement occurs for D = 0.1L. On lower Rayleigh numbers (Ra = 104) as well as Darcy numbers (Da = 10−6), doubling the diameter of the cylinder increases heat transport by 41.5%. Consequently, when the diameter is multiplied by four, the improvement is 211%. At Ra = 106, the rate of augmentation from D = 0.2L–0.3L is lower than for the case when D = 0.1L and 0.2L. At D = 0.4L maximal transfer of heat arises when the cylinder is extremely permeable (i.e., Da = 10−2). This study has applications in the thermal management of a bank of electronic components.

Reconstructing Rayleigh-Bénard flows out of temperature-only measurements using Physics-Informed Neural Networks.

We investigate the capabilities of Physics-Informed Neural Networks (PINNs) to reconstruct turbulent Rayleigh-Bénard flows using only temperature information. We perform a quantitative analysis of the quality of the reconstructions at various amounts of low-passed-filtered information and turbulent intensities. We compare our results with those obtained via nudging, a classical equation-informed data assimilation technique. At low Rayleigh numbers, PINNs are able to reconstruct with high precision, comparable to the one achieved with nudging. At high Rayleigh numbers, PINNs outperform nudging and are able to achieve satisfactory reconstruction of the velocity fields only when data for temperature is provided with high spatial and temporal density. When data becomes sparse, the PINNs performance worsens, not only in a point-to-point error sense but also, and contrary to nudging, in a statistical sense, as can be seen in the probability density functions and energy spectra. Visualizations of temperature (top) and vertical velocity (bottom) for the flow with [Formula: see text]. The left column shows the reference data, the other three columns show the reconstructions obtained with [Formula: see text], 14 and 31. The locations of the measuring probes (corresponding to the case with [Formula: see text]) are marked with white dots on top of [Formula: see text]. All visualizations share the same colorbar.

Evaluation and optimization on heat transfer performance of a composite phase change material embedded in porous ceramic skeleton: A lattice Boltzmann study

The thermal performances of phase change materials (PCMs) are of great importance to latent heat thermal energy storage applications. In order to improve the thermal properties, the composite PCM of inorganic salt embedded in porous ceramic skeleton was proposed and investigated in this study. The numerical model for the phase change process of PCM was developed by applying the lattice Boltzmann method. Simulation results indicate that the existence of porous ceramic materials could not only enhance the heat conduction of PCM but also hinder the convective heat transfer. In addition, the results show that Rayleigh number has a significant effect on the melting process of PCM. At low Rayleigh number, the existence of ceramic skeleton can significantly improve the thermal conductivity of composite PCM. However, at high Rayleigh number and porosity, the reduction of convective heat transfer might be greater than the heat conduction enhancement due to the addition of porous skeleton materials. By designing an appropriate non-uniform pore network of porous skeleton materials, further enhancement of heat conduction without obvious loss of convective heat transfer has been achieved. The research results obtained in this study could provide useful guidance for designing high-performance phase change energy storage materials.

Transition of natural convection of liquid metal in an annular enclosure under a magnetic field

Natural convection of a low-Prandtl-number conductive fluid driven by a horizontal temperature gradient in an annular enclosure with a square cross section was investigated. The surface temperatures of the inner and outer cylinders were differentially maintained. A static magnetic field was applied in the azimuthal direction. A three-dimensional (3D) numerical simulation was performed for a part of an annulus divided into 20 or 28 equal parts. The natural convection found changes on the order of a two-dimensional (2D) steady, a 3D steady, a 3D non-half-symmetric simply periodic oscillatory, a 3D indefinite oscillatory, a 3D half-symmetric simply periodic oscillatory, and a 3D aperiodic oscillatory flow as the Hartmann number decreases. This transition pattern is identical to that as the Rayleigh number increases in the same system without a magnetic field. In high Rayleigh numbers, the transition is accompanied by an axisymmetric oscillation. A disturbance causing the transition consists of three modes as a 3D steady, a 3D half-symmetric oscillatory, and a 2D axisymmetric oscillatory mode. The Nusselt numbers in most 3D flows are smaller at low Rayleigh numbers and larger at high Rayleigh numbers than that in 2D flows at a same condition, while the kinetic energy of a 3D flow is necessarily smaller than that of a 2D flow.

Unsteady conjugate heat transfer characteristics in hexagonal cavity equipped with a multi-blade dynamic modulator

PurposeThe transient analysis of the thermal response and frictional loss characteristics for flow-modulated conjugate heat transfer phenomena has been investigated in the present study. The flow domain is a partitioned cavity of a hexagonal structure equipped with a multi-blade flow modulator. The clockwise rotating blade is adiabatic and stirrers the internal flow along with the natural convection caused by the bottom heated floor of uniform heat flux. The conjugate behavior is introduced through the solid subdomains consisting of two brick-made partitions and one glass partition of uniform thickness. The material of the partition wall reflects the physical aspects of industrial applications. ApproachThe two-dimensional unsteady continuity, momentum, and energy equations are expressed in a non-dimensional form where the buoyant force is modeled through the Boussinesq approximation. The Arbitrary Lagrangian Euler (ALE) finite element is adopted to solve the moving mesh problem by formulating a free triangular discretization scheme. Parametric computational investigations are carried out for air as the working fluid (Pr = 0.71) and 3 different configurations of the rotating modulator while varying the other parameters, i.e., Reynolds number (Re) and Rayleigh number (Ra) for a fixed Biot number (Bi = 104). This dynamic mesh problem encompasses a wide range of parameters, i.e., (100 ≤Re≤ 103), and (104≤Ra≤ 106) for Bi = 104 to evaluate the thermodynamic response of the present thermo-fluid system. Various thermo-fluid system responses are visualized through the spatially average Nusselt number evaluated on the heated surface, system effectiveness, average thermal storage capacity, and frictional power loss of the flow domain. The thermal response is fragmented into individual responses in terms of component signal frequency by the Fast Fourier Transform (FFT) analysis. FindingsAccording to the current analysis, increasing the number of blades increases the rate of heat transfer by a negligible amount. On the other hand, among three different types of modulators, the three-blade modulator shows the lowest power loss coefficient and the lowest power instability. Thus, a three-blade modulator qualifies as the optimum design to impart external motion to the working fluid to introduce forced convection. LimitationsThis research has some scope for improvement. Future studies can be conducted on the improvement of blade designs, thickness, and size of the blades. Practical ImplicationsThe present study can shed light on the modeling of a better storage system where heat transfer and moisture control are integrated for the proper functioning of the storage, such as food storage, cold storage, garment inventory, etc. OriginalityThis study is original, and no previous research has been conducted considering the hexagonal domain and variation of the number of blades. ConclusionThe present study reveals that a modulator best serves its purpose at low Rayleigh and high Reynolds numbers. Moreover, the three-blade modulator has the lowest power loss coefficient and lowest power instability, making it the most suitable modulator to impart external excitation to the working fluid.

Efficient Numerical Simulation of Density‐Driven Flows: Application to the 2‐ and 3‐D Elder Problem

AbstractModeling density‐driven flow in porous media is challenging due to the nonlinear coupling between flow and transport equations, the large domains of interest and the wide range of time and space scales involved. Solving this type of problem numerically using a fixed mesh can be prohibitively expensive. Here, we apply a dynamic mesh optimization (DMO) technique along with a control‐volume‐finite element method to simulate density‐driven flows. DMO allows the mesh resolution and geometry to vary during a simulation to minimize an error metric for one or more solution fields of interest, refining where needed and coarsening elsewhere. We apply DMO to the Elder problem for several Rayleigh numbers. It is demonstrated that DMO accurately reproduces the unique two‐dimensional (2D) solutions for low Rayleigh number cases at significantly lower computational cost compared to an equivalent fixed mesh, with speedup of order ×16. For unstable, high Rayleigh number 2D cases, multiple steady‐state fingering solutions exist and are all captured by our approach with high accuracy and significantly reduced computational cost, with speedup of order ×6. Velocity‐dependent dispersion is shown to have a small impact on the 2D numerical solutions. The lower computational cost of simulations using DMO allows extension of the high Rayleigh number case to a three dimensional (3D) configuration. We demonstrate new 3D fingering patterns that have not been observed previously. Early time, transient 3D patterns represent combinations of the previously observed, steady‐state 2D solutions, but all evolve to a single, steady‐state finger in the late time limit.

Residence time of inertial particles in 3D thermal convection: Implications for magma reservoirs

The dynamic behaviour of crystals in convecting fluids determines how magma bodies solidify. In particular, it is often important to estimate how long crystals stay in suspension in the host liquid before being deposited at its bottom (or top, for light crystals and bubbles of volatiles). We perform a systematic 3D numerical study of particle-laden Rayleigh-Bénard convection, and derive a robust model for the particle residence time. For Rayleigh numbers higher than 107, inertial particles' trajectories exhibit a monotonic transition from fluid tracer-like to free-fall dynamics, the control parameter being the ratio between particle Stokes velocity and the mean amplitude of the fluid velocity. The average settling rate is proportional to the particle Stokes velocity in both the end-member regimes, but the distribution of residence times differs markedly from one to the other. For lower Rayleigh numbers (<107), an interaction between large-scale circulation and particle motion emerges, increasing the settling rates on average. Nevertheless, the mean residence time does not exceed the terminal time, i.e. the settling time from a quiescent fluid, by a factor larger than four. An exception are simulations with only a slightly super-critical Rayleigh number (∼104), for which stationary convection develops and some particles become trapped indefinitely. 2D simulations of the same problem overestimate the flow-particle interaction – and hence the residence time – for both high and low Rayleigh numbers, which stresses the importance of using 3D geometries for simulating particle-laden flows. We outline how our model can be used to explain the depth changes of crystal size distribution in sedimentary layers of magmatic intrusions that are thought to have formed via settling of a crystal cargo, and discuss how the micro-structural observations of solidified intrusions can be used to infer the past convective velocity of magma.

Off-centre gravity induces large-scale flow patterns in spherical Rayleigh–Bénard convection

We perform direct numerical simulations to study the effect of the gravity centre offset in spherical Rayleigh–Bénard convection. When the gravity centre is shifted towards the south, we find that the shift of the gravity centre has a pronounced influence on the flow structures. At low Rayleigh number $Ra$ , a steady-state large-scale meridional circulation induced by the baroclinic imbalance, created by the misalignment of the gravity potentials and isotherms, is formed. At high $Ra$ , an energetic jet is created on the northern side of the inner sphere that is directed towards the outer sphere. The large-scale circulation induces a strong co-latitudinal dependence in the local heat flux. Nevertheless, the global heat flux is not affected by the changes in the large-scale flow organization induced by the gravity centre offset.

Mixed convection heat transfer in a two-dimensional annular cavity using an off-lattice Boltzmann method

In the present work, a characteristic-based off-lattice Boltzmann method is used to study mixed convection heat transfer in a two-dimensional concentric annular cavity. First, the numerical method is verified using two benchmark cases: the Taylor–Couette flow and mixed convection in a concentric annular cavity. Thereafter, the effects of strength and the direction of rotation of the cylinders on the flow and heat transfer characteristics are analyzed. To this end, four different configurations of the cylinders, namely, the counter-rotating-cylinders, the co-rotating-cylinders, outer-rotating-cylinder with a stationary inner-cylinder, and inner-rotating-cylinder with a stationary outer-cylinder are considered. Further, a range of Rayleigh numbers, Ra=104,105 and 106 and a range of Reynolds numbers, Re=0 to 104 are considered for a Prandtl number of, Pr=0.71. It is observed that irrespective of the Reynolds number of the flow, the forced convection always results in a lower heat transfer rate. At a lower Rayleigh number of Ra=104, heat transfer in the natural convection is always higher than the mixed convection heat transfer for all the four rotation configurations considered. Both the co-rotating-cylinders and inner-cylinder-rotating configurations always result in a lower heat transfer rate than the natural convection heat transfer rate. However, up to certain Reynolds numbers, the counter-rotating-cylinders and outer-rotating-cylinder configurations result in a higher heat transfer rate for Ra=105 and 106. Beyond this Reynolds number, the heat transfer rate begins to decrease with an increase in the Reynolds number. Compared to other configurations, the co-rotating-cylinders configuration behaves similar to forced convection at lower Reynolds numbers. The profiles of the overall Nusselt number as a function of the Richardson number are studied for all four configurations, and the map thus obtained could be divided into three different zones. The distinguishing features of each of these zones are explained.

Free convection to cool a hot square block by embedding in center of a chamber by nanofluid and magnetohydrodynamic

Hot block is observed in numerous industries and applications that can being an electronic component, solid matrix, battery, etc. In the present 2D simulation, a uniform magnetic field (MHD model) in the x-direction was utilized to affect the free convection of nanofluid water- A l 2 O 3 for aim of improvement and control the heat transfer and flow characterizations. The used geometry consisted of square chamber and hot block embedded in center of square chamber. The walls of the hot block and chamber performed as hot and cold sources led to create buoyancy force. This study investigated for Varity inclined angles of hot block ( 0 < η < 45 ), Rayleigh numbers ( 10 2 < R a < 10 4 ) and Hartmann numbers ( 0 < H a < 40 ) when the volume fraction of suspension was φ = 0.04 . Also, the effects of the mentioned parameters were studied on the streamlines, temperature contours, average Nusselt number. Observations showed that Adding magnetic field increased the heat transfer rate by 200% At low Rayleigh numbers, but it reduced the heat transfer rate 48% At high Rayleigh numbers.

Oscillatory natural convection in a square enclosure containing a PCM suspension

In this study, a numerical simulation is performed to explore oscillatory natural convection in a square enclosure with a phase change material (PCM) suspension using the implicit finite difference method. The following parameters are considered: aspect ratio of the physical model = 1; ratio of the buoyancies caused by temperature and concentration gradients = 1; Rayleigh number = 103-106; initial mass fraction (or concentration) of PCM particles = 0–0.1; Stefan number = 0.005–0.1; and subcooling factor = 0–1.0. The results show that high Rayleigh numbers can easily cause oscillations in the flow field and temperature distribution. However, even under low Rayleigh number conditions, when the initial mass fraction or subcooling is increased or the Stefan number is decreased, oscillations occur.

Numerical study of natural convection heat transfer of vertical cylinder with multiple lateral baffles in square enclosure for sodium beta-alumina batteries

A computational study was carried out to assess the natural convection around a cylinder having multiple lateral baffles in a square enclosure for length ratios from 0.4 to 0.9, Rayleigh numbers from 2.5 × 103 to 5.0 × 107, and Prandtl number 0.71. Using a three-dimensional calculation with the Boussinesq approximation, the average Nusselt numbers on the cylinder and the enclosure surfaces were summarized. For low Rayleigh numbers, a conduction-dominated regime was found, showing that the average Nusselt number on the cylinder surface is mainly dependent on the distance between the hot and cold surfaces. For high Rayleigh numbers, the thermal field became convection-dominated, and the case with large cavity spacing showed large heat transfer. A new average Nusselt number correlation was proposed with and without lateral baffles on the cylinder surface. The flow pattern in the cavity was identified for various conditions, and the stratified temperature distribution and corresponding local Nusselt number distributions were summarized. Finally, the contribution of the vortices in the enclosure to the Nusselt number was assessed by adopting Q-criterion analysis. Presents results will provide useful information for thermal design of hot box modules that contain stacked planar battery cells.