Rayleigh Number Research Articles

On the boundary-layer asymmetry in two-dimensional annular Rayleigh–Bénard convection subject to radial gravity

Radial unstable stratification is a potential source of turbulence in the cold regions of accretion disks. To investigate this thermal effect, here we focus on two-dimensional Rayleigh–Bénard convection in an annulus subject to radially dependent gravitational acceleration $g \propto 1/r$ . Next to the Rayleigh number $Ra$ and Prandtl number $Pr$ , the radius ratio $\eta$ , defined as the ratio of inner and outer cylinder radii, is a crucial parameter governing the flow dynamics. Using direct numerical simulations for $Pr=1$ and $Ra$ in the range from $10^7$ to $10^{10}$ , we explore how variations in $\eta$ influence the asymmetry in the flow field, particularly in the boundary layers. Our results show that in the studied parameter range, the flow is dominated by convective rolls and that the thermal boundary-layer (TBL) thickness ratio between the inner and outer boundaries varies as $\eta ^{1/2}$ . This scaling is attributed to the equality of velocity scales in the inner ( $u_i$ ) and outer ( $u_o$ ) regions. We further derive that the temperature drops in the inner and outer TBLs scale as $1/(1+\eta ^{1/2})$ and $\eta ^{1/2}/(1+\eta ^{1/2})$ , respectively. The scalings and the temperature drops are in perfect agreement with the numerical data.

Turbulent convection in rotating slender cells

Turbulent convection in the interiors of the Sun and the Earth occurs at high Rayleigh numbers $Ra$ , low Prandtl numbers $Pr$ , and different levels of rotation rates. To understand the combined effects better, we study rotating turbulent convection for $Pr = 0.021$ (for which some laboratory data corresponding to liquid metals are available), and varying Rossby numbers $Ro$ , using direct numerical simulations in a slender cylinder of aspect ratio 0.1; this confinement allows us to attain high enough Rayleigh numbers. We are motivated by the earlier finding in the absence of rotation that heat transport at high enough $Ra$ is similar between confined and extended domains. We make comparisons with higher aspect ratio data where possible. We study the effects of rotation on the global transport of heat and momentum as well as flow structures (a) for increasing rotation at a few fixed values of $Ra$ , and (b) for increasing $Ra$ (up to $10^{10}$ ) at the fixed, low Ekman number $1.45 \times 10^{-6}$ . We compare the results with those from unity $Pr$ simulations for the same range of $Ra$ and $Ro$ , and with the non-rotating case over the same range of $Ra$ and low $Pr$ . We find that the effects of rotation diminish with increasing $Ra$ . These results and comparison studies suggest that for high enough $Ra$ , rotation alters convective flows in a similar manner for small and large aspect ratios, so useful insights on the effects of high thermal forcing on convection can be obtained by considering slender domains.

Effects of rotation and chemical reactions on an electroconvection in Maxwell dielectric nanofluids within anisotropic porous media

ABSTRACT This study explores the complex interactions between rotation, chemical reactions, and electroconvection in Maxwell dielectric nanofluids within anisotropic porous media. The research aims to elucidate how these factors influence the heat transfer efficiency and fluid dynamics under the influence of external alternating current (AC) electric fields. The normal mode method is employed to analyse the stability of the system, allowing for the examination of oscillatory modes and their growth rates. By introducing perturbations in the physical parameters, the study derives a set of ordinary linear differential equations that characterize the system's response to external influences. The coupled differential equations were solved using the Galerkin approach for first approximation while meeting the necessary boundary conditions. Analytical solution of the representative equation for stress-free boundary states yields Rayleigh number formulas for nonoscillatory and oscillatory mode occur. Oscillatory modes are seen for both bottom and top-heavy nanoparticle distributions. The electric Rayleigh number, thermal Prandtl number, and stress relaxation parameter increases, whereas the Brinkman-Darcy number delays the onset of stationary and oscillatory convection. The study finds that positive concentration Rayleigh numbers stabilize the system, while negative ones lead to instability. Additionally, it demonstrates that external alternating current electric fields influence convection behavior and provides formulas for critical Rayleigh numbers, enhancing our understanding of fluid interactions in various engineering and technological applications.

Deep learning based hybrid POD-LSTM framework for laminar natural convection flow in a rectangular enclosure

Abstract Laminar natural convection in side-heated enclosures is characterized by transient phenomena of the working fluid till it reaches steady state. The side heating can done in several ways the most common way being heating one end at constant temperature and cooling the other end. One of the other ways is heating both sides of the enclosure at a constant heat flux. Mathematical modeling of such problems using Computational Fluid Dynamics (CFD) essentially involves considerable amount of computational time and power to predict the flow phenomena observed in actual experimentation. In the last few years, data driven model frameworks have proven to be anefficient way in saving both time and computational cost in several applications. In the present study, a data driven model framework using a combination of unsupervised machine learning (using Proper Orthogonal Decomposition [POD]) and supervised deep learning models (using Long Short Term Memory [LSTM]) has been developed and referred to as POD-LSTM framework. The selection of a few dominant spatial bases and accompanying temporal modes provides us with a reduced order model of the system. The flow is then reconstructed and compared with results of CFD simulations. The Rayleigh number (Ra) chosen for the study is 3.27 × 1010. The estimated time to reach stedy state for this Ra number is 15,000 s. The POD-LSTM framework is trained using data obtained from a validated CFD model for the first 1,000 s. The trained model was then tested to predict temporal dynamics for the entire 15,000 s. The predictions provided by POD-LSTM framework were found upto 98 % accurate compared to the ones predicted by CFD. The computational time and power was however an order of magnitude lower for the POD-LSTM framework than that required for the CFD model.

Optimization of Thermal Performance by Enhancing Natural Convection of Diverse Configurations of Fin Heat Sink Filled With Nano‐Enhanced Phase Change Materials: A Numerical Study

ABSTRACTElectronic components require faster propagation of heat to prevent overheating as well as to maintain a stable operating condition. Incorporating phase change materials (PCMs) in fin heat sinks (FHSs) can be a viable solution to enhance natural convection. In the present work, an extensive investigation has been carried out on three types (square, circular, and triangular) of FHSs filled with PCMs to find the best combinations for the thermal cooling of a heat sink. To increase the thermal conductivity of the PCMs, Cu–water nanofluid is added. The effects of three types (paraffin wax, stearic acid, and polyethylene glycol) of PCMs have been studied. Nondimensional equations have been solved numerically by using Galerkin's finite element method. A parametric investigation has been conducted by varying the Rayleigh number within the range of 103–106 to calculate the Nusselt number. Results reveal that a heat sink with PCMs can reduce the temperature rise by 6.41% and increase the Nusselt number by 4.6% compared to a heat sink without PCMs. As the height of the fins increases from 10 to 16 mm, thermal efficiency increases. Moreover, square FHSs show the best thermal performance by reducing the temperature rise by as much as 13.41% compared to circular and triangular FHSs. Therefore, this comparative study shows that the dimensional configurations of FHSs with varying PCMs have a great impact on thermal performance and thus provide one the opportunity to obtain an effective arrangement of heat sinks.

Transition of the thermal boundary layer and plume over an isothermal section-triangular roof: an experimental study

The development of thermal boundary layers and plume near a section-triangular roof under different isothermal heating conditions has been the focus of numerous numerical studies. However, flow transition in this type of flow has never been observed experimentally. Here, phase-shifting interferometry and thermistor measurements are employed to experimentally observe and quantify the flow transitions in a buoyancy-driven flow over an isothermal section-triangular roof. Visualisation of temperature contours is conducted across a wide range of Rayleigh numbers from laminar at 103 to chaotic state at 4 × 106. Power spectral density of the temperature measurements reveals the type of bifurcations developing as the Rayleigh number is increased. This flow transition is characterised as a complex bifurcation route with the presence of two fundamental frequencies, a low and a high frequency. We found that the thermal stratification in the environment plays a significant role in the flow transition. The spatial development of flow is also quantitatively and qualitatively described. In addition to clarifying flow transition in experiments, the work demonstrates the implementation of phase-shifting interferometry and punctual temperature measurements for characterisation of near-field flow over a heated surface.

Turbulent convection in emulsions: the Rayleigh–Bénard configuration

This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh–Bénard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in dispersed-phase volume fractions, $0.0 \leq \varPhi \leq 0.5$ , and ratios of dynamic viscosity, $\lambda _{\mu }$ , and thermal diffusivity, $\lambda _{\alpha }$ , within the range $[0.1\unicode{x2013}10]$ . The Rayleigh, Prandtl, Weber and Froude numbers are held constant at $10^8$ , $4$ , $6000$ and $1$ , respectively. Initially, when both fluids share the same properties, a 10 % Nusselt number increase is observed at the highest volume fractions. In this case, despite a reduction in turbulent kinetic energy, droplets enhance energy transfer to smaller scales, smaller than those of single-phase flow, promoting local mixing. By varying viscosity ratios, while maintaining a constant Rayleigh number based on the average mixture properties, the global heat transfer rises by approximately 25 % at $\varPhi =0.2$ and $\lambda _{\mu }=10$ . This is attributed to increased small-scale mixing and turbulence in the less viscous carrier phase. In addition, a dispersed phase with higher thermal diffusivity results in a 50 % reduction in the Nusselt number compared with the single-phase counterpart, owing to faster heat conduction and reduced droplet presence near walls. The study also addresses droplet-size distributions, confirming two distinct ranges dominated by coalescence and breakup with different scaling laws.

Particle transport and deposition in wall-sheared thermal turbulence

We studied the transport and deposition behaviour of point particles in Rayleigh–Bénard convection cells subjected to Couette-type wall shear. Direct numerical simulations (DNSs) are performed for Rayleigh number ( $Ra$ ) in the range $10^{7} \leq Ra \leq ~10^9$ with a fixed Prandtl number $Pr = 0.71$ , while the wall-shear Reynolds number ( $Re_w$ ) is in the range $0 \leq Re_w \leq ~12\,000$ . With the increase of $Re_w$ , the large-scale rolls expanded horizontally, evolving into zonal flow in two-dimensional simulations or streamwise-oriented rolls in three-dimensional simulations. We observed that, for particles with a small Stokes number ( $St$ ), they either circulated within the large-scale rolls when buoyancy dominated or drifted near the walls when shear dominated. For medium $St$ particles, pronounced spatial inhomogeneity and preferential concentration were observed regardless of the prevailing flow state. For large $St$ particles, the turbulent flow structure had a minor influence on the particles’ motion; although clustering still occurred, wall shear had a negligible influence compared with that for medium $St$ particles. We then presented the settling curves to quantify the particle deposition ratio on the walls. Our DNS results aligned well with previous theoretical predictions, which state that small $St$ particles settle with an exponential deposition ratio and large $St$ particles settle with a linear deposition ratio. For medium $St$ particles, where complex particle–turbulence interaction emerges, we developed a new model describing the settling process with an initial linear stage followed by a nonlinear stage. Unknown parameters in our model can be determined either by fitting the settling curves or using empirical relations. Compared with DNS results, our model also accurately predicts the average residence time across a wide range of $St$ for various $Re_w$ .

The Role of Heater Size and Location in Modulating Natural Convection Behavior in Cu-Water Nanofluid-Loaded Square Enclosures

Enhancing the energy efficiency of thermal systems reduces their consumption, lowers costs, and reduces undesired environmental impact, thus making these systems more sustainable. The current work introduces a passive method for heat transfer enhancement that is carried out using natural convection by nanofluid. This work introduces a computational study of the process of natural convection within a square cavity containing Cu/H2O nanofluid. The cavity wall on the left side undergoes partial isothermal heating, while the opposing side is fully cooled isothermally, with all other boundaries maintained adiabatic. A mathematical model formulated based on a 2-D model was used to provide the solution for the system of governing equations of mass, momentum, and energy conservation, employing the finite element technique. A commercial CFD package is utilized to perform the computational simulation. The present investigation delves into the impact of the Rayleigh number, nanoparticle concentration, heater length, and heater location on the flow field and heat transfer characteristics. The model outcomes were displayed for a wide range of the pertinent parameters as 103 ≤ Ra ≤ 106, 0.25 ≤ lh ≤ 1.0, 0.125 ≤ hc ≤ 0.875, and 0.02 ≤ ϕ ≤ 0.10. Also, correlation equations relating the average Nusselt number to these crucial parameters are derived. These equations are simple and can be applied in practice easily in many fields, such as electric and electronic equipment cooling and thermal management of heat sources. Also, these equations gather all the parameters that affect the heat transfer process. They are shedding light on the intricate interplay between these parameters in the natural convection heat transfer process.

Photometric detection of internal gravity waves in upper main-sequence stars. IV. Comparable stochastic low-frequency variability in SMC, LMC, and Galactic massive stars

Massive main-sequence stars have convective cores and radiative envelopes, but can also have sub-surface convection zones caused by partial ionisation zones. However, the convective properties of such regions strongly depend on opacity and therefore a star's metallicity. Non-rotating 1D evolution models of main-sequence stars between $7 M odot $ and metallicity of the Small Magellanic Cloud (SMC) galaxy suggest tenuous (if any) sub-surface convection zones when using the Rayleigh number as a criterion for convection owing to their substantially lower metallicity compared to Galactic massive stars. We test if massive stars of different metallicities both inside and outside of asteroseismically calibrated stability windows for sub-surface convection exhibit different properties in stochastic low-frequency (SLF) variability. Thus we aim to constrain the metallicity dependence of the physical mechanism responsible for SLF variability commonly found in light curves of massive stars. We extract customised light curves from the ongoing NASA Transiting Exoplanet Survey Satellite (TESS) mission for a sample of massive stars using an effective point spread function (ePSF) method, and compare their morphologies in terms of characteristic frequency, $ char $, and amplitude using a Gaussian process (GP) regression methodology. We demonstrate that the properties of SLF variability observed in time-series photometry of massive stars are generally consistent across the metallicity range from the Milky Way down to the SMC galaxy, for stars both inside and outside of the sub-surface stability windows based on the Rayleigh number as a criterion for convection. We conclude that non-rotating 1D stellar structure models of sub-surface convection cannot alone be used to explain the mechanism giving rise to SLF variability in light curves of massive stars. Additionally, the similar properties of SLF variability across a large range in metallicity, which follow the same trends in mass and age in the Hertzsprung--Russell (HR) diagram at both high and low metallicity, support a transition in the dominant mechanism causing SLF variability from younger to more evolved stars. Specifically, core-excited internal gravity waves (IGWs) are favoured for younger stars lacking sub-surface convection zones, especially at low-metallicity, and sub-surface convection zones are favoured for more evolved massive stars.

Enhanced Efficiency of Latent Heat Energy Storage by Inclination

Latent heat storage (LHS) has emerged as a promising solution for addressing the challenges of large-scale and long-term energy storage, offering a clean and reusable system. Being in the developmental stage, and with only limited theoretical predictions being available, there is a need to enhance the efficiency of LHS systems. In this study, we use numerical simulations to study the melting process of a phase-change material (PCM) in a rectangular domain. A significant enhancement in the melt rate of the PCM is found by a simple inclination of the domain, with a 60% increase in melt rate compared to a standard square unit without inclination through enhanced heat transfer. We establish a theoretical relation for the optimal PCM melt rate, based on the inclination angle and the domain aspect ratio, outlining the optimal conditions for the PCM melt rate, which is solely dependent on the domain geometry. We further propose a heat-transfer model that predicts the optimal aspect ratio for achieving the maximum melt rate as a function of the Rayleigh and Prandtl numbers. Published by the American Physical Society 2024

Numerical Investigation of Turbulent Convection Flow in a Rectangular Closed Cavity

Natural turbulent convection in closed cavities has many practical applications in the field of engineeringsuch as the design of electronic computer chips, atomic installation and industrial cooling among others. Inparticular, it enables in achieving a desired micro-climate and efficient ventilation in a building. Recent studiesshow that turbulent flow is affected by variations in Rayleigh numbers, aspect ratio, and heater positionamong others. Temperature is kept constant in all these studies hence inadequate literature on the effectsof temperature on a turbulent flow. In this study, aspect ratio and Rayleigh numbers are kept constant at2 and 1012 respectively and natural turbulent convection flow in a closed rectangular cavity is investigatednumerically as the operating temperature is varied from 285.5K to 293K. The rectangular cavity’s lower wallwas heated and cooling done at the top face wall while the rest of the vertical walls were kept in adiabaticcondition. Material properties such as density of the fluid kept on changing at any given temperature. Thethermal profile data generated influenced the nature of the turbulent flow. The non-linear averaged continuity,momentum, and energy equation terms were modeled by the SST k − ω model to generate streamlines,isotherms, and velocity magnitude for a different operating temperature and presented graphically. The finitedifference method and FLUENT were used to solve two SST k − ω model equations, vortices, and energy withboundary conditions. It was discovered that, as the operating temperature increased turbulence decreaseddue to a decrease in the velocity of the elements and vortices became more parallel and smaller.

Effect of Variable Gravity Field on Dual Component Convection in a Couple Stress Fluid Saturated Anisotropic Porous Layer With Temperature‐Dependent Heat Source

ABSTRACTThis study examines how gravity fluctuations, the couple stress parameter, anisotropic parameters, and heat source collectively influence dual‐component convection in the porous layer. The linear analysis is conducted utilizing the normal mode technique. The authors proposed three categories of gravity fluctuation, namely: (a) linear, (b) parabolic, and (c) exponential. Expressions for both stationary and oscillatory Rayleigh numbers are derived using the Galerkin approach. Neutral stability curves for both stationary and oscillatory modes are analyzed, with graphical representations to show the effects of various stability parameters, including gravity fluctuations, couple stress, anisotropy, and heat source. The results show that the mechanical anisotropy parameter and Vadasz number lead to system destabilization, while the couple stress parameter, Lewis number, gravity parameter, solute Rayleigh number, and thermal anisotropy parameter help to stabilize the system. Furthermore, the system is more stable with exponential gravity fluctuations and less stable with parabolic gravity fluctuations. This finding offers insights into thermal convective instability in porous media, impacting applications in geoscience, engineering, and environmental science.

Experimental study of convective heat transfer with a multi-scale roughness

The heat transfer in a turbulent Rayleigh-Bénard convection with a multi-scale roughness at the bottom is studied experimentally. Two different regimes for the heat transfer are found. The first regime has scaling exponent γI=0.4 and corresponds to the reduced values of the Nusselt number. The second regime with enhanced values of the Nusselt number has a scaling exponent γII=0.32, which is noticeably larger than in the case of smooth boundaries. Significant variation in the Prandtl number (from 6.4 to 62) does not change the scaling exponent value of the second regime but increases the values of Nusselt number. The scaling exponent for the relation Re∼Raα is insensitive to the change of the heat transfer regime and is close to 1/2 for all values of Ra. The characteristic ratio of the velocity pulsations to the mean velocity does not depend on the Rayleigh number and is characterized by close values (about 0.8). The local temperature measurements support the mechanism of the transition from the reduced Nusselt number regime to the enhanced one, which is based on the formation of flows between obstacles.

Estimation of Recovery Efficiency in High‐Temperature Aquifer Thermal Energy Storage Considering Buoyancy Flow

AbstractWith their high storage capacity and energy efficiency as well as the compatibilities with renewable energy sources, high‐temperature aquifer thermal energy storage (HT‐ATES) systems are frequently the target today in the design of temporally and spatially balanced and continuous energy supply systems. The inherent density‐driven buoyancy flow is of greater importance with HT‐ATES, which may lead to a lower thermal recovery efficiency than conventional low‐temperature ATES. In this study, the governing equations for HT‐ATES considering buoyancy flow are nondimensionalized, and four key dimensionless parameters regarding thermal recovery efficiency are determined. Then, using numerical simulations, recovery efficiency for a sweep of the key dimensionless parameters for multiple cycles and storage volumes is examined. Ranges of the key dimensionless parameters for the three displacement regimes, that is, a buoyancy‐dominated regime, a conduction‐dominated regime, and a transition regime, are identified. In the buoyancy‐dominated regime, recovery efficiency is mainly correlated to the ratio between the Rayleigh number and the Peclet number. In the conduction‐dominated regime, recovery efficiency is mainly correlated to the product of a material‐related parameter and the Peclet number. Multivariable regression functions are provided to estimate recovery efficiency using the dimensionless parameters. The recovery efficiency estimated by the regression function shows good agreement with the simulation results. Additionally, well screen designs for optimizing recovery efficiency at various degrees of intensity of buoyancy flow are investigated. The findings of this study can be used for a quick assessment and characterization of the potential HT‐ATES systems based on the geological and operational parameters.

Transport of particles in a model of 2D Rayleigh-Benard convection that conserves energy and vorticity

In contrast with the Lorenz model for 2-dimensional Rayleigh - Bénard system, the model proposed by Howard - Krishnamurti (HK) allows the possibility of a large scale horizontally shear flow making feasible the study of particles transport. However, this model lacks conservation of energy and vorticity in the absence of forcing and dissipation. A model that incorporates conservation of energy and vorticity was proposed by A. Gluhovsky et al (GTA). We perform the linear stability analysis of this later model and study the transport process on this velocity field background and make a comparison with the features of the former model. We found that the basic bifurcation structure is retained by the GTA model and discuss the differences that they indeed have. In regard to the transport processes, the basic features found using the HK velocity field background are also kept by the GTA model. We determine the size of the rather small gap in the Rayleigh number where the transport process shift from being shear flow dominated to a Brownian diffusion process.

Energy-consistent discretization of viscous dissipation with application to natural convection flow

A new energy-consistent discretization of the viscous dissipation function in incompressible flows is proposed. It is implied by choosing a discretization of the diffusive terms and a discretization of the local kinetic energy equation and by requiring that continuous identities like the product rule are mimicked discretely. The proposed viscous dissipation function has a quadratic, strictly dissipative form, for both simplified (constant viscosity) stress tensors and general stress tensors. The proposed expression is not only useful in evaluating energy budgets in turbulent flows, but also in natural convection flows, where it appears in the internal energy equation and is responsible for viscous heating. The viscous dissipation function is such that a consistent total energy balance is obtained: the ‘implied’ presence as sink in the kinetic energy equation is exactly balanced by explicitly adding it as source term in the internal energy equation.Numerical experiments of Rayleigh–Bénard convection (RBC) and Rayleigh–Taylor instabilities confirm that with the proposed dissipation function, the energy exchange between kinetic and internal energy is exactly preserved. The experiments show furthermore that viscous dissipation does not affect the critical Rayleigh number at which instabilities form, but it does significantly impact the development of instabilities once they occur. Consequently, the value of the Nusselt number on the cold plate becomes larger than on the hot plate, with the difference increasing with increasing Gebhart number. Finally, 3D simulations of turbulent RBC show that energy balances are exactly satisfied even for very coarse grids. Therefore, the proposed discretization also forms an excellent starting point for testing sub-grid scale models and is a useful tool to assess energy budgets in any turbulence simulation, with or without the presence of natural convection.

Dynamics of a hot flexible cantilever plate under natural convection heat transfer in a square cavity

This study investigates the fluid-structure interactions of a flapping plate within a square cavity under four distinct boundary conditions, where two opposing walls are heated isothermally, and the others are adiabatic. These configurations are defined as case 1 (cooled side walls), case 2 (cooled top and bottom walls), case 3 (heated bottom and cooled top wall), and case 4 (heated top wall and cooled bottom wall). The effects of non-dimensional parameters, including Rayleigh number (Ra), Cauchy number (Ca), and mass ratio (β) on plate dynamics and convective heat transfer are analyzed. Numerical investigations are executed utilizing the SU2 open-source multi-physics computational fluid dynamics solver, with a fixed Prandtl number (Pr) set at 0.71 and dimensionless temperature difference (ϵ) established at 0.6. The results show that in cases 1 and 4, the plate exhibits no observable unsteadiness, while cases 2 and 3 reveal different oscillatory behavior within certain parameter ranges, including static mode, periodic flapping mode, quasi-periodic flapping mode, and chaotic flapping mode. In particular, the configuration in case 3 possesses higher inherent instability than case 2, causing the earlier onset of Hopf bifurcation. These findings provide valuable insights into the influence of boundary conditions on the behavior of flexible structures in fluid environments, highlighting the critical role of flow instabilities and boundary conditions in determining the dynamic response of the system.

Unlocking Heat Transfer Potential in Multi-Sided Porous Geometries: A Study on Magnetothermal Effects and Entropy Generation

This study investigates heat transfer efficiency and irreversibility generation in multi-sided porous thermal systems filled with a Cu-Al2O3-water hybrid nanofluid. The research examines convective heat transfer across various polygonal geometries, ranging from four-sided to infinitely-sided (circular) structures, aiming to maximize thermal system performance intended for scientific and industrial applications. For a standardized comparison, the fluid volume and active heating and cooling lengths are kept constant for all the geometries considered. The analysis includes varying flow-controlling variables like the modified Rayleigh number (Ram), Hartmann number (Ha), and Darcy number (Da) to evaluate how they affect heat transfer efficiency and entropy generation, including total, magnetic, and viscous entropy. The numerical simulations, conducted using the finite element approach, explore Ram values ranging from 10 to 104, Ha from 0 to 70, and Da from 10-4 to 10-2. Streamline and isothermal contours analyze flow behavior, while heatline tools reveal thermal energy transport dynamics. Results show up to a 20% improvement in heat transfer efficiency in optimized configurations. Key findings indicate that hexagonal structures can be viable alternatives to circular tubes in space-constrained applications, offering comparable thermal performance. Interestingly, pentagonal cavities exhibit the highest irreversibility due to symmetry loss. The study offers insightful information for enhancing thermal system design in various industrial settings, particularly for applications requiring efficient heat transfer in limited spaces.

Thermal analysis of packed bed thermal energy storage system with dimpled spherical capsules

The thermal storage potential of a packed bed filled with paraffin wax capsules was examined. Heat transfer fluid (HTF) at 70 °C inlet temperature for dimpled and plain stainless-steel capsules was compared for three different flow rates, 1 L/min, 3 L/min and 5 L/min. In general, dimpled spherical capsules sustain more heat than plain spherical capsules at the same flow rate, according to instantaneous and cumulative heat stored. Spherical capsules with dimples exhibited a 30 % improvement in charging rate compared to smooth spheres, particularly at elevated flow rates. Specifically, at a flow rate of 5 L/min, dimpled capsules achieved faster charging and sustained higher temperature compared to plain capsules. Higher flow rates (3 and 5 L/min) result in steeper temperature increases and an earlier peak temperature phase compared to the lower flow rate (1 L/min). Key dimensionless heat transfer numbers were examined. The Stefan number was found to be 0.1966 for an HTF inlet temperature of 70 °C and a latent heat of fusion (Lm) of 213 kJ/kg. Heat transfer increases when Reynolds numbers increased from laminar (123.8 at 1 L/min) to turbulent (619.1 at 5 L/min). Rayleigh number decreased over time but increased for dimpled capsules, indicating improved convection. Dimpled capsules had higher Nusselt numbers and increases with flow rate, indicating better convective heat transfer. Dimpled capsules absorbed heat faster and stored more energy, giving them a viable and efficient Packed Bed Latent Thermal Energy Storage system design.