High Rayleigh Number Research Articles

Entropy analysis of convective nanofluid flow with Brownian motion in an annular space between confocal elliptic cylinders

Purpose This study aims to provide an in-depth analysis of entropy generation (EG) during natural convection within the annular space between confocal elliptic cylinders, with a specific focus on the influence of Brownian motion on nanofluid behavior. Design/methodology/approach A finite volume control method was used to conduct a detailed numerical analysis, examining the behavior of various nanofluids across a range of volume concentrations (2%–6%) and Rayleigh numbers. The study explores heat transfer (HT) and fluid flow mechanisms, particularly highlighting the role of nanoparticle Brownian motion in enhancing thermal conductivity. Findings The findings reveal that increased Rayleigh numbers significantly improve HT rates, while at lower Rayleigh values, EG is primarily governed by thermodynamic irreversibility. At higher Rayleigh numbers, this irreversibility plays a less dominant role in overall entropy production. Originality/value This study offers a novel perspective on the interplay between Rayleigh numbers, Brownian motion and EG, providing valuable insights for optimizing HT processes in engineering applications involving nanofluids.

Improving Thermal Performance in Building Heating, Ventilation, and Air Conditioning Systems: A Study of Natural Convection and Entropy in Plus‐Shaped Cavity

ABSTRACTThe impact of building design on energy efficiency has been widely studied, with cavity cooling emerging as an effective solution for indoor thermal comfort, where obstacles within the cavity can enhance fluid flow and improve natural convection heat transfer (HT). This research builds on the principles of cavity cooling for indoor thermal comfort, investigating entropy generation and HT behavior in a unique plus‐shaped cavity containing a cold cylindrical element, analyzed through Computational Fluid Dynamics simulations. The Rayleigh number (Ra) ranges from 103 to 106, with a fixed Prandtl number (Pr) of 0.71, representing air as the working fluid, radius (r) of the cylinder ranges from 0 to 0.1, where r = 0 indicates no cylinder. The results indicate significant shifts in flow structure and temperature distribution across the cavity at varying Ra values, impacting the local and global entropy generation. High Rayleigh numbers lead to enhanced convective flows, intensifying entropy production near the cylinder surface due to steeper thermal gradients and vigorous recirculation zones. The increase in Ra from 103 to 106 leads to an increase in Nuavg from 24.27 to 56.40 for the model without a cold object while from 39.62 to 123.83 for the model with a cold object. Moreover, the maximum enhancement in Nuavg was 137.48% for Ra = 105. Whereas, for the same value of Ra = 105, the maximum increase in Egen and Be was 474.92% and 33.16%, respectively. Also, a new correlation is proposed to calculate Nuavg using response surface methodology. This study offers a comprehensive examination of heat flow characteristics and entropy generation rates in confined geometries, contributing valuable knowledge to thermal management and optimization in systems with internal obstacles.

Free convection investigation for a Casson-based Cu-H 2 O nanofluid in semi parabolic enclosure with corrugated cylinder.

The optimization of heat transfer in various engineering applications, such as thermal management systems and energy storage devices, remains a crucial challenge. This study aims to investigate the potential of Casson-based Cu-H2O nanofluids in enhancing free convection heat transfer within complex geometries. The research examines the free convection heat transfer and fluid flow characteristics of a Casson-based Cu-H2O nanofluid within a semi-parabolic enclosure that includes a wavy corrugated cylinder. Utilizing numerical simulations based on the Galerkin Finite Element Method, the study investigates the impact of different factors, including the Rayleigh number (103≤Ra ≤ 106), Casson fluid parameter (0.1≤γ≤1), corrugation number (3≤N≤10), nanoparticle volume fraction (0≤ϕ≤0.15), and enclosure inclination angle (0°≤ζ≤60°), on both heat transfer efficiency and flow patterns. The results reveal that increasing the Rayleigh number and Casson fluid parameter enhances heat transfer performance, with the average Nusselt number increasing by up to 165% as Ra increases from 103 to 106. An optimal range of corrugation numbers is identified for maximizing heat transfer at higher Rayleigh numbers. The addition of nanoparticles significantly improves heat transfer, with a 20% increase in the average Nusselt number observed at Ra=105 when the nanoparticle volume fraction increases from 0 to 0.15. These findings provide valuable insights for designing more efficient thermal management systems in applications such as electronics cooling, solar thermal collectors, and heat exchangers, potentially leading to improved energy efficiency and performance in various industrial and technological sectors.

Buoyancy-driven flow for surface reaction on vertical walls in multilayered open cavities.

This study analyzes the influences of surface reactions on the natural convective flow, temperature, and oxygen concentration distributions in vertically placed multilayered cavities. A mathematical model for this problem is formulated with proper boundary conditions. At first, the governing equations are made dimensionless using the variable transformations. Then, those are solved utilizing the finite element method (FEM), and the stream function is calculated from the Poisson equation. Numerical results show that the maximum stream function is significantly increased while maximum temperature and remaining oxygen concentration are considerably decreased with higher Rayleigh number. On the contrary, the buoyancy force parameter and the Lewis number cause an increase in maximum values of stream function and temperature but a decrease in remaining concentration. For increasing Lewis number and reactant consumption parameter, the flow structure in cavities significantly changes. In addition, maximum values of stream function and temperature are significantly increased with the increase of the heat release parameter. When the opening heights are wider, maximum stream function and remaining concentration are higher, however maximum temperature first becomes lower and then becomes higher. For any value of the parameters, the maximum flow intensity occurs adjacent to the bottom opening of the top cavity of the multilayered open cavities. However, maximum temperature is seen at the top left corner of the top cavity of the system.

Investigation of asymmetric heating in Poiseuille-Rayleigh-Bénard water flow: A numerical study

In this paper, a numerical investigation of the impact of asymmetric heating on laminar mixed convection in Poiseuille-Rayleigh-Bénard water flow within parallel horizontal channels is presented. The study has been carried out in a rectangular channel with a transverse aspect ratio of 10, and considered both low (Ra = 1.28 × 104) and high (Ra = 1.4 × 105) Rayleigh numbers, with Reynolds numbers of 50 and 100. A uniform heat flux was applied to the top and bottom walls of the heated region to assess its effect on the system's thermoconvective behavior and heat transfer efficiency. Two flux ratio scenarios were considered: qt/qb = 1 and qt/qb = 2.The results indicate that increasing the flux ratio intensifies the destabilizing temperature gradient and significantly enhances buoyancy-induced flow, thereby influencing the patterns of thermoconvective structures. Specifically, flux ratios lead to an increased number of plumes originating from the bottom of the channel, while reducing their height and confining them between the bottom wall and the upper thermal boundary layer. It is also observed that flux ratios do not affect the mechanisms involved in the formation of longitudinal rolls. Furthermore, at low Rayleigh numbers, asymmetric heating has a pronounced impact on the establishment length. In contrast, this effect diminishes and becomes negligible at higher Rayleigh numbers. Numerical computations further reveal that near the bottom wall, the Nusselt number exhibits singular behavior, approaching infinity. Regardless of Reynolds and Rayleigh numbers, flux ratios significantly enhance heat transfer within the system. Additionally, near the top wall, the buoyancy effects from the bottom wall have negligible impact on heat transfer, except in the case where qt/qb = 2, Re = 50 and Ra = 1.4 × 105, where instability in the upper thermal layer was observed.

Convective Heat Transfer in the Strongly Viscous Mantle in Different Aspect Ratio Cells

Mantle convection, a fundamental mechanism controlling the dynamics of the Earth’s surface and interior, shows different behaviors caused by different factors such as viscosity variation, viscous dissipation, internal heating, and so on. In this paper, the effects of temperature-dependent viscosity, temperature and pressure-dependent viscosity and viscous dissipation on mantle convection are investigated in elongated and narrow cells. The Rayleigh-B´enard convection model is solved numerically with the full form of the Arrhenius viscosity function at a high Rayleigh number for viscosity contrasts up to 1030. The root mean square velocity and Nusselt number are computed and tabulated. The thermal characteristics and flow dynamics inside the convection cell are presented by temperature profiles and stream function contours. These simulated results indicate that increasing viscosity contrasts with the incorporation of viscous dissipation weakens the convection vigour and heat transfer in the mantle. The selected narrow cell remains stable for a very high viscosity contrast at different viscous pressure number μ, whereas the selected elongated cell with temperature-dependent viscosity and strong viscous dissipation becomes unstable and single-cell pattern breaks down at high viscosity variation. J. Bangladesh Math. Soc. 44.2 (2024) 077–096

Numerical Analysis of Magnetohydrodynamic Convection in an Inclined Cavity with Three Fins and a Ternary Composition of Nanoparticles

The natural convection heat transfer of a trihybrid nanofluid comprising Fe2O3, MoS2, and CuO nanoparticles dispersed in water (Fe2O3 + MoS2 + CuO/H2O) has been investigated within a cavity exposed to a uniform magnetic field. Three cold fins were strategically positioned on the top, right, and left walls of the enclosure. The study employs numerical simulations conducted using a custom-developed FORTRAN code. The computational approach integrates the finite volume method and full multigrid acceleration to solve the coupled governing equations for continuity, momentum, energy, and entropy generation, along with the associated boundary conditions. Prior to obtaining the results, a meticulous parameterization process was undertaken to accurately capture the fluid dynamics and thermal behavior characteristic of this geometric configuration. The findings underscored the key parameters’ significant impact on the flow structure and thermal performance. The results revealed that natural convection is more dominant at high Rayleigh and low Hartmann numbers, leading to higher Nusselt numbers and stronger dependence on the tilt angle α. Moreover, the optimal heat transfer conditions were obtained for the following parameters: Ha = 25, α = 45°, ϕ = 6%, and Ra = 106 with a rate of 4.985. This study offers valuable insights into achieving a balance between these competing factors by determining the optimal conditions for maximizing heat transfer while minimizing entropy generation. The findings contribute to enhancing the design of thermal systems that utilize magnetic nanofluids for efficient heat dissipation, making the research particularly relevant to advanced cooling technologies and compact thermal management solutions.

Design of an Axisymmetric Triangular Heatsink with Radial Arrangement: An Experimental Investigation of Natural Convection Heat Transfer

Radial heat sinks are often employed as heat transfer enhancers because they increase the heat transfer surface area. Novel shapes of fins are used to enhance thermal heat performance under free convection heat transfer. The present experimental study investigates a new-fin shape effect on the thermal behavior of a radial heat sink with a circular base. The objective is to select the best reference model by comparing the three heat sink models, I, II, and III. The study was conducted for the heat-supplied rates of 20.16, 66.03, 105.30, 157.62, and 196.08 W. The present results showed that the fin in case I configurations dissipated heat transfer up to 12.07% and 30% compared to cases II and III, respectively, at high Rayleigh numbers. The thermal resistance in case III reduced to 13.91% and 16.23% compared to case I and case II, respectively, at the maximum Rayleigh number value. Then, based on experimental data, a correlation was suggested to estimate the Nusselt number for free convection from radial heat sink with vertically oriented double triangular fins.

Effects of Solid-to-Fluid Conductivity Ratio on Thermal Convection in Fluid-Saturated Porous Media at Low Darcy Number

Abstract This study presents experimental data on the effects of the solid-to-fluid thermal conductivity ratio on natural convective heat transfer in a fluid-saturated porous medium heated from below. Argon is used as the saturating fluid, while a bed of glass, steel, or aluminum spheres constitutes the solid porous matrix. Emphasis is placed on attaining high Rayleigh numbers while maintaining low Darcy numbers (5.68 × 10−8 ≤Da≤5.22 × 10−7). At low modified Rayleigh numbers (Ra*) corresponding to the Darcy regime, the Nusselt number is independent of the medium conductivity. As Ra* increases and the system transitions into Forchheimer regime, the data diverge, with Nusselt numbers decreasing with increased thermal conductivity ratio at a fixed Ra*. This non-intuitive result is shown to be the result of the traditional choice of Ra* and Da as the controlling parameters since the heat transfer coefficient appears independent of the conductivity ratio. Scaling arguments are used to identify transition points between the regimes, which yield the transition criterion Ra* ~ Prp, where Prp is the modified Prandtl number. When the data are expressed by scaling with Prp, it is shown that the data for multiple parameter combinations collapse onto a single curve, which also agrees well with theoretical predictions. In light of this finding, the data from available literature are assessed, and it is proposed that deviations from theory are likely the result of the strong porous medium condition (low Da) not being satisfied.

Asymmetry of Two-Dimensional Thermal Convection at High Rayleigh Numbers

While thermal convection cells exhibit left–right and top–bottom symmetries at low Rayleigh numbers (Ra), the emergence of coherent flow structures, such as elliptical large-scale circulation in Rayleigh–Bénard convection (RBC), breaks these symmetries as the Rayleigh number increases. Recently, spatial double-reflection symmetry was proposed and verified for two-dimensional RBC at a Prandtl number of 6.5 and Ra values up to 1010. In this study, we examined this new symmetry at a lower Prandtl number of 0.7 and across a wider range of Rayleigh numbers, from 107 to 1013. Our findings reveal that the double-reflection symmetry is preserved for the mean profiles and flow fields of velocity and temperature for Ra<109, but it is broken at higher Rayleigh numbers. This asymmetry at high Ra values is inferred to be induced by a flow-pattern transition at Ra=109. Together with the previous study, our results demonstrate that the Prandtl number has an important influence on the symmetry preservation in RBC.

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.

Two-dimensional Rayleigh–Bénard convection without boundaries

We study the effects of Prandtl number $\mathit {Pr}$ and Rayleigh number $\mathit {Ra}$ in two-dimensional Rayleigh–Bénard convection without boundaries, i.e. with periodic boundary conditions. For Prandtl numbers in the range $10^{-3} \leqslant \mathit {Pr} \leqslant 10^2$ , the viscous dissipation scales as $\epsilon _\nu \propto \mathit {Pr}^{1/2}\mathit {Ra}^{-1/4}$ , which is based on the observation that enstrophy $\langle {\omega ^2}\rangle \propto \mathit {Pr}^0 \mathit {Ra}^{1/4}$ , and the Nusselt number tends to follow the ‘ultimate’ scaling $\mathit {Nu} \propto \mathit {Pr}^{1/2}\mathit {Ra}^{1/2}$ for all values of $\mathit {Pr}$ considered. The inverse cascade of kinetic energy forms the power-law spectrum $\hat {E}_u(k) \propto k^{-2.3}$ , which is close to $k^{-11/5}$ proposed by the Bolgiano–Obukhov (BO) scaling. The potential energy flux is not constant, in contrast to one of the main assumptions underlying the BO phenomenology. So, the direct cascade of potential energy forms the power-law spectrum $\hat {E}_\theta (k) \propto k^{-1.2}$ , which deviates from the expected $k^{-7/5}$ . Finally, at $\mathit {Pr} \to 0$ and $\infty$ , we find that the dynamics is dominated by vertically oriented elevator modes that grow without bound, even at high Rayleigh numbers and with large-scale dissipation present.

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

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

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

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

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

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

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

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

SAMPO-P: A prototypical scale low-temperature experiment on two-layer melt pool heat transfer in LWR lower head

To better understand the thermal behavior of a two-layer melt pool with a high Rayleigh number—a pattern observed in the RASPLAV study, which indicates a significant risk to pressure vessel integrity and the success of in-vessel retention (IVR) strategies—this paper reports experimental findings from a 2D, full-scale (1:1 ratio) prototypical stratified melt pool (SAMPO-P). A series of experimental tests were carried out with varying heating powers and top layer heights, achieving a Rayleigh number of 3.77×1015, comparable to that found in light water reactors (LWR). Water was used to simulate the bottom layer, while n-octanol represented the top layer. Internal decay heat was modeled in the bottom layer using electric heating rods. After analyzing the main heat transfer parameters from the experiment, this paper derived several useful heat transfer correlations. The normalized temperature and heat flux distributions remained consistent across different power levels, and the normalized heat flux in the bottom layer aligned well with existing experimental correlations. In the bottom layer, the downward heat transfer coefficient was lower compared to other single-layer correlations, likely due to increased upward heat transfer.

A SUPS formulation for simulating unsteady natural/mixed heat convection phenomena in square cavities under intense magnetic forces

This paper presents stabilized finite element simulations of unsteady natural and mixed heat convection phenomena occurring in square enclosures. It is assumed that the enclosures are subject to intense uniform magnetic fields applied perpendicular to the vertical walls. It is well known that the classical Galerkin finite element method (GFEM) is prone to yielding nonphysical oscillations when simulating convection-dominated flows. Therefore, in order to handle such flows occurring at high Hartmann (0≤Ha≤100\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0 \\le {\\rm Ha} \\le 100$$\\end{document}) and Rayleigh (103≤Ra≤108\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{3} \\le {\\rm Ra} \\le 10^{8}$$\\end{document}) numbers, the stabilization of the GFEM is accomplished with the streamline-upwind/Petrov–Galerkin and pressure-stabilizing/Petrov–Galerkin formulations. Temporal discretizations are performed with the backward Euler formula. At each time step, the nonlinear systems are linearized with the Newton–Raphson (N–R) method, and the linearized systems are solved directly using the sparse lower–upper decomposition. The incompressible flow solvers are developed in-house, run in parallel within the FEniCS ecosystem, and tested on a comprehensive set of numerical experiments with various thermal boundary conditions. Numerical simulations and comparisons reveal that the proposed formulation performs quite well at high Hartmann and Rayleigh numbers without exhibiting any significant localized or globally spread numerical instabilities. Moreover, it achieves this by using uniform meshes and only linear elements, making the formulation much more computationally efficient. Mesh convergence analyses are also performed to demonstrate the reliability of the numerical results obtained.

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

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

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

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