Thermogravitational Convection Research Articles

Double diffusive thermogravitational convection in a convex U-shaped porous chamber filled with radiative ternary hybrid nanoliquid

This research deals with the intricate dynamics of double diffusive thermogravitational convection within a convex U-shaped porous chamber and sheds light on the use of a radiative ternary hybrid nanoliquid. In this configuration, the lower flat boundary is assumed to be thermally hot and densely concentrated while the curved lateral boundaries remain cold and dilute. The other boundaries of the enclosure are kept under adiabatic conditions. The governing Navier–Stokes equations along with thermal and species equations are effectively solved by employing a higher order compact technique. The developed in-house program has been rigorously verified against experimental and computational benchmark results. The research meticulously examines the impact of several pivotal parameters, including the Lewis number (1≤Le≤20), buoyancy ratio (0≤N≤10), Darcy number (10−4≤Da≤10−2), Rayleigh number (104≤Ra≤106), volumetric heat source/sink coefficient (−10≤q≤10), radiation parameter (1≤Rd≤5), aspect parameter of the U-shaped chamber (0.2≤AR≤0.6), and solid particles concentration (0.0≤ϕthnp≤0.04) of the ternary hybrid nanofluid. The findings are eloquently portrayed through graphical representations by showcasing streamlines, iso-solutals, isotherms, and the dimensionless Nusselt (Nuavg) and Sherwood (Shavg) parameters. Our investigation demonstrates that the ternary hybrid nanofluid outperforms both hybrid and mono nanofluids in facilitating double diffusion processes. Moreover, optimal heat transfer efficiency is achieved under conditions characterized by an aspect ratio of AR = 0.2, Rayleigh number Ra=106, Darcy number Da=10−2, buoyancy ratio N = 10, Lewis number Le = 1, and solid volume fraction ϕthnp=0.04.

Numerical assessment of thermomagnetic convection of ferrofluid in a porous cavity employing a local thermal nonequilibrium model

Utilizing a two-temperature model, this study investigates the thermomagnetic convection of a ferrofluid within a porous cavity. The cavity is heated from the bottom and cooled from the sides to establish thermo-gravitational convection, whereas the thermomagnetic convection is induced by permanent magnets. The equations that govern flow and heat transfer are discretized using the finite volume method and the SIMPLE algorithm. The first part of the study evaluates the impact of the permanent magnet’s position on the flow pattern and ferrofluid and solid temperature fields. The results showed that positioning the magnet at the bottom of the cavity enhances heat transfer rate. The second part investigates the impact of the distance between two magnets at different magnetic, Rayleigh, and Darcy numbers, as well as the conduction ratio. The numerical findings exhibit that the heat transfer rate attains a peak at a certain distance between the magnets, depending on the Rayleigh number. With increasing Rayleigh number and conduction ratio, or decreasing Darcy number, the role of the magnetic field in improving heat transfer becomes less important. It is observed that thermomagnetic convection is replaced by thermo-gravitational one at high conduction ratios. The study emphasizes the need to use a local thermal non-equilibrium model in porous media with high magnetic and Darcy numbers, as well as large conduction ratios, to accurately capture the heat transfer phenomenon. It is observed that by placing two magnets at an appropriate distance, the heat transfer rate could be augmented by more than 136 %.

Gravitational modes of convection in water liquid bridges

The modes of pure buoyant (thermogravitational) convection emerging in a liquid bridge of water (Pr ≅ 6.1), uniformly heated from below and cooled from above are investigated experimentally by means of a microscale facility, a related laser-cut technique (used to illuminate isodense tracers dispersed in the liquid) and a particle image velocimetry method. In particular, the following conditions are examined: aspect ratio (A = length/diameter) in the range 0.3 ≤ A ≤ 0.9, volume ratio 0.7 ≤ S ≤ 1.3, and Rayleigh number spanning the interval from the initial quiescent state up to the development of oscillatory motion. A multitude of patterns is obtained, revealing the coexistence of different branches of steady flows in the space of parameters in the form of multiple solutions. These can evolve into oscillatory states featured by disturbances with the characteristics of standing waves (a kind of rocking motion). The analysis largely relies on a novel approach where the position of the center of the main vortex of buoyant nature established in the liquid bridge is carefully monitored in space. The related trajectory is used to discern the flow spatial degrees of freedom, which are progressively enabled as the temperature difference is increased. It is shown that the effective volume of liquid held by surface tension between the hot and cold walls can have an appreciable impact on the onset of unsteadiness and the related oscillation frequency.

Magneto-thermo-gravitational Rayleigh–Bénard convection of an electro-conductive micropolar fluid in a square enclosure: Finite volume computation

This article presents both a theoretical and a numerical analysis of thermo-gravitational magnetic convection in electro-conductive Eringen micropolar fluids in a two-dimensional enclosure. The computational regime is bound with cold top, hot bottoms, and adiabatic side walls. The governing equations were transformed via scaled variables into dimensionless partial differential equations. A Finite volume method (FVM) is used to get a solution of the computational regime. Validation of the FVM solutions is included for non-magnetic special case from the literature. Streamline contours, isotherm contours, iso-microrotation contours (lines of constant angular velocity) and local Nusselt number at the left hot wall is depicted graphically for the impact of Hartmann (magnetic) number (Ha), Prandtl number (Pr), micropolar parameter (K) and Rayleigh number (Ra). A significant modification in internal circulation and micro-rotation in addition to temperature distribution is observed with increasing vortex viscosity parameter. Significant warping of isotherms is induced with stronger magnetic field and the mushroom-shaped core structure encountered at weak magnetic field transitions to a sigmoidal topology.

Thermogravitational Convection in a Controlled Rotating Darcy-Brinkman Nanofluids Layer Saturated in an Anisotropic Porous Medium Subjected to Internal Heat Source

Thermogravitational convection in a controlled rotating Darcy-Brinkman nanofluids layer saturated in an anisotropic porous medium heated from below is Thermogravitational convection in a controlled rotating Darcy-Brinkman nanofluids layer saturated in an anisotropic porous medium heated from below is investigated. The presence of a uniformly distributed internal heat source and considers the Brinkman model for different boundary conditions: rigid-rigid, free-free, and lower-rigid and upper-free are considered. The effect of a control strategy involving sensors located at the top plate and actuators positioned at the bottom plate of the nanofluids layer is analysed. Linear stability analysis based on normal mode technique is employed. The resulting eigenvalue problem is solved numerically using the Galerkin method implemented with Maple software. The model used for the nanofluids associates with the mechanisms of Brownian motion and thermophoresis. The influences of the internal heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection. Conversely, the Darcy number, thermal anisotropy parameter, porosity, rotation, and controller effects are observed to slow down the process of convective instability.investigated. The presence of a uniformly distributed internal heat source and considers the Brinkman model for different boundary conditions: rigid-rigid, free-free, and lower-rigid and upper-free are considered. The effect of a control strategy involving sensors located at the top plate and actuators positioned at the bottom plate of the nanofluids layer is analysed. Linear stability analysis based on normal mode technique is employed. The resulting eigenvalue problem is solved numerically using the Galerkin method implemented with Maple software. The model used for the nanofluids associates with the mechanisms of Brownian motion and thermophoresis. The influences of the internal heat source strength, mechanical anisotropy parameter, modified diffusivity ratio, nanoparticles concentration Darcy-Rayleigh number and nanofluids Lewis number are found to advance the onset of convection. Conversely, the Darcy number, thermal anisotropy parameter, porosity, rotation, and controller effects are observed to slow down the process of convective instability.

Thermogravitational Convection in a Multiple Baffled Enclosure Filled with Magneto-Hybrid Nanofluid Subjected to Magnetic Field Dependent Viscosity

This study explores the significant impacts of thin baffles and magnetic field dependent viscosity on magnetohydrodynamic (MHD) thermogravitational convection of Cu-Al2O3 (50%–50%) water hybrid nanoliquid in a cavity. Considering different arrangements of baffle sticks on both the vertical walls, four geometrical configurations (Case-I, Case-II, Case-III and Case-IV) have been analyzed. Numerical simulation has been performed for the governing Navier-Stokes (N-S) equations in streamfunction - vorticity form having energy equation. These coupled equations are solved by proposing a higher-order compact finite difference method. The combination of five important aspects (hybrid nanofluid, multiple baffles, magnetic field dependent viscosity (MFDV), magnetic field and compact computation) signifies the novelty of this work. Fluid flow and transportation of thermal energy within the stipulated domain are presented for various flow pertinent parameters. The outcomes show that the increase in number of baffles diminishes the average Nusselt number values. It is concluded here that an increase in Hartmann number from 0 to 90 leads to a decrease in average Nusselt number up to 23.7% for Case-I, 23.8% for Case-II, 21.2% for Case-III and 28% for Case-IV in presence of MFDV effects.

Thermal gradient and elastic dependence of induced charge electro-osmosis in viscoelastic fluids

Induced charge electro-osmosis has notable implementation possibilities in thermal management and efficient electrokinetic micropumps. We present the coupled numerical implementation around a polarized cylinder subject to an external electric field with the influence of different polymer elasticity and thermal gradients. The azimuthal velocity, flow types, kinetic energy, elastic energy, ion transport behavior, and heat transfer capability are investigated in detail. The results show that the inflow and outflow rates approximately overlap for a typical small voltage limit ϕ < 0.1. The Rayleigh number (Ra) significantly influences the elastic energy accumulation and evolution time to the final steady state. The thermal buoyancy forces are not sufficient to create typical thermogravitational convection with passive heat transfer when Ra < 1.3 × 10−3, resulting in heat diffusion and electro-osmosis velocity dominating the temperature distribution. The Nusselt number (Nu) plot with a weak viscoelastic effect implies an asymptotic Nu=0.44+2.65Ra0.35 relation. Relevant results open possibilities for enhanced mixing and heat transfer in microdevices, providing insight into barriers to the non-Newtonian nature of electrokinetic dynamics.

Convective Heat Transfer of a Pseudoplastic Nanosuspension within a Chamber with Two Heated Wall Sections of Various Heat Fluxes

Cooling of heat-generating elements in different engineering fields is a very important and crucial topic. The present research is devoted to numerical analysis of thermogravitational convection of a pseudoplastic nanosuspension in a chamber with two heated bottom wall sections of various heat fluxes and isothermally cooling vertical walls. A mathematical model formulated employing the time-dependent Oberbeck–Boussinesq equations with non-primitive variables has been worked out by the finite difference technique. It has been revealed that a mixture of 1% carboxymethylcellulose with water can be the most effective medium to cool the heat-generating elements. At the same time, aluminum oxide nano-sized solid particles have a more essential cooling impact on the heated sections.

Natural Thermogravitational Convection in a Partially Blocked Square Area Heated from Below

Natural Thermogravitational Convection in a Partially Blocked Square Area Heated from Below

Thermogravitational convection of a pseudoplastic nanofluid with varying parameters in an enclosure having a thermally generating wall section

AbstractResearching new and optimizing existing methods of cooling electronic devices are the most important tasks in the modern world. Based on this, our work is devoted to the study of the possibility of intensifying the heat removal from a heated element using natural convective energy transport of a pseudoplastic nano liquid in a cavity. The problem is described by unsteady Oberbeck‐Boussinesq differential equations and is solved on the basis of the finite difference method. To calculate the effective parameters of a nanofluid, three sets of different models are used, including temperature dependences. The work also studied the effect of nanoparticles' various types and their volume fraction on flow structure and heat transfer. The results showed that the use of copper oxide as nanoparticles and the correlations of Guo et al. and Jang & Choi can lead to intense cooling of the bottom wall heated section.

Magneto-thermogravitational convection for hybrid nanofluid in a novel shaped enclosure

The proposed work exhibits a numerical simulation of steady thermogravitational convection of Cu–Al2O3(50%−50%) water hybrid magneto-nanofluid in a novel shaped enclosure regulated by magnetic field dependent (MFD) viscosity in presence of flush mounted variable heaters. Various cases (Case-I to Case-IV) have been considered depending on the location of the heaters on the bottom and left boundaries. Pertaining to this analysis, the streamfunction (ψ)- vorticity (ζ) form including the energy transport equation of coupled partial differential equations are evaluated with the help of an efficient higher order compact finite difference scheme. Results are exhibited in terms of streamlines, isotherms and Nusselt numbers to describe the transport phenomena obtained for different physical parametric values to this simulation. The influence of the physical parameters such as, Rayleigh number (104≤Ra≤106), Hartmann number (0≤Ha≤60), hybrid nanoparticles volume fraction (0≤ϕhnp≤0.04), orientation of magnetic field (00≤γ≤600) and magnetic number (0≤δ0≤1) on the hybrid nanofluid flow and energy transfer are analyzed. Obtained results indicate that the combinations of the heaters location and the shaped of the geometry have major impact on all the transport phenomena. Moreover, Cu–Al2O3 hybrid nanoparticles play an essential role to levitate the thermal transmission compared to other physical parameters. An addition of hybrid nanoparticles leads to an increase in the average Nusselt number up to 10.8% in Case-I, 12% in Case-II, 11.66% in Case-III and 11.65% in Case-IV. The novelty of the present work is to examine the rheological properties of hybrid nanoliquid in a novel shaped cavity subjected to magnetic field dependent viscosity (MFDV) along with flush mounted variable heaters.

Milk curd self-segmentation in cheesemaking tank

The purpose of this work is to describe and study the previously unknown phenomenon of self-segmentation of a milk curd in an open-type cheesemaking tank. Based on the analysis of the kinetics of gel formation, it has been determined that self-segmentation of the gel begins near the gel point, develops over several tens of seconds, and becomes stable as the gel condenses. The segments in the milk curd do not have a definite regular shape; their average size varies from 5 to 50 cm. The shape and size of the segments do not repeat and do not correlate with the type of cheese being produced. The displacement of the segments of the milk curd in the cheesemaking tank relative to each other in height is from 0.5 to 2 mm. The width of the boundary layer between the curd segments increases during the secondary phase of gelation from 3 to 10 mm. As a result of experimental studies, it has been shown that self-segmentation of milk gel is caused by thermogravitational convection, which forms Benard convection cells. A description of a possible mechanism of milk gel self-segmentation in open-type cheesemaking tanks is proposed. The effective role of fat globules in the mechanism of self-segmentation of the milk curd has been noted. It has been suggested that self-segmentation of the milk curd in the cheesemaking tank may cause some organoleptic defects in the finished cheese, in particular inhomogeneity of texture and color.

Microstructure characteristics of the directionally solidified TiAl-Nb alloys with different solidification modes

Microstructure characteristics are investigated for the TiAl-Nb alloys with four typical solidification modes, namely, single β, hypo-peritectic, hyper-peritectic and single α solidification. The fully lamellar structures is formed in both the dendrite and interdendritic regions in single β, hypo-peritectic, and hyper-peritectic solidification alloys, and the order of lamellar thickness is hyper-peritectic, hypo-peritectic and single β solidification alloys. Some γ islands originating from the prior interdendritic regions are formed by the chemical segregation in hyper-peritectic solidification alloy, but in single α solidification alloy, some fine lamellar structure only exist in the dendritic core and the granular γ grains are observed in the primary α interdendritic region. For hypo-peritectic solidification alloy, lamellar grain boundaries are almost located in the core of primary β phases. Lamellar orientation can be changed along either the boundaries of dendrites or the ridge-like Nb-segregations. However, for hyper-peritectic solidification alloy, the lamellar boundary locates in both the interdendritic region and the core of primary β dendrite. The lamellar orientation is changed mainly along the dendritic Nb-segregation, not along the dendrite boundary. Not every α2 in lamellar grain has Burgers orientation relationship with the prior β dendrite for both hypo- and hyper-peritectic solidification alloys. Several macrosegregation regions consisting of the curved coarsened lamellae are produced only in hypo-peritectic alloy. These regions may be induced by relatively weak thermo-gravitational convection (TGC) effect, which do not change the lamellar grain orientation but make a small orientation angle deviation of the α2 phase from each other in the grain.

Thermal performance of an environmentally friendly nanoliquid in a cabinet with two l-shaped heaters: application for electronic cooling

Purpose The purpose of this paper is to analyze numerically the nanofluid natural convection inside a square enclosure with two L-shaped heaters using lattice Boltzmann method. Design/methodology/approach An environmentally friendly nanofluid, clove-treated graphene nanoplatelet (CGNP), is used to study the enhancement of heat transfer. Six various heaters configurations are considered and effects of nanoparticle concentration (0–0.1%) and Rayleigh number (10^3–10^6) on streamlines, isothermal lines and heat transfer parameters are studied. The developed computational code has been validated using mesh sensitivity analysis and numerical data of other authors. Findings It is observed that in contrast to distilled water, CGNP/water nanofluid is an efficient coolant and the Nusselt number is increased as the nanoparticle concentration and Rayleigh numbers increment. The nanoparticle concentration cannot change the flow pattern inside the enclosure. However, the Rayleigh number and heaters configuration can change the flow pattern significantly. Several heaters configurations (Cases 1–4) related to the symmetry of geometrical shape and corresponding boundary conditions, illustrate the symmetry of streamlines and isotherms about the vertical line (X = 0.5). The formation of vortices inside the enclosure is affected by the raising heat plume above the heaters. Moreover, at different Rayleigh numbers, the relative magnitude of average Nu for various cases is different. At Ra = 103, the energy transport characteristic depends on the relative location of heaters and cold walls, and the order of average Nusselt number is Case 3 ˜ Case 4 ˜ Case 6 > Case 1 ˜ Case 2 ˜ Case 5. However, at Ra = 106, an influence of thermal convection mechanism on heat transfer is significant and the ranking of average Nusselt number is Case 1 ˜ Case 4 > Case 5 > Case 6 > Case 2 > Case 3. Originality/value The originality of the research lies in both the study of thermogravitational convection in a closed chamber with two L-shaped heaters, and the analysis of the influence of control parameters for an environmentally friendly nanoliquid on electronics cooling process.

Thermogravitational convection of water-based nanofluids with entropy generation in a wavy cabinet having a localized non-uniform heat source

Thermogravitational convection of water-based nanofluids with entropy generation in a wavy cabinet having a localized non-uniform heat source

Publisher's Note: “On the analysis of magnetohydrodynamics and magnetic field-dependent viscosity effects on thermogravitational convection of hybrid nanofluid in an enclosure with curved walls” [Phys. Fluids 33, 102010 (2021)

First Page

Thermogravitational convection of ferrofluid combined with the second law of thermodynamics for an open chamber with a heat-generating solid block under an influence of uniform magnetic field

The present numerical study scrutinizes the effect of uniform Lorentz force on the thermogravitational energy transport and entropy production of nanosuspension in an open domain with a heat-generating solid element. The left border is kept at low temperature (Tc) whilst the horizontal borders are assumed to be adiabatic. Finite volume method (FVM) is employed to work out the heat and mass transfer equations. For fixed value of Rayleigh number (Ra = 107), numerical analysis was optimized for wide ranges of nanoparticle volume fraction (ϕ = 1%–4%), thermal conductivity ratio of a heat generating body (k⁎ = 0.1–5), Hartmann parameter (Ha = 0–100), angle of inclined magnetic field (γ = 0°–90°) and non-dimensional temperature drop (Ω = 0.001–0.1). The numerical solutions were analyzed employing patterns of temperature and stream function as well as average Nusselt number and entropy lines. The outcomes indicated that, an increasing magnetic parameter Ha leads to reduction of mean Nu and the rate of entropy production. An addition of nano-sized particles enhances the energy transport and average entropy production for the system. It is also revealed that the maximum energy transport strength occurs at high thermal conductivity ratio (k⁎ = 5).

Thermogravitational convection of power‐law nanofluid in a cavity with a heat‐generated section on the bottom wall

Optimization of cooling systems for electronic devices is one of the crucial challenges in the modern engineering world. Inclusion of nanosized particles to working heat transfer liquids can enhance the heat removal from the heated elements in electronics. Taking into account these data, the present research is devoted to numerical analysis of natural convection in a cavity filled with a non‐Newtonian nanosuspension under an influence of a heat‐generating wall section. The paper contains the simulation outcomes for two different cases, namely, a heat‐generating wall section with constant heat flux and a heat‐generating wall section with constant temperature. The considered phenomenon has been described using the single‐phase nanofluid model where the base liquid is a pseudoplastic fluid. The rheological parameters of the host liquid including the coefficient of flow density and an indicator of fluid behavior are the empirical data of MWCNT nanofluids. The non‐Newtonian nature of the nanoliquid has been described by the Ostwald‐de‐Waele power law. Detailed analysis has been carried out for different governing parameters including the Rayleigh number, the volume fraction of nanoparticles, and the size of the heater using the non‐primitive dimensionless variables and the finite difference method. Obtained results illustrate different temperature patterns for various boundary conditions. Moreover, in the case of heat‐generating element, the average Nusselt number is greater than for the isothermal heater. It should be noted that the considered nanofluid model reflects the energy transference degradation with a growth of the nanoparticles concentration.

On the analysis of magnetohydrodynamics and magnetic field-dependent viscosity effects on thermogravitational convection of hybrid nanofluid in an enclosure with curved walls

This work deals with the impact of magnetic field-dependent viscosity and magnetohydrodynamics on the natural convection heat transfer of Ag–MgO (50%–50%) water hybrid nanoliquid in a complicated enclosure. The considered cavity with concave or convex horizontal boundaries has been differentially heated and cooled by multiple heat sources and heat sinks. The governing equations (Navier–Stokes equations) constituting stream function (ψ)-vorticity (ζ) formulation with energy equation are solved by adopting a compact finite difference scheme. Meanwhile, the flow domain that is influenced by several factors including Hartmann number (0≤Ha≤60), hybrid nanoparticles volume fraction (0≤ϕhnp≤0.02), Rayleigh number (103≤Ra≤106), orientation angle of magnetic field (00≤γ≤900), magnetic number (0≤δ0≤1), different cases (Case-I to III), and internal heat generation or absorption (−2≤Q≤2) is analyzed generously. Experimentally based correlations for thermal conductivity and dynamic viscosity have been used throughout the study. The outcomes show that the geometric parameters can be used as an excellent controller of the thermal performance inside the wavy chamber.

Numerical Investigation of Conjugate Natural Convection in a Cavity with a Local Heater by the Lattice Boltzmann Method

A numerical study of conjugate thermogravitational convection in a closed cavity with a local heater of square or triangular shape placed on a heat-conducting substrate using the double distribution function of the lattice Boltzmann method has been carried out. The side walls of the research area are maintained at a constant minimum temperature. The influence of the geometric shape of the heating element, the Rayleigh number, and the material of the heat-removing substrate on the thermohydrodynamic parameters has been studied. As a result of the research, the joint effect of these mentioned parameters on the efficiency of heat removal from the heater surface has been established. It has been found that a rise of the bottom wall thermal conductivity causes an increase in the average Nusselt number at the heater surface.