Flux Coefficient Research Articles

Effect of wavy corrugations on the performance enhancement of direct contact membrane distillation modules: A numerical study

This study employs three-dimensional (3D) computational fluid dynamics (CFD) simulations to investigate the influence of corrugations on direct contact membrane distillation (DCMD) modules. The accuracy of 3D CFD simulations is validated by the comparison of water flux and temperature polarization coefficient (TPC) against literature data for empty and spacer-filled DCMD modules. The dusty gas model is used to predict the permeate flux as a function of temperature and pressure over the surface of the membrane. We consider single and double sinusoidal corrugated membranes and examine the performance of DCMD membranes in terms of TPC, concentration polarization coefficient (CPC), power number (Pn), and Nusselt number (Nu) against various corrugation geometrical parameters. These parameters include the amplitude, streamwise, and spanwise frequency of corrugation waves. Our results show that corrugated membranes can successfully improve the membrane system by disrupting the boundary layer by an intense secondary flow. The mechanism works the best at high flow rates. Our results suggest that singly corrugated membranes improve the water flux and TPC by 32% and 25% at Re=1500. Also, doubly corrugated membranes provide 45% and 36% improvements in water flux and TPC at the same Reynolds number.

Intermittency and critical mixing in internally heated stratified channel flow

Through direct numerical simulations we investigate the effects of spatiotemporal intermittency as a result of stable stratification in surface heated stratified open channel flow. By adapting the density inversion criterion method of Portwood et al. [J. Fluid Mech., vol. 807, 2016, R2] for our flow, we demonstrate that the flow may be robustly separated into regions of active turbulence for which $Re_B \gtrsim {O}(10)$ and surrounding quiescent fluid, where $Re_B$ is the buoyancy Reynolds number. The intermittency in the flow spontaneously manifests as a deformed horizontal interface between the upper quiescent and lower turbulent flow, characterised by vigorous mixing from ‘overturning’ shear instabilities. The resulting vertical intermittency profile is accurately predicted by a local Monin–Obukhov length normalised by viscous wall units $\varLambda ^+$ such that the flow displays intermittency within the parameter range of $2.5 \lesssim \varLambda ^+ \lesssim 260$ . By considering conditional averages of the ‘turbulent’ and ‘quiescent’ flow separately, we find the ‘turbulent’ flow within this region to be described by constant critical gradient Richardson and turbulent Froude numbers of $Ri_{g,c} \approx 0.2$ and $Fr_c \approx 0.3$ . We find that the turbulent flow continues to display a $\varGamma \sim Fr^{-1}$ relationship when $Fr < Fr_c$ , whereas the quiescent flow shows no correlation between $\varGamma$ and $Fr$ , where $\varGamma$ is the flux coefficient. Hence, we demonstrate directly that for our flow, the emergence of an asymptotic ‘saturated’ $\varGamma$ regime in the limit of a low ‘global’ $Fr$ occurs due to intermittency and increasing contributions to measurements of $\varGamma$ from the quiescent flow.

In-situ hierarchical micro/nanocrystals on copper substrate for enhanced boiling performance: An experimental study

Micro/nano structures on the Cu substrate are normally used for the enhancing the heat transfer capacity for many boiling-related applications. Conventional methods for fabricating these structures, however, require additional processing equipment and involve relatively complex processes. In this study, a simple immersion method for generating in-situ micro/nanocrystal structures on Cu substrates is developed for simplifying the fabrication with reduced cost and improving the boiling performance in the meantime. Using characterization analytical instruments including SEM, AFM, XRD, EDS and XPS, the surface morphology and chemical contents of the micro- and nanocrystals generated on the Cu substrate were examined. The experimental results showed that the hierarchical micro/nanocrystals enabled simultaneous enhancements in critical heat flux (CHF) and heat transfer coefficient (HTC), indicating the superiority of the hierarchical micro/nanocrystals in facilitating the boiling performance compared to conventional structured surfaces. It is found that the nanosheet and micro-flowers (NSMF) surface provides the largest enhancement amongst other micro/ nano structures including the nanograss forests (NG), nanograss forests and micro-petals (NGMP), and nanograss forests and micro-flowers (NGMF). Comparatively, the CHF and HTC could achieve 65.7 W/cm2 and 4.9 W/cm2K, showing an increase of the CHF and HTC by 56.5 % and 170 %, respectively, using the smooth surface in the same condition as the benchmark. It is implied that the liquid circulation is apparently promoted through the separation of vapor–liquid pathway and the bubble blanket formation is remarkably inhibited due to the special structure and morphology of the hierarchical surface. However, vital factors including the surface wettability and the experimental accuracy need to be considered for optimizing the boiling performance in diverse scenarios.

Biomimetic Micropillar Wick for Enhanced Thin-Film Evaporation

Sustainable liquid cooling solutions are recognized as the future of thermal management in the chip industry. Among them, phase change heat transfer devices such as heat pipes and vapor chambers have shown tremendous potential. These devices rely on the physics of capillary-driven thin-film evaporation, which is inherently coupled with the design and optimization of the evaporator wicks used in these devices. Here, we introduce a biomimetic evaporator wick design inspired by the peristome of the Nepenthes alata that can achieve significantly enhanced evaporative cooling. It consists of an array of micropillars with multiple wedges along the sidewall of each micropillar. The efficacy of the wedged micropillar is evaluated based on a validated numerical model on the metrics of dryout heat flux and effective heat transfer coefficient. The wedge angle is chosen such that wedged micropillars cause liquid filaments to rise along the micropillar vertical walls. This results in a significant increase in thin-film area for evaporation. Additionally, the large mean curvature of the liquid meniscus produces strong capillary pumping pressure and simultaneously, the wedges increase the overall permeability of the wick. Consequently, our model predicts that the wedged micropillar wick can attain ∼234% enhancement of dryout heat flux compared to a conventional cylindrical micropillar wick of similar geometrical dimensions. Moreover, the wedged micropillars can also attain a higher effective heat transfer coefficient under dryout conditions, thus outperforming the cylindrical micropillar in terms of heat transfer efficiency. Our study provides insight into the design and capability of the biomimetic wedged micropillars as an efficient evaporator wick for various thin-film evaporation applications.

Designing and evaluation of dermal targeted combinatorial nanostructured lipid carrier gel loaded with curcumin and resveratrol for accelerating cutaneous wound healing

A nanostructured lipid carrier containing combined curcumin (CUR) and resveratrol (RSV) was prepared and tested for its potential to accelerate wound healing through topical administration. Prepared nano lipid carrier (NLC) formulation had a particle size of 132.3 ± 4.54 nm, polydispersity index (PDI) of 0.478, and zeta potential of −16.6 mV. Entrapment efficiency (EE) for CUR and RSV was found to be 94.21 ± 0.28% and 84.61 ± 0.15%, respectively. Drug loading was found to be 8.560 ± 0.948% (for CUR) and 7.602 ± 0.452% (for RSV). NLC formulation was converted to NLC gel by incorporation of Carbopol 934 for enhancing its dermal applicability. Flux and permeability coefficient for CUR and RSV in NLC gel was found to be 22.087 µg/cm2/h, 11.299 µg/cm2/h, and 0.2208, 0.1129, respectively, through goat ear skin and 19.213 µg/cm2/h, 22.66 µg/cm2/h and 0.1921, 0.2266, respectively, through Strat-MTM membrane. Dermatokinetic study revealed significant enhancement in Cskin max and AUC0–12h in skin sample treated with NLC gel in comparison with plain gel. Also, NLC gel showed longer retention time which indicates prolonged drug action at targeted site thus, NLC gel may show better therapeutic efficacy than plain gel.

Dropwise Condensate Comb for Enhanced Heat Transfer.

Dropwise condensation on superhydrophobic surfaces could potentially enhance heat transfer by droplet spontaneous departure via coalescence-induced jumping. However, an uncontrolled droplet size could lead to a significant reduction of heat transfer by condensation, due to large droplets that resulted in a flooding phenomenon on the surface. Here, we introduced a dropwise condensate comb, which consisted of U-shaped protruding hydrophilic stripes and hierarchical micro-nanostructured superhydrophobic background, for a better control of condensation droplet size and departure processes. The dropwise condensate comb with a wettability-contrast surface structure induced droplet removal by flank contact rather than three-phase line contact. We showed that dropwise condensation in this structure could be controlled by designing the width of the superhydrophobic region and height of the protruding hydrophilic stripes. In comparison with a superhydrophobic surface, the average droplet radius was decreased to 12 μm, and the maximum droplet departure radius was decreased to 189 μm by a dropwise condensate comb with 500 μm width of a superhydrophobic region and 258 μm height of a protruding hydrophilic stripe. By controlling the droplet size and departure on hierarchical micro-nanostructured superhydrophobic surfaces, it was experimentally demonstrated that both the heat transfer coefficient and heat flux could be enhanced significantly. Moreover, the dropwise condensate comb showed a maximum heat transfer coefficient of 379 kW m-2 K-1 at a low subcooling temperature, which was 85% higher than that of a superhydrophobic surface, and it showed 113% improvement of high heat flux or heat transfer coefficient when it was compared with that of the hierarchical micro-nanostructured superhydrophobic surface at a high subcooling temperature of ∼10.6 K. This work could potentially transform the design and fabrication space for high-performance heat transfer devices by spatial control of condensation droplet size and departure processes.

Effect of electric field, mass flow rate, and subcooling degree on subcooled flow boiling in a micro-slit channel

This study investigated the design and cooling performance of a micro-slit-channel heat sink for electrical device cooling. The subcooled flow-boiling performance of a dielectric liquid, HFE-7000, was experimentally characterized. A flat electrode made from stainless steel with 10 narrow slits, each 1 mm width and 17 mm long, was placed at 600 μm above the heated surface to generate a high electric field. The flow boiling heat transfer performance of an electroplated diamond surface was evaluated. Four electric field intensities from 0 to −5 kV/mm, three mass flow rates from 1.83 to 4.8 g/s, and four inlet subcooling from 5 to 25 K were tested at an atmospheric system pressure. Four flow boiling patterns were categorized using a high-speed camera: single-phase flow, subcooled nucleate boiling, saturated nucleate boiling, and local dry out boiling. The maximum critical heat flux (CHF) and heat transfer coefficient were 95 W/cm2 and 30 kW/m2K, respectively, for mass flow rate of 4.83 g/s, electric field of −5 kV/mm, subcooling degree of 9 K, and mass flow rate of 4.83 g/s. A semi-empirical prediction of the CHF exhibited good agreement with the experimental results within ±18 %.

A REVIEW OF POOL BOILING HEAT TRANSFER PROPERTIES BY NANOFLUID

Boiling heat transfer has maintained a high degree of interest due to the range of its applications in the energy sector. In recent years, much research has focused on improving the nucleate pool boiling by modifying the fluid properties. In this review article, the basic properties and characteristics of Al2O3 nanofluids and few other nanofluids are explored and discussed through past research findings. Next, previous studies that involved pool boiling heat transfer enhancement using Al2O3 nanofluid and its performance in terms of critical heat flux (CHF) and heat transfer coefficient (HTC) are further highlighted. These studies have employed methods that affected the performance of CHF and HTC such as electric field and surface modification. Maximum enhancement in CHF measured is approximately 200%. On the other hand, usage of prediction models to predict enhancements are also discussed thoroughly. Regardless of boiling performance enhancements with the deployment of nanofluids, several concerns must first be addressed before it is able to be deployed for practical use.

Mixing across stable density interfaces in forced stratified turbulence

Understanding how turbulence enhances irreversible scalar mixing in density-stratified fluids is a central problem in geophysical fluid dynamics. While isotropic overturning regions are commonly the focus of mixing analyses, we here investigate whether significant mixing may arise in anisotropic statically stable regions of the flow. Focusing on a single forced direct numerical simulation of stratified turbulence, we analyse spatial correlations between the vertical density gradient $\partial \rho /\partial z$ and the dissipation rates of kinetic energy $\epsilon$ and scalar variance $\chi$ , the latter quantifying scalar mixing. The domain is characterized by relatively well-mixed density layers separated by sharp stable interfaces that are correlated with high vertical shear. While static instability is most prevalent within the mixed layers, much of the scalar mixing is localized to the intervening interfaces, a phenomenon not apparent if considering local static instability or $\epsilon$ alone. While the majority of the domain is characterized by the canonical flux coefficient $\varGamma \equiv \chi /\epsilon =0.2$ , often assumed in ocean mixing parametrizations, extreme values of $\chi$ within the statically stable interfaces, associated with elevated $\varGamma$ , strongly skew the bulk statistics. Our findings suggest that current parametrizations of turbulent mixing may be biased by undersampling, such that the most common, but not necessarily the most significant, mixing events are overweighted. Having focused here on a single simulation of stratified turbulence, it is hoped that our results motivate a broader investigation into the role played by stable density interfaces in mixing, across a wider range of parameters and forcing schemes representative of ocean turbulence.

In vitro skin permeation of potassium hexachloroplatinate and a comparison with potassium tetrachloroplatinate

Halogenated platinum salts are known respiratory sensitizers in the workplace, and occupational exposure to platinum via the respiratory system and skin has been reported. The aim of this study was to compare the permeability and skin retention of potassium hexachloroplatinate to previously published data of potassium tetrachloroplatinate. Experiments were performed using female Caucasian skin and Franz diffusion cells with the application of 0.3 mg Pt/mL in the donor solution for 24-h. After 8-h of exposure, 1.87 ng/cm2 of Pt was detected in the receptor solution with exposure to potassium hexachloroplatinate, whereas 0.47 ng/cm2 was detected with exposure to potassium tetrachloroplatinate. After 24-h of exposure the Pt retention in the skin was 1861.60 ng/cm2 and 1486.32 ng/cm2 with exposure to potassium hexa- and tetrachloroplatinate respectively. The faster rate of Pt permeation from exposure to potassium hexachloroplatinate was confirmed by the flux and permeability coefficient values. The results indicate a higher permeability and skin retention of Pt when exposed to potassium hexachloroplatinate, confirming a higher risk associated with occupational exposure to this platinum compound relative to potassium tetrachloroplatinate.

Single bubble nucleation in water-filled 59-nm nanochannel

Bubble nucleation, by surface heating, is simulated in a water-filled 59 nm height silicon-dioxide nanochannel using computational fluid dynamics. Disjoining pressure of water is integrated in the continuum-level simulations to capture the molecular effects of nanoscale confinement. Input parameters of imposed heat flux and phase-transition coefficient are widely varied to perform a set of 50 simulations. Bubble nucleation occurs within a narrow temperature range of 124.7 ± 2.5 °C, and in excellent agreement with prior experimental finding. Onset of bubble nucleation occurs at the center of the channel rather than at the surface due to the presence of disjoining pressure, i.e., no three-phase contact line forms and a water film is present between the bubble and the surface. Post nucleation, three distinct paths of bubble collapse, steady-state, and continuous growth are observed, with the last case leading to formation of three-phase contact line. Such behavior is attributed to a critical thickness of the water film and associated disjoining pressure. The present work sheds light on the importance of disjoining pressure and its dominance in governing the bubble onset and growth behavior. Such fundamental understanding can potentially advance the development of future thermal management devices, such as heat pipes.

Magnetized flow of naturally convective viscous fluid in permeable rhombus-shaped annulus by executing FEM simulations

The present work is deliberated to investigate the flow and thermal behavior of viscous fluid flow in permeable rhombic-shaped enclosure. Annular region lying below inner and outer rhombuses is the area of concentration during this study. Magnetic field is employed in horizontal direction to envision aspects of Lorentz field. Governing equations are developed in dimensional form of partial differential setup. Numerical experiments via finite element approach are capitalized to find solution. Grid convergence test is executed to show domain distribution along with decision about mesh level at which computations are to conducted. Streamlines and isothermal maps are sketched to show comprehensive change in associated flow fields against governing parameters. Kinetic energy and average heat flux coefficient are evaluated in comparative manner for magnetic and hydrodynamic situations. Through attained outcomes, it is concluded that kinetic energy and heat flux coefficient enhances reduction against Hartmann number.

Study of steam heat transfer enhanced by CO2 and chemical agents: In heavy oil production

Steam flooding with the assistance of carbon dioxide (CO 2 ) and chemicals is an effective approach for enhancing super heavy oil recovery. However, the promotion and application of CO 2 and chemical agent-assisted steam flooding technology have been restricted by the current lack of research on the synergistic effect of CO 2 and chemical agents on enhanced steam flooding heat transfer. The novel experiments on CO 2 -chemicals cooperate affected steam condensation and seepage were conducted by adding CO 2 and two chemicals (sodium dodecyl sulfate (SDS) and the betaine temperature-salt resistant foaming agent ZK-05200). According to the experimental findings, a “film” formed on the heat-transfer medium surface following the co-injection of CO 2 and the chemical to impede the steam heat transfer, reducing the heat transfer efficiency of steam, heat flux and condensation heat transfer coefficient. The steam seepage experiment revealed that the temperature at the back end of the sandpack model was dramatically raised by 3.5–12.8 °C by adding CO 2 and chemical agents, achieving the goal of driving deep-formation heavy oil. The combined effect of CO 2 and SDS was the most effective for improving steam heat transfer, the steam heat loss was reduced by 6.2%, the steam condensation cycle was prolonged by 1.3 times, the condensation heat transfer coefficient was decreased by 15.5%, and the heavy oil recovery was enhanced by 9.82%. Theoretical recommendations are offered in this study for improving the CO 2 -chemical-assisted steam flooding technique.

Pool boiling heat transfer enhancement and bubble visualization on a microporous copper over CuO filmed surface through combination of chemical etching and electrochemical deposition

For high heat flux engineering application, a Microporous Copper over CuO Film Surface (MCCFS) is prepared to find out the Critical Heat Flux (CHF) and Boiling Heat Transfer Coefficient (BHTC). The bare Cu surface is modified into MCCFS through a combination of two chemical processes, i.e., chemical etching and electrochemical deposition. Various properties of the MCCFS, like porosity, wettability, and roughness, are also analyzed. The saturated pool boiling experiment is carried out by taking distilled water as the boiling liquid at atmospheric pressure. Results show that the CHF and the BHTC of the MCCFS are improved by 71% and 78%, respectively, than the bare Cu. This improvement is mainly due to the increased roughness and decreased wettability of the MCCFS. A visualization-based quantitative analysis of the bubble during boiling is also done to correlate the enhanced heat transfer from the MCCFS. Bubble characteristics like nucleation site density, bubble departure diameter, and bubble departure frequency are analyzed. The enhanced bubble site density, decreased departure diameter, as well as the enhanced departure frequency of the bubble supported the improvement of heat transfer from the MCCFS. A comparative analysis of the performance of heat transfer from the MCCFS is also presented.

Influence of liquid height on pool boiling heat transfer over open rectangular microchannels

Open rectangular microchannels surface (ORMS) has been extensively studied in pool boiling heat transfer because of lower cost of fabrication, ease of application and better heat transfer performance. Researchers have examined liquid height effect on heat transfer performance at various heat fluxes for copper plain surface (CPS). However, few studies have revealed the underlying mechanisms of liquid height for ORMS. This study tested different liquid heights of 1 mm, 3 mm, 5 mm, 7 mm, 9 mm, 12 mm, 15 mm, 20 mm and 50 mm over both ORMS and CPS with deionized water at atmospheric pressure. Critical heat flux (CHF) and heat transfer coefficient (HTC) were determined and considered as functions of liquid height for each liquid level. For ORMS, three different HTC variation trends versus liquid height were evaluated. The results show that the distinction is primarily determined by heat flux, as follows: Type-I has critical liquid level, Type-II has both critical liquid level and optimum liquid level, and Type-III has optimum liquid level. Type-II, however, did not appear for CPS. This research also showed that ORMS and CPS have a critical liquid level of 5 mm, whereas ORMS may be able to achieve a higher heat flux in shallow liquid levels of 1 mm and 3 mm due to its improved liquid replenishment capability.

Achieving robust and enhanced pool boiling heat transfer using micro–nano multiscale structures

Vapor chamber thermal management technology has become a high-reliability cooling method to solve the heat dissipation problem. However, this is still a crucial challenge to overcome when the capillary wick is exposed to harsh service environments. In this paper, a fabrication method of capillary wicks with micro–nano multiscale structures combining micro hot embossing and high-pressure hydrothermal treatment is proposed. Micro pyramid-channel is fabricated by micro hot embossing, and when the axis-to-diameter ratio of nanobars reaches 3.16–3.17, superhydrophilicity is realized. In the pool boiling experiment, the heat transfer performance of the pyramid-channel is better than that of the triangular-channel. Importantly, the superhydrophilic micro–nano structures achieve significantly improved critical heat flux and heat transfer coefficient simultaneously, increased by 162.1% and 180.8%. Moreover, the fabricated micro–nano capillary wick, which comprise high-strength pyramid-channel and specific wettability nanostructures, can maintain their outstanding superhydrophilicity and superhydrophobicity and their enhanced boiling property even after high-pressure high-velocity fluid scouring. The proposed cost-effective fabrication method provides an ideal and industrialized approach for the mass production of vapor chamber capillary wicks suitable for severe application environments.

Simultaneous enhancement of critical heat flux and heat transfer coefficient via in-situ deposition of ionic liquids during pool boiling

Two-phase heat transfer processes such as boiling are required to address waste heat management challenges. Among the various regimes, the nucleate boiling regime, which relies on the ebullition cycle to dissipate large amounts of heat within narrow temperature budgets is desired in such applications. However, an insulating vapor blankets the heater at higher heat fluxes to interrupt this high heat transfer coefficient (HTC) regime. This limiting heat flux beyond which a thermal runaway occurs in boiling systems is known as the critical heat flux (CHF). Accordingly, easy-to-implement and reliable strategies for simultaneous enhancement in HTC and CHF are desired. Typical surface modification/coating strategies used in this regard are often expensive and suffer from the issues of delamination and fouling. Here we utilize aqueous solutions of imidazolium ionic liquids (ImILs) to propose a facile, scalable, and robust strategy to address these issues. We show that the in-situ deposition of short-chain ImILs such as [C2mim][Cl] enhances heater surface wettability to remarkably increase the CHF to ≈1600kW/m2, i.e., ≈1.6× increase compared to the baseline case of pure water. We explain the mechanism of this atypical CHF enhancement with molecular additives via thorough surface tension, foamability, surface, and wettability characterization experiments. We next vary the hydrophobic chain length of the ImILs to facilitate a simultaneous enhancement in CHF and HTC. We perform a quantitative comparison with the existing studies in the literature to demonstrate the potential of our approach. Ease of implementation along with the flexibility to favorably manipulate the heater surface and the boiling fluid properties simultaneously by tuning the structure of ImILs are promising for current and future thermal management challenges.

Formulation and Evaluation of Niosomal Gel Loaded with Asparagus racemosus Extract for Anti-inflammatory Activity

Abstract: Background/Aim: Inflammation typically occurs when infectious microorganisms enter the body, settle in specific tissues, and/or circulate in the blood. Asparagus racemosus extract contains various saponins and flavonoids and plant-origin drugs have fewer side effects and toxicity. The phytoconstituents have less permeability through the skin; to enhance their permeability and effectiveness it was loaded in niosomes. Therefore, the study aimed to formulate and characterize the niosomal gel loaded with Asparagus racemosus extract for anti-inflammatory activity. Materials and Methods: The niosomes containing saponins in the extract were prepared using thin film hydration method and 23 full factorial design was employed to assess the influence of independent variables span 60 and cholesterol on vesicle size, PDI, zeta potential, and percentage entrapment efficiency. 10% of niosomal and conventional gels were prepared by incorporating optimized niosomes and extract containing total saponin in 1% carbopol gel. Ex vivo permeability studies of prepared gels were performed through goat skin using Franz diffusion cell. An anti-inflammatory study was conducted on albino rat. Results: The statistical analysis revealed the significant effect of independent variables on vesicle size, PDI, entrapment efficiency and zeta potential. SEM image shows vesicles are spherical in shape and uniform in size. The niosomal gel provided a significantly higher amount of steady-state flux and permeability coefficient into the skin than conventional gel. The animal model proved that niosomal gel loaded with total saponins in extract showed significant anti-inflammatory compared to the control. Conclusion: It was concluded that the niosomal gel had better efficacy than the conventional gel. Keywords: Asparagus racemosus, Niosomes, Span 60, Cholesterol, Factorial design, Carbopol 934.

Significance of Dufour and Soret aspects on dynamics of water based ternary hybrid nanofluid flow in a 3D computational domain

The prime motive to conduct this communication is to explicate hydrothermal attributes of water by inducing new composition of nanoparticles termed as ternary particles. For this purpose, two differently natured groups one with lesser densities (Carbon nanotubes, Graphene and Aluminium oxide) and with higher densities (Copper oxide, Copper and Silver) are accounted. A 3D permeable surface is considered as a physical configuration of problem by providing dual stretching. Initially, mathematical structuring in dimensional representation expressing the constitutive relations for mass, momentum and energy conservation is manifested. Later on, a set of similar variables are executed to express attained coupled system into ordinary form. Numerical simulations are performed to find solution by employing shooting and RK-4 methods in conjunction. Description about change is displayed through graphical visualization. Subsequently, temperature distribution and heat flux coefficient against sundry variables are also measured and comprehensively discussed in pictorial and tabular format. Wall drag coefficients along (x, y) directions are also computed. It is inferred from the outcomes that velocity, temperature and concentration of base fluid is higher for ternary group 1 containing particles of low densities than for group 2 with more denser particles. It is also deduced that elevation in temperature of fluid is revealed against Soret number whereas contrary aspects is observed in view of concentration distribution. Dufour number has declining impact on temperature profile whereas it upsurges the mass distribution. It is depicted that skin friction in case of group containing particles with less densities are more than other group.

Stratified Taylor–Green vortex by lattice Boltzmann methods: Influence of stencils, forcing schemes, and collision models

Stably stratified Taylor–Green vortex simulations are performed by lattice Boltzmann methods (LBM) and compared to other recent works using Navier–Stokes solvers. The density variation is modeled with a separate distribution function in addition to the particle distribution function modeling the flow physics. Different stencils, forcing schemes, and collision models are tested and assessed. The overall agreement of the lattice Boltzmann solutions with reference solutions from other works is very good, even when no explicit subgrid model is used, but the quality depends on the LBM setup. Although the LBM forcing scheme is not decisive for the quality of the solution, the choice of the collision model and of the stencil are crucial for adequate solutions in underresolved conditions. The LBM simulations confirm the suppression of vertical flow motion for decreasing initial Froude numbers. To gain further insight into buoyancy effects, energy decay, dissipation rates, and flux coefficients are evaluated using the LBM model for various Froude numbers.