Volume Fraction Profiles Research Articles

A three-phase dispersion profile model for stratified pipe flow: Effects of gas bubbles on the distribution of oil and water droplets

A three-phase dispersion profile model for stratified gas/oil/water pipe flow was developed. The main goal was to incorporate the effects of gas bubbles on the cross-sectional distribution of oil and water droplets in the continuous liquids. Gas bubbles entrain from the gas layer above the oil/water layers and modify the oil and water dispersion profiles in several different ways. Increased hindered settling due to gas bubbles, reduction of the effective background mixing density that affects buoyancy, turbulence suppression due to droplets and bubbles and finally reduction of oil and water droplet entrainment rate due to area blocking by gas bubbles at the oil/water interface. All three dispersion profiles were modelled consistently with respect to their mutual coupling. The tuned model qualitatively reproduced the shapes and magnitude of the volume fraction profile data obtained from X-ray measurements. Several areas were identified where more fundamental experimental research would be needed.

Brownian dynamics simulation of the structural evolution in monodisperse hard-sphere suspensions during drying and sedimentation processes.

The drying behavior of monodisperse colloidal films, with a focus on the influence of process variables on film microstructures, is explored via Brownian dynamics (BD) simulations. In our model, hard-sphere colloidal particles are dispersed in a Newtonian liquid with an initial particle volume fraction of 0.1. The effects of the drying rate and sedimentation on the evolving microstructures are systematically investigated using two dimensionless numbers: the Péclet number (Pe), which represents the competition between evaporation and diffusion, and the sedimentation number (Ns), which reflects the relative influence of sedimentation on evaporation. First, we analyze the local particle volume fraction and film structure at various Pe and Ns. As Pe increases, particle accumulation occurs near the liquid-gas interface, whereas a high Ns promotes dense packing near the substrate owing to sedimentation. The BD simulation results, viz. the local volume fraction profiles and drying regime maps, are in good agreement with those of the continuum model proposed by Wang and Brady. Structural analysis of the dried films reveals that at a low Pe (Pe = 0.1), a face-centered cubic (FCC) structure dominates, primarily independent of the sedimentation effects. In contrast, a high Pe leads to hexagonal close-packed or amorphous structure formation. Notably, at intermediate drying rates (Pe = 10), an increase in Ns promotes additional FCC ordering in the final film structure. Our study provides new insights into the hitherto underexplored role of sedimentation in the structural evolution of drying colloidal films, revealing the mechanisms of drying-induced assembly in colloidal systems.

Mass and momentum balance during particle migration in the pressure-driven flow of frictional non-Brownian suspensions

The transient shear-induced particle migration of frictional non-Brownian suspensions is studied using particle-resolved simulations. The numerical method – the fictitious domain method – is well suited to heterogeneous flows thanks to a frame-invariant formulation of the subgrid (lubrication) corrections that does not involve the ambient flow (Orsi et al., J. Comput. Phys., vol. 474, 2023, 111823). The paper aims to give an accurate quantitative picture of the mass and momentum balance during the flow. The various assumptions and local constitutive laws that together form the suspension balance model (SBM) are thoroughly examined. To this purpose, the various quantities of interest are locally averaged in space and time, and their profile across the channel is extensively studied, with specific attention to the time evolution of the different contributions, either hydrodynamic in nature or from contact interactions, to the shear and normal stresses. The latter, together with the velocity gradient in the wall-normal direction and the volume fraction profile, yield the local constitutive laws, which are compared with their counterpart obtained in homogeneous shear flow. A fair agreement is observed except in a layering area at the boundaries and at the very centre of the channel. In addition, the main assumption of the SBM, i.e. the local relation between the hydrodynamic force on the particles and the particle flux, is meticulously investigated. The hydrodynamic force is found to be mainly a drag, except in the lower range of the probed volume fractions, where a non-drag contribution is observed.

Shear-induced migration of rigid spheres in a Couette flow

Concentration inhomogeneities occur in many flows of non-Brownian suspensions. Their modeling necessitates the description of the relative motion of the particle phase and of the fluid phase, as well as the accounting for their interaction, which is the object of the suspension balance model (SBM). We systematically investigate the dynamics and the steady state of shear-induced migration in a wide-gap Couette flow for a wide range of particle volume fraction, and we test the ability of the SBM to account for the observations. We use a model suspension for which macroscopic particle stresses are known. Surprisingly, the observed magnitude of migration is much lower than that predicted by the SBM when the particle stress in the SBM is equated to the macroscopic particle stress. Another noteworthy observation is the quasi-absence of migration for semidilute suspensions. From the steady-state volume fraction profiles, we derive the local particle normal stress responsible for shear-induced migration according to the SBM. However, the observed dynamics of migration is much faster than that predicted by the SBM when using this stress in the model. More generally, we show that it is not possible to build a local friction law consistent with both the magnitude and the dynamics of migration within the standard SBM framework. This suggests that there is a missing term in the usual macroscopic constitutive law for the particle normal stress driving migration. The SBM is indeed capable of accurately predicting both the magnitude and the dynamics of migration when a tentative phenomenological term involving a concentration gradient is added to the particle normal stresses determined in macroscopic experiments.

Atmospheric Bubbling Fluidized Bed Risers: Effect of Cone Angle on Fluid Dynamics and Heat Transfer

Abstract In this paper, a comparative study of fluid flow behavior and thermal characteristics of sand particles has been carried out numerically and experimentally in bubbling fluidized beds for five-cone angles of the riser wall having 0 deg, 5 deg, 10 deg, 15 deg, and 20 deg. An Eulerian model with a k–ε turbulence model is used to explore the numerical analysis, and the findings are compared to those of the experiments. For the study, the inlet air velocity is fixed at 1.5 m/s with sand particles filled up to 30 cm to maintain bubbling conditions in the risers. The results indicate that increasing the cone angle up to 10 deg while maintaining the amount of bed materials constant leads to a reduction in pressure drop. The expansion of particles along the riser is observed to decrease with the increase in the cone angle up to 10 deg. The radial solid volume fraction profile transforms to a U shape from the W-type profile as the cone angle increases up to 10 deg. Correspondingly, the solid velocity is found to have an inverted U-type and W-shaped profile for the risers. The granular temperature is also found to increase with a decrease in the solid percentage at any location. The average bed temperature, interphase, and bed-to-wall heat transfer coefficient at a location of 10 cm axial height also increase with the cone angle increase up to 10 deg. As a result, the conical riser, when designed with a greater cone angle up to 10 deg, exhibits more efficiency in terms of heat transfer characteristics. The 3D simulation results are in strong concurrence with the experimental results in all investigations.

Comparative Performance Assessment between Incompressible and Compressible Solvers to Simulate a Cavitating Wake

To study the effects of fluid compressibility on the dynamics of a cavitating vortex street flow in a regime where the vortex shedding frequency increases as a result of the cavitation increase, the cavitating wake behind a wedge was simulated employing both incompressible and compressible solvers. To do this, a compressible cavitation model was implemented, modifying the Zwart-Gerber-Belamri (ZGB) incompressible solver and including a pressure limit and absorbing boundary conditions to prevent a non-physical pressure field. To validate the performance of the compressible model, preliminary simulations were carried out on a 1D Sod cavitating tube and the cavitating vortex shedding behind a circular body at laminar flow conditions. The results of the cavitating wake behind the wedge with the incompressible and the compressible solvers showed similar predictions in terms of pressure, vortex shedding frequency, and instantaneous and average vapor volume fraction profiles. In spite of this, differences were obtained in the energy content of the fluid force fluctuations on the body at higher frequencies, which appear to be better resolved and amplified when the compressibility model is considered. Overall, both solvers provided comparable results in terms of cavitation phenomena that are well aligned with experimental observations.

Effect of different beam distances in laser soldering process: a numerical and experimental study

PurposeThis paper aims to investigate the effect of different beam distance by understanding laser beam influence on solder joint quality. The utilisation numerical-based simulations and experimental validation will help to minimise the formation of micro void in PTH that can lead to cracks and defects on passive devices.Design/methodology/approachThe research uses a combination approach of numerical-based simulation using Finite Volume Method (FVM) and experimental validation to explore the impact of different laser beam distances on solder joint quality in PTH assemblies. The study visualises solder flow and identifies the optimal beam distance for placing a soldering workpiece and a suitable tolerance distance for inserting the solder wire.FindingsThe simulation results show the formation of micro void that occurs in PTH region with low volume fraction and unbalance heat concentration profile observed. The experimental results indicate that the focus point of the laser beam at a 99.0 mm distance yields the smallest beam size. Simulation visualisation demonstrates that the laser beam’s converging area at +4.6 mm from the focus point which provides optimal tolerance distances for placing the solder wire. The high-power laser diode exhibits maximum tolerance distance at 103.6 mm from the focus point where suitable beam distance for positioning of the soldering workpiece with 50% laser power. The simulation results align with the IPC-A-610 standard, ensuring optimal filling height, fillet shape with a 90° contact angle and defect-free.Practical implicationsThis research provides implications for the industry by demonstrating the capability of the simulation approach to produce high-quality solder joints. The parameters, such as beam distance and power levels, offer practical guidelines for improving laser soldering processes in the manufacturing industry.Originality/valueThis study contributes to the field by combining high-power laser diode technology with numerical-based simulations to optimise the beam distance parameters for minimising micro void formation in the PTH region.

Sensitivity analysis of a dense discrete phase model for 3D simulations of a tapered fluidized bed

This study aims to conduct a sensitivity analysis of closure models and modeling parameters for the Dense Discrete Phase Modeling (DDPM) approach in order to investigate the hydrodynamics of a 3D lab-scale Tapered Fluidized Bed (TFB). The closure models and model parameters under investigation include the gas-solid drag force, viscous models, particle-particle interaction models, restitution coefficient, specularity coefficient, and rebound coefficient. The primary objective of this sensitivity analysis is to optimize the numerical model's performance. The numerical results, in terms of axial and lateral Solid Volume Fraction (SVF) profiles obtained from the sensitivity analysis, indicate that the drag force and restitution coefficient significantly influence the hydrodynamics of the TFB. Properly selecting these parameters could result in the improved performance of the numerical model. However, the sensitivity of turbulence models, particle-particle interaction models, specularity coefficient, and rebound coefficient has a lesser impact on the hydrodynamics results. This work concludes with the recommendation of a set of closure models and modeling parameters that offer the most accurate prediction of the hydrodynamics of the TFB.

IMPACT OF CHEMICAL REACTION ON MHD BOUNDARY LAYER FLOW OF NANOFLUIDS OVER A NONLINEAR STRETCHING SHEET WITH THERMAL RADIATION HAAR WAVELET COLLOCATION METHOD

In this paper, we investigate the effects of chemical reaction and thermal radiation on MHD boundary layer fluid flow of nanofluid moving over a nonlinearly stretching sheet through semi-numerical approach. The nanofluid physical model of the problem comprises with effects of thermophoresis, radiation and chemical reaction parameters. The mathematical model scrutinizes mass, momentum, heat transfer and concentration equations are reduced to couple nonlinear ordinary differential equations over infinite domain using proper similarity variables. Haar wavelet collocation method is used to solve the resulting equations. The obtained results are compared with available numerical findings and are comparable which confirms and verifies the wavelet method. The effects of various non-dimensional parameters on the rate of heat and mass transfer are depicted through tables and graphs. It predicts that, the local Sherwood number increases with increase in the parameters of Brownian motion and thermophoresis. For both temperature and volume fraction profiles decreases due to an increase in the Schmidt number.

Nonlinear convective transport of nanofluid over an inclined plate situated in a Darcy–Forchheimer porous medium with viscous dissipation and varying thermo-physical features

This article presents a theoretical analysis of the effects of varying thermo-physical properties, chemical reactions, and activation energy on the quadratic convective transport of nanofluids. The flow is created through an inclined plate in a Darcy–Forchheimer porous medium. The nanofluid model includes thermophoresis and Brownian motion to account for nanoparticle movement. The original flow equations are transformed using similarity transformations, and the resulting dimensionless equations are solved with a multi-domain spectral collocation approach. The effects of physical parameters on flow variables, heat and mass transfer coefficients are discussed. Comparisons between vertical and inclined plates reveal that inclination improves thermal performance but decreases velocity and engineering-related quantities. Fluctuating viscosity and nonlinear convection speed up fluid flow, whereas temperature rises with variable thermal conductivity and Biot number. Variable fluid properties, nonlinear convection, and convective heat conditions enhance heat transport coefficients. Activation energy boosts nanoparticle volume fraction profiles but decreases mass transport rates.

Numerical Study of Natural Convective Flow of a Nanofluid Over Rotating Truncated Cone with Convective Heating

In this paper, we consider the natural convection flow of a nanofluid simultaneously heat and mass transfer over a truncated rotating porous cone with convective boundary condition. Buongiorno’s model is used to describe the present nanofluid flow problem which is represented by Brownian motion and thermophoresis effects. Governing set of nonlinear boundary layer equations for the nanofluid over a rotating truncated cone is converted into a set of non-similar forms through non-similarity transformations. The obtained reduced nonlinear PDE system is linearized locally and solved via an accurate Chebyshev Spectral Collocation Method. The accuracy of the obtained numerical solutions is tested against existing results in the literature for specific cases and demonstrates good agreement. In addition, the impacts of active parameters such as the rotational parameter (0 ≤ χ ≤ 3), Biot number (0.1 ≤ Bi ≤ 1), and suction/injection parameter (−0.5 ≤ fw ≤ 0.5) on velocities, temperature, and nanoparticle volume fraction profiles along with heat and mass transfer rates are examined. It is found that the local surface drag and heat transfer rate increase, and the nanoparticle mass transfer rate decreases, with the increase in both the spinning parameter and Biot number.

Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation

Abstract In the current study, we delve into examining the movement of a nanofluid within a Williamson boundary layer, focusing on the analysis of heat and mass transfer (HMT) processes. This particular flow occurs over a sheet that undergoes nonlinear stretching. A significant facet of this investigation involves the incorporation of both the magnetic field and the influence of viscous dissipation within the model. The sheet is situated within a porous medium, and this medium conforms to the Darcy model. Since more precise outcomes are still required, the model assumes that both fluid conductivity and viscosity change with temperature. In this research, we encounter a system of extremely nonlinear ordinary differential equations that are treated through a numerical technique, specifically by employing the spectral collocation method. Graphical representations are used to illustrate how the relevant parameters impact the nanoparticle volume fraction, velocity, and temperature profiles. The study involves the computation and analysis of the effect of physical parameters on the local Sherwood number, skin friction coefficient, and local Nusselt number. Specific significant findings emerging from the present study highlight that the rate of mass transfer is particularly influenced by the thermophoresis factor, porous parameter, and Williamson parameter, showing heightened effects, while conversely, the Brownian motion parameter demonstrates an opposing pattern. The results were computed and subjected to a comparison with earlier research, indicating a notable degree of conformity and accord.

On the Flow of a Cement Suspension: The Effects of Nano-Silica and Fly Ash Particles.

Additives such as nano-silica and fly ash are widely used in cement and concrete materials to improve the rheology of fresh cement and concrete and the performance of hardened materials and increase the sustainability of the cement and concrete industry by reducing the usage of Portland cement. Therefore, it is important to study the effect of these additives on the rheological behavior of fresh cement. In this paper, we study the pulsating Poiseuille flow of fresh cement in a horizontal pipe by considering two different additives and when they are combined (nano-silica, fly ash, combined nano-silica, and fly ash). To model the fresh cement suspension, we used a modified form of the power-law model to demonstrate the dependency of the cement viscosity on the shear rate and volume fraction of cement and the additive particles. The convection-diffusion equation was used to solve for the volume fraction. After solving the equations in the dimensionless forms, we conducted a parametric study to analyze the effects of nano-silica, fly ash, and combined nano-silica and fly ash additives on the velocity and volume fraction profiles of the cement suspension. According to the parametric study presented here, larger nano-silica content results in lower centerline velocity of the cement suspension and larger non-uniformity of the volume fraction. Compared to nano-silica, fly ash exhibits an opposite effect on the velocity. Larger fly ash content results in higher centerline velocity, while the effect of the fly ash on the volume fraction is not obvious. For cement suspension containing combined nano-silica and fly ash additives, nano-silica plays a dominant role in the flow behavior of the suspension. The findings of the study can help the design and operation of the pulsating flow of fresh cement mortars and concrete in the 3D printing industry.

Three-dimensional numerical investigation of a suspension flow in an eccentric Couette flow geometry

This paper investigates the influence of eccentricity on flow characteristics and particle migration in Couette geometries. The study involves numerical simulations using the recent frame-invariant model developed by Badia et al. [J. Non-Newtonian Fluid Mech. 309, 104904 (2022)]. The study begins with a two-dimensional analysis, focusing first on the Newtonian fluid in order to thoroughly characterize the specific properties of this flow configuration. Next, the impact of eccentricity on particle migration in an isodense suspension is examined by numerical simulations based on the experiments conducted by Subia et al. [J. Fluid Mech. 373, 193–219 (1998)]. Furthermore, the study is extended to include a full three-dimensional analysis of a dense suspension flow in an eccentric Couette geometry based on resuspension experiments conducted by Saint-Michel et al. [Phys. Fluids 31, 103301 (2019)] and D'Ambrosio et al.[J. Fluid Mech. 911, A22 (2021)]. The main objective of the latter study is to investigate the influence of eccentricity on the resuspension height and on the calculation of the particle normal stress in the vertical direction through the volume fraction profile analysis. Our results show that even minimal eccentricity can lead to significant changes compared to the centered case.

Experimental and kinetic modeling of soot formation in counterflow non-premixed flames of surrogate fuel components: n-dodecane and iso-dodecane

Normal dodecane (n-C12) and iso-dodecane (i-C12) are often used as components for surrogate mixtures of aviation and diesel fuels. Although studies have been performed to understand the combustion and spray behavior of dodecane isomers, the soot formation from the combustion of n- and i-C12 in non-premixed flames is not well studied. In this work, soot volume fraction (SVF) profiles of n- and i-C12 were measured across a wide range of strain rates and mixture conditions in a counterflow burner facility at the University of Connecticut. Neat and binary mixtures of n- and i-C12 were investigated to study the influence of alkane branching on soot formation. A soot model was developed and validated in this study by extending the detailed kinetic model developed at the Lawrence Livermore National Laboratory (LLNL) for the formation of polycyclic aromatic hydrocarbons (PAHs) to simulate soot formation and growth based on the discrete sectional method. Additional gas phase reactions forming pyrene and ring enlargement reactions were added to the existing PAH model. The LLNL kinetic model was validated with SVF data obtained in this work for n-C12 and i-C12 flames along with data available in literature for ethylene, iso-butene, n-heptane, and iso-octane. The soot precursor reactions added in this work were found to play a critical role in simulating the experimentally observed non-linear trend of the peak SVF with increased branched alkanes. Reaction path analysis was conducted to illustrate the fuel structure effects on soot formation pathways in n- and i-C12 mixtures. In view of the satisfactory agreement between modeling results and experimental data, as well as capturing the non-linear variation in peak SVF with the alkane branching for the first time, further investigation within the framework of the soot model is discussed and critical insights are provided into the reaction pathways which require further attention.

A COMPUTATIONAL STUDY FOR AIR-€“SOLID PARTICLES FLOW PATTERNS IN RIB-ROUGHENED FLUIDIZED BED VESSELS

This paper includes analysis of the flow of air and solid particles in fluidized bed units using a computational fluid dynamics (CFD) technique. The CFD simulations are carried out with three geometries, one plane vessel and the other two with ribs of square and triangle shape. The results are obtained in terms of velocity, volume fraction distribution, and bed expansion. The effect of other parameters, such as coefficient of restitution, initial bed height, and particle diameter, is also examined. When the particle diameter is large, airflow in an upward direction increases the solid bed height but the flow is almost steady. In the case of small-sized particles, the velocity field and volume fraction profiles for both phases vary with time. In certain regions within the bed, the air becomes concentrated and takes the form of a bubble. The results also show that in fluidized bed units, the unsteady behavior is usually enhanced when ribs are used. The comparison in terms of root mean square values indicates that velocity variation is ~50% more when triangular ribs are used The overall results show that placement of triangle-shaped ribs can be favorable for enhancing momentum and related processes/phenomena in the fluidized bed devices.

Investigation of the Influence of Inner Geometries of the Receiver Tube of a Parabolic Trough Collector System Used for Water Heating

Solar collectors are devices that help to harvest solar thermal radiation and convert into other forms of energy. Because of its low fabrication cost and simple design, the Parabolic Trough Collector (PTC) is one of the finest alternatives for medium-temperature (i.e., in 80°𝐶𝐶-250°𝐶𝐶 range) needs among all types of concentrated solar collectors. The absorber tube or the receiver tube is one of the main critical components of a PTC. Thermal radiation of the sun falling onto a parabolic reflector is reflected to its focal line where the receiver tube is placed. Therefore, the performance of a PTC system significantly depends on Receiver Geometries (RGs). A locally developed PTC system with a new and accurate tracking system was designed and fabricated in the current study and steam generation inside the receiver was considered in the performance analysis. The experimental analysis was performed using seven different RGs. The experiments were carried out by measuring generated steam every 10 minutes for all the RGs, and simultaneously, solar insolation data was taken by a domestic solar Photovoltaic (PV) system with a capacity of 5 kW. The steam generation data was taken only when the power output of the reference solar PV system was ≥ 4kW. Having tested seven different RGs, the researchers were able to improve the steam generation to a maximum of 10.0% compared to the reference geometry using direct experimental data. This was 8.1% in accordance with the statistical approach via multiple linear regression model. A three-dimensional mathematical model for two-phase flow was formulated for a closed domain. Restricting this model into twodimensional geometry, the steam generation process was simulated as a TPF problem using ANSYS Fluent software. The volume fraction profiles clearly show the phase transition, which leads to evaporation and condensation inside the tube.

Influence of Architecture on the Interfacial Properties of Polymers: Linear Chains, Stars, and Microgels.

Surface-active polymers have important applications as effective and responsive emulsifiers, foaming agents, and coatings. In this contribution, we explore the impact of the polymer architecture on the behavior at oil-water interfaces by comparing different poly(N-isopropylacrylamide) (pNIPAM)-based systems, namely, monolayers of linear and star-shaped macromolecules, ultralow cross-linked, regular cross-linked, and hollow microgels. Compression isotherms were determined experimentally as well as by computer simulations. The latter provides information about the conformational changes of the individual macromolecules as well as the interfacial properties of the monolayer, including the surface structure and the density distribution of an ensemble of interacting macromolecules near an interface. Surprisingly, the isotherms of the linear polymer, of the star polymer, and of the ultralow cross-linked microgel have an identical shape that differs from the isotherms of regular and hollow microgels. We introduced the mass fraction of adsorbed polymer, which gives a measure of the polymer segments contributing to the isotherm in relation to the most flexible architecture, i.e., the linear polymer, and allows a comparison of polymers with different architectures. The data demonstrate that increasing the number of cross-links leads to a significantly lower amount of polymer in the proximity of the interface as the increase in cross-linker reduces the deformability or softness of the polymers at the interface. The volume fraction profiles along the normal to the interface are essentially different in the microgel monolayers as compared to those in the linear and star polymer. The profiles through the microgel contact line and their growth upon initial compression are similar to those of the linear chains. Herewith, the profiles through the center of mass practically do not change upon compression. Therefore, the initial growth in the microgel surface pressure reveals the polymer-like behavior and is related to the deformation of the peripheral part of the microgel. Further compression of the microgel monolayer leads to 3D interactions of the microgels within the aqueous side of the interface and soft colloid-like behavior.

Euler-Euler LES of bubble column bubbly flows by considering sub-grid scale turbulent dispersion effect on modulating bubble transport

It has now been recognised and generally accepted that turbulent dispersion may be modelled using the time average of the fluctuating part of the interphase momentum, employing the drag the Favre averaged drag model for turbulent dispersion in Eulerian multi-phase flows. As the turbulent eddies in the surrounding of bubbles interact strongly with the bubbles in bubbly flow, the bubble trajectories and bubble oscillation take place accordingly as the consequence of continuous deformation of the bubble surfaces. When using large eddy simulation for modelling bubbly flow, the sub-grid scale (SGS) filtered velocity fluctuations of liquid phase can be interpreted as many small eddies that may act on the surface of bubbles, consequently giving rise to bubble shape variations and the dispersion of bubbles. This study employs Euler/Euler large-eddy simulation (LES) modelling to demonstrate that the turbulent dispersion force model can be used to effectively indicate the influence of turbulent eddies on bubble dynamics, in particular the bubble cluster oscillations, which leads to remarkable improvements in the prediction of bubble lateral dispersion behaviour. The use of spatial filtering to model the SGS bubble dispersion is proposed with a modification on SGS eddy viscosity to reflect turbulent dispersion due to bubble induced turbulence. The results of the time-averaged LES modelled bubble velocities and bubble volume fraction profiles are in good agreement with the experimental data while the turbulent kinetic energy spectrum obtained at different locations on the centreline of the bubble column still exhibits the conventional −5/3 scaling for shear induced turbulence and a −3 scaling for bubble induced turbulence.

Analytical analyzing mixed convection flow of nanofluid in a vertical channel using python approach

This study uses analytical methods to investigate the impact of parameters on the mixed convection flow of nanofluid in a vertical channel. The research aims to explore the heat transfer characteristics of nanofluids for more efficient heat transfer in devices. The study analyzes the influence of the Reynolds, Grashof, and Prandtl numbers on nanofluid flows. It also examines the effects of temperature and nanoparticle concentration distributions on parameters such as Brownian motion (Nb), thermophoresis (Nt), and Lewis number (Le). The presence of nanoparticles significantly enhances the heat transfer characteristics in the flow problem. Reynolds number, Grashof number, and Prandtl number significantly impact flow behavior. Velocity, temperature, and nanoparticle volume fraction profile trends are thoroughly investigated and found to vary. Akbari-Ganji's method (AGM) and the homotopy perturbation method (HPM) demonstrate the potential of computational tools in analyzing nanotechnology fluid dynamics. The accuracy and reliability of the proposed analytical techniques are confirmed through comparisons with a numerical method. The novelty of this research lies in its comprehensive analysis of parameter effects on the mixed convection flow of nanofluid, the enhanced heat transfer characteristics in the presence of nanoparticles, and the unique contributions offered by the utilization of Python programming in this field. The outcomes of this study provide insights for designing and optimizing heat transfer systems using nanofluids, contributing to advancements in nanotechnology.