Buoyancy Ratio Research Articles

Behavior of weak axisymmetric fountain in homogeneous fluid with coexistent temperature and concentration effects

The behavior of weak axisymmetric fountains in homogeneous fluid with coexistent temperature and concentration effects is studied numerically over 0.25 ≤ FrT ≤ 2.0, − 0.75 ≤ N ≤ 5.0, and 20 ≤ Re ≤ 300, where FrT is the Froude number defined with temperature only, N is the buoyancy ratio representing the relative contribution of concentration to density compared to that of temperature, and Re is the Reynolds number. For each FrT, the maximum fountain height, fountain upflow width, and whole fountain width reduce with increasing N, as the combined negative buoyancy from temperature and concentration becomes stronger, while as FrT becomes larger, they increase due to the reduced overall negative buoyancy. Re has strong effects on these parameters, with a larger Re value leading to increased values of these parameters. If the overall Froude number, Fr, which is defined with combined temperature and concentration, is used instead of FrT, the existing scaling relations for the maximum fountain height for weak axisymmetric fountains with density coming from temperature only, are also applicable for the weak axisymmetric fountains with density coming from both temperature and concentration, when Fr ≲ 2.0. The quantified correlations for the characteristic parameters under the combined effects of Re and Fr have also been obtained with the numerical results.

Double-diffusive convection of two rods in a novel cavity saturated by porous media and suspended by nano-encapsulated phase change materials

The double-diffusive convection of two rotating rods inside an infinite-shaped saturated porous cavity filled by a suspension of nano-encapsulated phase change material was investigated numerically using the (ISPH) method. The cavity includes two rotating rods, (NEPCM) particles, and porous media. The inner left and right rods are located inside the left and right sides of an infinite-shaped cavity. In the present work, two types of boundary conditions between the inner rods and outer boundary walls of the cavity are considered. The results were produced for the dimensionless fusion temperature (0.05 ≤ ≤ 0.95), the length of the inner rotating rods (0.2 ≤ LR ≤ 0.6), the buoyancy ratio number (−2 ≤ N ≤ 2), the solid volume fraction (0.01 ≤ ϕ ≤ 0.05), the dimensionless time (0 ≤ ≤ 0.3) and Darcy number (10−2 ≤ Da ≤ 10−5). But, the Lewis and Stefan numbers were considered fixed at (Le = 10) and (Ste = 0.2), respectively. The effects of several parameters on the melting-solidification zones, temperature, concentration, and velocity fields were also investigated. It was found that the location and the strength of the melting-solidification zone are influenced significantly by the variation of the boundary conditions. The average Nusselt and Sherwood numbers are influenced clearly by the variation of the boundary conditions for rods and cavity walls and by increasing the length of the inner rods.

Investigation of transport mechanism in transient mixed convective flow of magnetize Maxwell nanofluid subject to nonuniform source/sink

Nowadays, the heat transfer potential of the base fluids can also be improved by adding nanoparticles to them. These nanotechnology-based fluids, called nanofluid, have superior properties such as high thermal conductivity, large critical heat flux (CHF) and improved heat transfer coefficient. The purpose of this paper is to study the thermal effectiveness of nanoparticles in transient flow of Maxwell fluid together the properties of mixed convection and magnetic field. Thermal field is controlled with the novel aspects of variable conductivity and nonuniform heat sink/source. Additionally, the impact of Brownian and thermophoretic diffusions is considered caused by nanoparticles dispersion in the fluid. The appropriate conversions yield the governing nonlinear ordinary differential system. Homotopic approach has been utilized to attain the solution of differential system and results are envisioned graphically. This study explores that the buoyancy ratio and mixed convection parameters enhance the velocity field. Further, the heat transfer rate rises significantly as the thermophoretic and Brownian diffusion parameters increase. Moreover, the effect of nonuniform heat source/sink on temperature field is noticed to be an increasing trend of temperature profile.

Dynamics of Triple Diffusive Free Convective MHD Fluid Flow: Lie Group Transformation

This analysis is interested in the dynamic flow of incompressible triple diffusive fluid flowing through a linear stretched surface. The current study simulates when Boussinesq approximation and MHD are significant. As for originality, a comparative study of all the results for opposing and assisting flow cases is provided. Lie-group transformation is utilized to determine symmetry depletions of partial differential equations. The transformed system of ordinary differential equations is solved using the Runge-Kutta shooting technique. The impacts of magnetic parameter, buoyancy ratio parameter of temperature and concentration, and Lewis number on velocity, temperature, and concentration are depicted through graphs. We observed that the magnetic field parameter decelerates in velocity distribution for both fluid flow cases. Additionally, the same phenomenon was noticed with the buoyancy ratio parameters on both salt concentration distributions. Finally, the influence of heat and mass transfer rates decreases for both fluid flow cases with an increase in Lewis number.

Soret and Dufour effects on unsteady MHD second-grade nanofluid flow across an exponentially stretching surface

The unsteady energy and mass transport of magnetohydrodynamics (MHD) second grade nanofluid via an exponentially extending surface with Dufour and Soret effects are investigated in this study. Variable thermal conductivity and mixed convection effects are used to investigate the heat transfer mechanism. There are also new characteristics such as slip flow, viscous dissipation, Brownian motion, nonlinear thermal radiation, and thermophoresis. In the problem formulation, the boundary-layer approximation is used. Using the suitable transformations, the energy, momentum, and concentration equations are generated into non-linear ordinary differential equations (ODEs). The solution to the resultant problems was calculated via the Homotopy analysis method (HAM). The effects of environmental parameters on velocity, temperature, and concentration profiles are graphically depicted. When comparing the current results to the previous literature, there was also a satisfactory level of agreement. In comparison to a flow based on constant characteristics, the flow with variable thermal conductivity is shown to be significantly different and realistic. The temperature of the fluid grew in direct proportion to the thermophoresis motion, buoyancy ratio, and Brownian motion parameters. According to the findings, the slippery porous surface may be employed efficiently in chemical and mechanical sectors that deal with a variety of very viscous flows.

Numerical modeling of magnetohydrodynamic thermosolutal free convection of power law fluids in a staggered porous enclosure

In this study, the influence of a magnetic field on thermosolutal free convective flow inside a staggered porous enclosure, filled with non-Newtonian power-law fluids is investigated using the Galerkin finite element method. The computational model has been validated against available data from the literature. Results indicate that the augmentation of Hartmann number (Ha) causes heat and mass transport to decrease significantly. However, the magnetic field has a greater influence on mass transfer in comparison with heat transfer. The maximum local Nu and Sh numbers are decreased respectively by 55% and 43% at Ha = 75. This reduction becomes more significant for Hartmann number values higher than 25. However, the increase of Darcy number reduces the influence of the magnetic field. In the presence or absence of magnetic field, the alteration of power law index provides different trends for the prediction of the convective flow intensity. The increase in Lewis (Le) number has a smaller effect on the heat transfer rate compared to the mass transfer rate. Increase in Le augments mass transfer rate by 230% but decreases heat transfer rate by 37%. Further, the augmentation of the buoyancy ratio causes a significant increase in the heat and mass transfer rates.

Numerical Investigation of the Double Diffusive Convection in 3D Trapezoidal Solar Still Equipped with Conductive Fins

In this paper a numerical investigation on the double diffusive natural convection in a finned solar still is performed using the finite volume method. The 3D vector potential-vorticity formalism is used to eliminate the gradient pressure terms and due to the complex shape of the cavity the blocked-off-region method is adopted. After getting the dimensionless governing equations, they are written in a generalised form then discretised. The effects of the buoyancy ratio, conductivity ratio and Rayleigh number of the flow structure, temperature field and heat and mass transfer are studied. The results show that the increase of conductivity ratio and Rayleigh number leads to an enhancement of the heat and mass transfer.

Analytic Simulation for Magnetohydrodynamic Unsteady Buongiorno Model Hybrid Nanofluid Flow over Stretching

In this work, we inspect and analyze a two dimensional, unsteady mixed convectional hybrid nanofluid hydromagnetic flow (Al2O3-Cu/H2O) over a convectional heated an extending/contracting surface with the influence of thermal radiation. Hybrid nanofluid (Al2O3-Cu/H2O) flows with magnetohydrodynamic and heat source or sink. Brownian motion and thermophoresis were incorporated using the Buongiorno model. Hybrid nanofluid with vol. fraction range limited to 1.5% and within the higher temperature range of 50°C to 70°C is considered for thermal conductivity and viscosity analysis. The proposed model is then converted into ODEs through similarity transformation with the help of homotopy analysis. The effect of embedded input factors on the temperature, velocity, and concentration profiles is visually demonstrated and explained. The magnetic field has inverse impact on velocity and temperature profiles. Velocity profile increases for both mixed convection and buoyancy ratio parameters. It has been noticed that the temperature profile increases with thermal radiation. For increasing values of Lewis number, the concentration of hybrid nanoparticles is considerably lowered. Moreover, we observed an increase in the concentration of hybrid nanoparticles through a destructive chemical reaction, whereas a generative chemical reaction has the reverse effect. It has been proved that skin friction is increasing function of ε , M and decreasing function of λ 1 , N r . On the other hand, Nusselt number increased with the increase of R , Q , N b , N t while Sherwood number is decreased, with the increase of N b , N t , L e .

Rayleigh-Bénard double-diffusive mixed convection in two-dimensional rectangular cavities filled with non-Newtonian fluids

The present work investigates numerically and analytically Rayleigh-Bénard double-diffusive mixed convection inside horizontal rectangular cavities filled with non-Newtonian fluids and subjected to uniform heat and mass fluxes along the sliding horizontal walls, while the vertical ones are considered insulated and impermeable. The problem is found to be governed by: Peclet number Pe, thermal Rayleigh number RaT, Lewis number Le, buoyancy ratio N, and power-law behavior index n. Both solutions show a good agreement for inclusive ranges of governing parameters; thus, validating the analytical approach and the numerical code. To gain further insight into convection phenomena, the dominance regions of convective regimes, namely natural, mixed, and forced convection are defined, where ratios RaT/Pe1.57, RaT/Pe1.92, and RaT/Pe2.27 accurately delineate the three regimes for n = 0.6, n = 1.0, and n = 1.4, respectively. As a result, the effects of governing parameters are amply discussed in each governing regime. Increasing Peclet number enhances flow intensity while heat and mass transfer rates increase only until reaching a higher plateau. For thermal Rayleigh number, increasing it intensifies fluid circulation while heat and mass transfer increase only for a given range of Pe values, where after a critical value Pecr the opposite happens as shear and buoyancy forces compete driving the transfer rates down. Such results are due to Pe strengthening forced convection contribution in the overall convection and RaT enhancing natural convection. As for Lewis number, a given range correlated with n strongly enhances natural regime contribution, which increases flow intensity while the outcome on heat transfer depends on the associated shear force magnitude. Further, increasing Le enhances mass transfer until reaching a higher plateau due to boosted forced convection contribution. In contrast, buoyancy ratio is found to strengthen natural convection leading to similar outcomes as for RaT. Finally, the rheological behavior of non-Newtonian fluids leads to some unforeseen effects on flow characteristics directly related to the dominant convective regime. The critical Peclet number Pecr signaling the change in n effect and leading to buoyancy forces reducing transfer rates instead of enhancing them is presented as a function of the remaining governing parameters RaT, Le, N, and n.

Impact of wind speed on urban heat and pollution islands

Large urban areas are typically subjected to excessive levels of heat and pollution. The formation of an urban-scale plume would arise from releasing heat in a stable atmosphere. The presence of wind may disrupt the pattern of the plume. This study explores the effect of wind intensity and ambient stability on the plume structure and pollution dispersion numerically. A metropolitan has been selected as the urban, and the average heat and pollution release rate is calculated based on a typical megacity. It has been found that for buoyancy ratios (the ratio between the horizontal velocity of the urban plume to wind speed) smaller than 0.5, the wind is the governing mechanism. For buoyancy ratio higher than 2, the urban heat island is governing mechanism. In stable conditions and the ratios smaller than 0.5, the urban average temperature difference reduces by about 0.125 K for a unit increase in wind speed. When the ratios are less than 0.2, there are 0.5 K temperature differences between urban and rural, and 0.072 μg/m3 averaged pollution for all stability conditions. It is also found that for ratios higher than 0.5, any increase in wind velocity does not reduce the pollution concentration significantly. For values smaller than 0.5, any increase in wind speed would result in a considerable drop in pollution concentration if the radiative effect of pollutants is ignored.

Keller box simulation of magnetic pseudoplastic nano-polymer coating flow over a circular cylinder with entropy optimisation

In this study, a Keller box calculation of magnetic nanopolymer coating flow over a circular cylinder in the presence of nonlinear convection is performed. A two-phase nanofluid model (Buongiorno model) is used to model the equations for nanofluid flow and heat and mass transfer. The problem at hand is first formulated in the dimensional form of nonlinear partial differential equations (PDEs) and then transformed into the dimensionless PDEs form by manipulating non-similar variables. The Keller box approach (implicit finite differences) is used for the calculations of the transformed PDEs. The characteristics of critical thermophysical physical parameters on the flow field, viz thermal convection, Brownian motion, Weissenberg number, thermophoresis, magnetic field, heat source/sink, Biot number, buoyancy ration parameter, Eckert number, and mixed convection, are graphically manifested. In addition, the flow control parameters estimate the sheath friction, heat transfer rate, and mass transfer rate in the flow coordinate. A significant increase in the velocity of the Williamson nanofluid is accompanied by an increase in the Biot number, magnetic field, and mixed convection. The isotherms show a higher fluid temperature near the wall in the absence of convection. The Weissenberg number, Biot number, and thermophoresis significantly increase the temperature of the Williamson nanofluid. The density of the streamlines is lowered with a larger buoyancy ratio parameter. The total entropy generation of the Williamson nanofluid is improved by increasing the Brinkman number and the Weissenberg number.

Thermodynamic analysis for bioconvection peristaltic transport of nanofluid with gyrotactic motile microorganisms and Arrhenius activation energy

Improving high-efficiency thermal systems to increase heat transmission has become quite prevalent nowadays. Various works were conducted to gain insight into the implementation of heat transfer for their practical use in increasing heat transfer. Therefore, the present study focuses on analyzing heat exchange and irreversibility rate (entropy generation) for bioconvection peristaltic transport of nanofluid with mass transfer. Investigation takes place inside an asymmetrical channel with flow subject to the action of gyrotactic motile microorganisms and Arrhenius activation energy. The considered flow situation is sculpted via Brownian diffusion, variable viscosity, nonuniform heat generation/absorption, viscous dissipation, porous medium, mixed convection, and thermophoresis diffusion assumptions. Lubrication approximations have been used in this modelling. Numerical computations of the governing equations along with related conditions are conducted using NDSolve in Mathematica. Quantities of physical interest such as temperature distribution, entropy production, concentration, density of motile microorganism and velocity profiles are computed and depicted through tables and graphs to demonstrate the effects of the related parameters. The results revealed that temperature distribution suppresses for higher activation parameters. Heat transfer rate at wall decreases for higher viscosity parameter. To minimize the generation of entropy in the system, we need to increase the porosity parameter. It is also found that the density of motile microorganism decreases for higher bioconvection Peclet number. Moreover, fluid motion strongly advanced by enhancing the Bioconvection Rayleigh number and buoyancy ratio parameter. Water-based nanofluid provides better heat and irreversibility properties as compared to methanol based nanofluid.

Evaluation of Magnetohydrodynamics of Natural Convective Heat Flow over Circular Cylinder Saturated by Nanofluid with Thermal Radiation and Heat Generation Effects

The current study focuses on the natural-convection flow of nanofluids with boundary layer over a circular cylinder of uniform thermal wall with varying magnetic force from 0 to 1.5, radiative effects from 0 to 1, heat generation effects from 0 to 1, and Joule heating effects from 0 to 1. The problem is represented in the form of partial differential equations. The dimensional form of the equations is converted into a dimensionless form with the help of suitable stream functions. Then, the resultant equations are further reduced into the system of first-ordered differential equations, and the Keller box scheme is applied to obtain a solution numerically with the help of MATLAB code. The numerical solutions for Nusselt number, skin friction coefficient, Sherwood number, velocity profile, temperature profile, and concentration profile are represented with the help of graphs. The most interesting fact of the analysis is the flow of the fluid; the heat-mass and energy transfer rates could be managed in a controlled way through slight variations in the Brownian motion parameter from 0.1 to 0.7, in the Lewis number from 1 to 40, in the Eckert number from 0.1 to 0.4, in the thermophoresis parameter from 0.1 to 0.7, in the Prandtl number from 0.1 to 0.7, and in the buoyancy ratio from 0.1 to 0.7, as it is here analyzed and discussed.

Magneto-convective flow through a porous enclosure with Hall current and thermal radiation effects: numerical study

This paper reports the numerical study of magnetohydrodynamic radiative-convective flow in a square cavity containing a porous medium with Hall currents. This study is relent to hydromagnetic fuel cell design and thermofluidic dynamics of complex magnetic liquid fabrication in enclosures. The governing equations of this fluid system are solved by a finite-difference vorticity stream function approach executed in MATLAB software. A detailed parametric investigation of the impact of Rayleigh number (thermal buoyancy parameter), Hartman number (magnetic body force parameter), Darcy number (permeability parameter), Hall parameter and radiation parameter on the streamline, temperature contours, local Nusselt number along the hot wall and mid-section velocity profiles is computed. Validation with previous special cases in the literature is included. Hall current and radiative effects are found to significantly modify thermofluidic characteristics. From the numerical results, it is found that the magnetic field suppresses the natural convection only for small buoyancy ratios. But, for larger buoyancy ratio, the magnetic field is effective in suppressing the thermal convective flow.

Natural convection process endorsed in coaxial duct with Soret/Dufour effect

PurposeThe purpose of this paper is to analyse the buoyancy flow, mass and heat transfer in coaxial duct under Soret and Dufour effect. The combined effects of the thermal-diffusion and diffusion-thermo coefficients, as well as the Schmidt number, on natural convection in a heated lower coaxial curve were explored using the proposed physical model. The Dufour and Soret effects are taken into consideration in the energy and concentration equations, respectively.Design/methodology/approachThe dominating mathematical models are converted into a set of non-linear coupled partial differential equations, which are solved using a numerical approach. The controlling non-linear boundary value problem is numerically solved using the penalty finite element method with Galerkin’s weighted residual scheme over the entire variety of essential parameters.FindingsIt was observed that different parameters were tested such as heat generation or absorption coefficient, buoyancy ratio, Soret coefficient, Dufour coefficient, Lewis number and Rayleigh number. Effect of Rayleigh number, absorption/generation and Dufour coefficient on isotherm are significantly reported. For greater values of Lewis number, maximum mass transfer in duct in the form of molecular particles is produced. Buoyancy ratio parameter decreases the average rate of heat flow and increases its mass transfer.Originality/valueThe main originality of this work is to make an application of Soret and Dufour effects in a coaxial duct in the presence of source sink.

Soret and Dufour effects on thresholds of stability in a horizontal Brinkman porous layer submitted to vertical temperature and species gradients using linear and non-linear analysis

The present study deals with Soret and Dufour effects on the onset of double-diffusive natural convection in a horizontal Brinkman porous layer with a free-stress upper boundary. The thresholds of stationary, oscillatory, and subcritical bifurcations are derived on the basis of linear and non-linear analysis, as functions of the governing parameters. The effect of Dufour ([Formula: see text]) and Soret [Formula: see text] parameters on the thresholds of instabilities is illustrated and discussed. There are critical combinations [Formula: see text] for which the thresholds of supercritical bifurcations are independent of the buoyancy ratio. Particularly, for [Formula: see text] and [Formula: see text], the stationary convection starts at the threshold of the pure thermal convection whatever the value of the buoyancy ratio.

Darcy resistance flow of Sutterby nanofluid with microorganisms with applications of nano-biofuel cells

The objective of current research is to endorse the thermal aspect of Sutterby nanofluid containing the microorganisms due the stretched cylinder. The features of nonlinear thermal radiation, Darcy resistance and activation energy are also incorporated to inspect the thermal prospective. The problem is further extended with implementation of modified Fourier and Fick’s theories. The results are presented for the stretched cylinder and also for stationary plate. The numerical formulation for the problem is presented by following the shooting technique. The comparative numerical is performed to verify the computed simulations. The results convey that the presence of Darcy resistance parameter enhanced the velocity more effectively for stretched cylinder. A reduction in velocity due to Sutterby fluid parameter and buoyancy ratio parameter has been observed. Moreover, the temperature profile enhanced with larger sponginess parameter more effectively for stretching cylinder.

Scrutinization of unsteady non-Newtonian fluid flow considering buoyancy effect and thermal radiation: Tangent hyperbolic model

The contemporary study is performed to evaluate the stagnation point flow and thermal features of tangent hyperbolic fluid over a vertical surface by implementing suitable rheological model. The considered fluid is presumed to be incompressible, viscous and non-Newtonian in nature. The physical situation is modeled by employing tangent hyperbolic fluid flow model. In addition to this the role of Soret and Dufour properties on non-Newtonian fluids are explored in this research work. The solutions are obtained via numerical computation. The influence of natural convection on non-Newtonian fluid flow is illustrated. Impact of different flow controlling constraints on flow and thermal distribution are scrutinized. The friction factor and heat transfer at the surface are analyzed for distinct parameters of physical interest. Outcomes for the Nusselt number and friction coefficient are offered using graphical illustration. This examination reveals the impact of buoyant force on non-Newtonian fluid flow. It is established that coefficient of skin friction enhances with buoyancy ratio parameter in assisting region and declines in opposing region. It is professed that the Nusselt number intensified with Dufour effect.

Fluid flow over a vertical stretching surface within a porous medium filled by a nanofluid containing gyrotactic microorganisms

In this paper, the boundary layer flow of a nanofluid containing gyrotactic microorganisms over a vertical stretching surface embedded in a porous medium. The fluid contains gyrotactic microorganisms. Nonlinear velocity stretches the surface, and the surface is isothermal. The governing boundary layer equations for steady, laminar, and two-dimensional are transformed into ordinary differential equations using a suitable similarity transformation. The fourth/fifth-order Runge–Kutta method solved the system of equations after linearization. The shooting method guesses the missing boundary conditions. Pertinent results are presented graphically and discussed quantitatively with respect to variation in the controlling parameters such as bioconvection Lewis number (Lb), Lewis number (Le), Peclet Lewis number (Pe), buoyancy ratio parameter (Nr), bioconvection Rayleigh number(Rb), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Richardson number (Ri), motile parameter (sigma), porosity parameter (user2{ }lambda), and Prandtl number (Pr) on dimensionless velocity, temperature, nanoparticle concentration, and microorganisms conservation. It is observed that increasing the porosity parameter retards the thermal boundary layer thickness which from application point of view, it is obvious that the surface cooling effect is enhanced and thus nanofluids are appropriate as heat transfer fluids. The comparison with the previous validates the applied numerical scheme.

Soret-Driven Convection of Non-Newtonian Binary Fluids in a Shallow Cavity Uniformly Heated from Below: Case of Opposing Flows

The project under study investigates Soret-generated convection in a horizontal rectangular cavity filled with a non-Newtonian binary fluid. The cavity's two horizontal walls are exposed to uniform fluxes of heat, whereas the two vertical walls are adiabatic and impermeable. The study focuses on the effects of different key parameters, including the cavity aspect ratio (A), the Lewis number (Le), the buoyancy ratio (N), the power-law behavior index (n), the generalized Prandtl (Pr) and thermal Rayleigh (RaT) numbers. The mathematical model, describing the Soret-generated convection phenomenon, is presented by non-linear differential equations, which are solved numerically on the basis of finite volume method. An analytical solution of the problem is proposed derived from the parallel flow approximation in the core of the cavity. The degree of agreement of the numerical finding and analytical predictions is seen to be good. Representative results for the central stream function, Nusselt and Sherwood numbers as well as streamlines, isotherms and iso-concentrations are depicted as functions of the main parameters mentioned above. For opposing flows, the initiation and development of convective motion are explored. The fluid flow's behavior was discovered to be highly influenced by the values of n and N. The beginning of motion is predicted to be governed by supercritical and subcritical Rayleigh numbers.