Thermal Buoyancy Forces Research Articles

Competition of localized thermal buoyancy and Lorentz forces in an electrolyte enclosed in a cavity

We study the flow of an electrolyte inside a slender square cavity produced by two competing localized forces, the thermal buoyancy force produced by the heating of a central part of the horizontal bottom wall and a vertical downward Lorentz force. This force is produced by a constant horizontal electric current between the slender vertical walls and a couple of circular magnets with opposing polarization placed on the center of both square vertical walls. The flow inside the cavity is considered two dimensional and simulated using the lattice Boltzmann equation method. We find the map of the flow patterns and their transitions for a Grashof number Gr in the range 0≤Gr≤4×103 and a Chandrasekhar number Ch in 0≤Ch≤1×107. For Gr≤2×103, the plane Gr-Ch can be divided in three regions with sharp changes in the flow patterns and the average Nusselt number on the top wall and the average asymmetry. One region is dominated by the buoyancy force, another by the Lorentz force, and there is an intermediate one, where neither of these forces dominates. For larger Gr, there are no sharp transitions.

Double diffusive mixed convection in a Cu-Al2O3/water nanofluid filled backward facing step channel with inclined magnetic field and part heating load conditions

The impact of inclined magnetic field on thermo-fluidic behaviour in a Cu-Al2O3/water nanofluid filled backward facing step channel, associated with thermo-solutal buoyancy induced mixed convection, has been numerically investigated. A novel part heating load boundary condition is applied at the bottom wall in order to model and analyse closer to the actual physics. The Navier-stokes equation in velocity-vorticity form along with energy and concentration equations are solved using Galerkin's FEM. The variation of buoyancy ratio (‒5≤N≤5), Hartmann number (0≤Ha≤50), inclination angle (0≤φ≤90) with two different part heating arrangements are analyzed systematically to understand the flow pattern and convective heat & mass transfer performance. Results show that at positive buoyancy ratio the solutal buoyancy force always supports the thermal buoyancy force augmenting the heat and mass transport phenomena. Increasing the inclination angle always give rise to the conductive mode of heat transfer compared to convective mode caused by the presence of stronger magnetic force. At N=5, change in Ha from 0 to 50 shows a maximum increment of 38% in Nuavg for φ= 0° wheras 5% reduction in Shavg is obtained for φ= 30°. Compared to case II, nearly 20 to 40% improvement in convective heat transfer is observed in case-I where heat sources are located closer to the channel step though hardly any change is observed in convective mass transfer between two different cases.

Insight into Newtonian fluid flow and heat transfer in vertical microchannel subject to rhythmic membrane contraction due to pressure gradient and buoyancy forces

The designing of the thermo-controlled micro pumping devices for diagnosis in health care and mixing of the samples at particular temperature are very much essential. Transient analysis for heat and mass transfer in a finite length vertical microchannel is presented in this article. This pumping model aims to analyze the streamlines and isotherms under various parameters at two different phases (contraction and relaxation) of membrane motion. The velocity fields under the effects of Grashof number and heat source parameter are also discussed to examine the velocity profile in the vertical microchannel. Considering the creeping nature of physiological transport phenomena, a lubrication approach has been employed. An analytical approache is adopted to derive the exact solutions, and finite difference method with in-house Matlab code are utilized to simulate the results and validate the anlytical results. Pressure is generated due to the kinematic of membrane motion and controlled by the thermal effects and buoyancy force. The contour of axial velocity enhanced by 28.32% as Grashof number changes from 0 to 2 and heat source parameter changes from 0 to 2 respectively. Volumetric flow rate also varies from 0.08 to 0.12 and 0 to 0.1 with change in Grashof number from 0 to 2 and heat source parameter from 0.01 to 4 respectively.

Assessment of pollutant dispersion in deep street canyons under different source positions: Numerical simulation

Reducing the pollution concentration on the urban street ventilation is significant for creating a healthy urban living environment. In this study, the effects of source location on airflow patterns and pollutant transmission in street canyons under the influence of wind and thermal buoyancy forces have been investigated using the CFD approach. Also using the RNG k-ε model, RANS equations, and the Boussinesq model the structure of airflow, thermal behavior, and dispersion of pollutants in a deep street canyon in three-dimensional space have been evaluated. The results show that the combined effect of wind force and buoyancy effect enhances air circulation and turbulence of air layers in street canyons; the source location of pollution in a street canyon can significantly alter the distribution and concentration of pollution in the canyon. Sunward sides, as a thermal plume, transport pollutants vertically to the windward area; the impact of wind force also profoundly complicates transmission pathways of pollutants. Since the pollution sources in this study are the buildings around the street canyon, the findings of the present study can improve the understanding of patterns of pollution distribution in street canyons and be useful in developing design standards for high-rise buildings in dense urban areas.

RETRACTED: Flow and thermal analysis of Jeffrey nanofluid in a microchannel: Buongiorno's Model

The present consideration explores the thermal energy and mass transfer process in conducting Jeffrey nanofluid flows through a microchannel. The slip boundary conditions, Brownian motion and temperature-dependent thermal conductivity were considered. The dimensionless governing models have been solved to the best possible investigative solutions using the Runge-Kutta-Fehlberg 4 −5th order numerical procedure. The impact of physical parameters on the momentum, energy, concentration, irreversibility and irreversibility ratio was revealed graphically in detail. It is concluded that the resultant momentum profile is augmented with the relaxation and retardation times parameter all over the flow region. The temperature-dependent thermal conductivity contributes to the resulting thermal energy of the flow system ever-growing to high. The concentration profile was diminutions through growing in the Brownian motion parameter. The irreversibility and irreversibility ratio were obtained mathematically and explained concerning the notable parameters. The magnetic parameter was to diminish the irreversibility rate, but it was augmented by increasing the parameter for the relaxation and retardation times ratio. Effect of thermal radiation, variable thermal conductivity, pressure gradient, buoyancy force and thermophoresis on the Jeffery nanofluid in a microchannel by the Buongiorno model have been inspected for the first time. The effects of this works are innovative and original.

Entropy generation in radiative MHD nanofluid flow past an inclined stretched surface with multiple slips in the presence of Arrhenius activation energy

In this article, a theoretical analysis on entropy generation in MHD nanofluid flow past an inclined stretched surface with multiple slips, binary chemical reaction, nonlinear thermal radiation and Arrhenius activation energy is carried out. In addition, the free-stream is moving with a uniform velocity and the presence of internal heat generation, thermal and solutal buoyancy forces are also taken into consideration. For estimating the radiative heat flux, Rosseland approximation is used. The prevailing governing equations are reformed and expressed in non-dimensional highly nonlinear ODEs with employing some suitable transformations (similarity). A numerical technique named as a shooting technique based on the Runge-Kutta Cash-Karp method is implemented to tackle this dimensionless set of equations. Graphical illustrations are made to understand the behaviors of velocity, temperature, concentration, Bejan number and entropy generation with respect to different controlling parameters. Moreover, the computed values of the quantities of engineering interest (local skin friction, local Nusselt and local Sherwood numbers) are presented with the help of tables and discussed. The numerical results obtained are also validated, under certain minimal conditions, with the results present in the paper, and excellent conformity is observed between the results.

Double Diffusive Convection of Power Law Fluids Through Taylor–Couette Flow

The proposed study focuses on the effect of double diffusive convection on the flow structures of power-law fluids between two coaxial cylinders of finite aspect ratios with end caps. We adopted a D2Q9 axisymmetric lattice Boltzmann model to predict the power-law fluid flow and D2Q4 (Lattice Boltzman method) model for azimuthal velocity, concentration, and the temperature. For ( is the solutal and thermal buoyancy forces ratio), fixed Taylor number with increasing Rayleigh number , the thermal base flow regime is more pronounced for the pseudoplastic fluid compared to the dilatant fluid. In addition, the thermal base flow in the annulus is delayed when increases. Thus, the increase of the behavior index has a stabilizing effect on the flow structure. On the other hand, when , the solute buoyancy forces in the annulus prevail over the centrifugal and thermal buoyancy forces, and the flow becomes ultimately a solute base flow for . For , the flow becomes a thermal base flow for . Thus, the mass transfer with negative values has a greater stabilizing effect on the flow structures than with positive .

EFFECTS OF THERMAL RADIATION AND BUOYANCY FORCE ON TRANSIENT HARTMANN FLOW IN A CHANNEL WITH PERMEABLE WALLS

The combined effects of thermal radiation, buoyancy force and variable heat source on an unsteady MHD flow of a conducting fluid through a porous walled channel is theoretically investigated. Base on some simplified assumptions, the model partial differential equations are obtained and tackled analytically using variable separable technique. Numerical solutions depicting the impact of various embedded thermophysical parameters on the fluid velocity and temperature profiles, skin friction and Nusselt number are displayed graphically and quantitatively discussed. An escalation in both skin friction and heat transfer rate is observed with a rise in fluid injection–suction at the channel walls.

Brownian motion and thermophoresis significance of Casson fluid flow in an elastic-radiated surface with a suspension of transpiration and non-Fourier heat flux

ABSTRACT Passive systems that need exceptional apparent geometries, thermal packaging, or fluid additives. In passive procedures, a number of foremost efforts have been conducted. The passive methods are divided into two groups: geometry modification (e.g. nano/microchannels) and solid additives (e.g. micro/nano solid particles). In a recent development in microfabrication – the development of fabrication of minuscule buildings of micrometer measures – a variation of microstrategies including heat transfer have been industrialized. Viewing this, the heat and mass transfer characteristics of a free convective Casson fluid over an elastic stretching surface are numerically studied. Thermal radiation and non-Fourier flux are incorporated in the energy to balance the transformation. Similarity transformations are used to translate partial differential equations relating to momentum, diffusion, and energy into nonlinear ordinary differential equations. The shooting approach is used to achieve numerical solutions to these equations. The effect of various physical pertinent parameters including thermal radiation parameter, Brownian motion, thermophoresis, suction, curie parameter, thermal and diffusion buoyancy forces, thermal relaxation, stretching, or shrinking parameters on the concentration and temperature profiles is investigated. It is observed that the nonlinear case has highly mixed performance when compared to the linear case of temperature and concentration fields.

Double-diffusive natural convection of non-Newtonian nanofluid considering thermal dispersion of nanoparticles in a vertical wavy enclosure

The flow field, thermal field, and solutal field exposed to thermal and solutal buoyancy forces have been investigated in detail within a wavy enclosure filled with copper(Cu)–water nanofluid incorporating the non-Newtonian characteristics predicted by the power-law viscosity model. During the convection process, the random motion of ultrafine Cu-nanoparticles causing an enhanced energy exchange rate is determined using the thermal dispersion model. The governing equations in a dimensionless form are numerically solved utilizing the finite volume method incorporated with the semi-implicit method for pressure linked equations-revised algorithm. The simulations are carried out with different pertinent parameters, such as the Rayleigh number, Lewis number, power-law index, volume fraction, and buoyancy ratio. The effect of the above parameters on the local Nusselt number (Nu) and the local Sherwood number (Sh) is analyzed to understand the heat and mass transfer properties from the heated wavy surface. Results show that the heat transfer rate from the wavy surface declines, but the mass transfer rate gets stronger with growing Lewis number. Both the heat and mass transfer rates become optimum when the nanofluid behaves as a shear thinning fluid. The distribution of Nu and Sh is found to be periodically attenuated from the lower end to the upper end along the hot wavy surface. The distribution of Nu and Sh is observed to be locally maximum at the crest point of the wavy surface. New correlations to predict the average heat and mass transfer rate concerning the studied parameters are proposed with remarkable accuracy.

Linear and Nonlinear Stability Analyses of Double-Diffusive Convection in a Vertical Brinkman Porous Enclosure under Soret and Dufour Effects

Analytical and numerical investigations were performed to study the influence of the Soret and Dufour effects on double-diffusive convection in a vertical porous layer filled with a binary mixture and subject to horizontal thermal and solute gradients. In particular, the study was focused on the effect of Soret and Dufour diffusion on bifurcation types from the rest state toward steady convective state, and then toward oscillatory convective state. The Brinkman-extended Darcy model and the Boussinesq approximation were employed to model the convective flow within the porous layer. Following past laboratory experiments, the investigations dealt with the particular situation where the solutal and thermal buoyancy forces were equal but acting in opposite direction to favor the possible occurrence of the rest state condition. For this situation, the onset of convection could be either supercritical or subcritical and occurred at given thresholds and following various bifurcation routes. The analytical investigation was based on the parallel flow approximation, which was valid only for a tall porous layer. A numerical linear stability analysis of the diffusive and convective states was performed on the basis of the finite element method. The thresholds of supercritical, RTCsup, and overstable, RTCover, convection were computed. In addition, the stability of the established convective flow, predicted by the parallel flow approximation, was studied numerically to predict the onset of Hopf’s bifurcation, RTCHopf, which marked the transition point from steady toward unsteady convective flows; a route towards the chaos. To support the analytical analyses of the convective flows and the numerical stability methodology and results, nonlinear numerical solutions of the full governing equations were obtained using a second-order finite difference method. Overall, the Soret and Dufour effects were seen to affect significantly the thresholds of stationary, overstable and oscillatory convection. The Hopf bifurcation was marked by secondary convective flows consisting of superposed vertical layers of opposite traveling waves. A good agreement was found between the predictions of the parallel flow approximation, the numerical solution and the linear stability results.

Study on the effect of flow velocity and thermal buoyancy on the dynamic behaviour of flow inside a two-hole chamber

This work aims to study the behaviour of the fluid inside a square chamber that has two openings at the top of vertical walls for the entry and exit of the fluid. Also, the chamber is arranged around two hot cylinders located vertically. The fact that the fluid is cold and the walls of the cylinders are hot, a vertical transfer of the fluid is shown due to thermal buoyancy force. The study was accomplished numerically. The pertinent parameters examined are as follows: the number of Reynolds (= 1-40) and the number of Richardson (= 0-1). The value of Prandtl number of the working fluid is (Pr = 1). The values of Nu number for the two cylinders are calculated and expressed in terms of the values of Re and Ri. The results showed that the effect of the fluid on the cylinders differs from the lower cylinder to the upper cylinder. Also, the presence of counter-flows in some cases creates hydrodynamic force in the opposite direction. For example, for Re = 40 increasing the Ri value from 0 to 1 increases Nu by an average of 3.84% for the upper obstacle and 81% for the lower one.

Radiative MHD flow of Casson hybrid nanofluid over an infinite exponentially accelerated vertical porous surface

The radiative unsteady magnetohydrodynamic (MHD) flow of an incompressible viscous electrically conducting non-Newtonian Casson hybrid nanofluid over an infinite exponentially accelerated vertical moving porous surface under the influence of slip velocity in a rotating frame has been explored in this paper. Water and ethylene glycol mixture have been considered as a base Casson fluid. A steady homogeneous magnetic field is applied under the assumption of low magnetic Reynolds number. The ramped temperature and time varying concentration at the surface is made into consideration. First order consistent chemical reaction and thermal absorption are also considered. Silver and Titania nanoparticles are disseminated in base fluid water and ethylene glycol mixture to be formed as hybrid nanofluid. Laplace transformation technique is employed on the non-dimensional governing equations for the closed form solutions. Based on those outcomes, the expressions for non-dimensional shear stress, rates of heat and mass transfer are also evaluated. The graphical representations are presented to scrutinize the effects of physical parameters on the significant flow characteristics. The computational values of the shear stresses, rate of heat transfer and rate of mass transfer at the surface are tabulated by the different implanted parameters. The resultant velocity is increasing with an increasing in thermal and concentration buoyancy forces, whereas rotation and slip parameters have overturn result on it for both cases of uniform wall temperature and ramped wall temperature. Species concentration of Casson hybrid Ag-TiO2/WEG nanofluid is decreased with an increase in Schmidt number and chemical reaction parameter. The Nusselt number is increased with an increase in heat absorption at the surface.

Magneto-mixed convection in a lid driven partially heated cavity equipped with nanofluid and rotating flat plate

In this study, mixed convection in a nanofluid filled cavity induced by thermal buoyancy force, moving wall and rotating flat plate subjected to external magnetic field is numerically investigated. The cavity is partially heated from its bottom wall and cooled from top wall moving with constant velocity in ±x direction and other walls are kept adiabatic. A counter-clockwise rotating flat plate is placed at the centre of the cavity. The cavity is permeated by a transverse magnetic field. Conservation equations are simulated through implementing finite element method. Numerical results are presented using streamlines, isotherms and bar charts to explore the effects of physical parameters on the flow and temperature fields. It is found that flow and thermal fields are impressively affected with the variations in length and speed of rotating flat plate. Besides, higher length and rotational speed of the plate causes maximum amount of heat transfer. Best heat transfer is ensured while the direction of rotating plate is same as the direction of lid wall. Moreover, optimal heat transfer performance is obtained up to 5% nanoparticles concentration which is 123.02% more than base fluid. Higher magnetic field strength attenuates the fluid motion and hence heat transfer rate significantly.

Chemical reaction, radiation and activation energy effects on MHD buoyancy induced nanofluid flow past a vertical surface

This paper explores the effects of thermal radiation, buoyancy force, chemical reaction, and activation energy on magnetohydrodynamic (MHD) nanofluid flow past a stretching vertical surface. The resulting nonlinear momentum, energy, solute, and nanoparticle concentration boundary layer equations are simplified by the transformation of similarity. The transformed equations solved numerically by using the shooting technique. For various related parameters, the corresponding results to the dimensionless velocity, temperature, solute, nanoparticle concentration profiles, Skin friction, local Nusselt number, local Sherwood number, and local nanoparticle Sherwood number are illustrated graphically. It is found that the temperature and nanoparticle concentration profiles increase on increasing thermal radiation and temperature difference parameters. With the increase of the regular buoyancy parameters, the local Nusselt number decreases on increasing the fitting rate constant, Biot number, and thermal radiation parameters.

Hall and induced magnetic field effects on MHD buoyancy-driven flow of Walters’B fluid over a magnetised convectively heated inclined surface

In this paper we discussed the impacts of Hall current and induced magnetic field on the steady flow of Walters’B fluid, driven by the thermal and concentration buoyancy forces, over a magnetised convectively heated inclined surface in a uniform porous regime. Suitable non-dimensional transformations are used to convert the problem to a similar non-dimensional problem. The resulting flow governing equations are solved by implementing the regular perturbation method. The flow behaviours for various system parameters are discussed with the help of graphs and tables that are computed and generated using MATHEMATICA software. It is examined that the rising values of angle of inclination reduce the buoyancy force that causes the reduction of the flow. Furthermore, it is noted that the current density at the magnetised inclined surface reduces as the angle of inclination rises.

Entropy scrutiny of couple stress nanoliquid flow with slip and convective conditions in an upright microchannel

This article delves into the steady flow of couple stress nanoliquid by applying the magnetic field in conjunction with the resultant entropy produced in an upright microchannel which is immersed with Titanium-dioxide nano-sized particles with water being base fluid. Both the walls facilitate injection and suction of the fluid. The entropy generated and Bejan number is figured out by making use of velocity and temperature profiles. The coalesce sequel of nanoparticle volume fraction, magnetic field, linear thermal radiation and buoyancy force along with heat source/sink are taken into account. The equations governing the fluid flow are formulated under the impact of viscous dissipation and the numerical computations of the non-linear equations are made by using the shooting technique together with Runge–Kutta–Fehlberg fourth-fifth scheme. The effect of the viscous dissipation, Grashof number, Hartmann number and couple stress parameter on nanoliquid flow and thermal distributions are thrashed out and exposed graphically. The results indicate that peak values of couple stress parameter diminishes the velocity, temperature and entropy profile whereas amplifies the Bejan number. Also lower values of Hartmann number and nanoparticle volume fraction promotes the flow and higher values of heat source parameter and Peclet number exhibits augmentation in the thermal profile.

Entropy generation to predict irreversibilities in poroelastic film with multiple forces: spectral study

The present investigation is useful in medical engineering treatments, in which biothermal therapy is one of the popular treatments. The investigation of transport phenomena of fluid flow and heat in those applications requires multi-physical models featuring heat transfer and deformable porous media. In view of this, it is anticipated to study the influence of thermal buoyancy force and nonlinear radiation on the irreversibility, flow field, solid deformation, and heat transfer characteristics in viscous radiated fluid flow in a vertical deformable porous film. The combined phenomenon of the flow field movement and solid deformation in the porous medium is considered. The flow governing equations are non-dimensionalized and solved numerically by employing Chebyshev spectral method. The impact of important parameters on the fluid velocity, solid displacement, and fluid temperature profiles is depicted graphically and interpreted at length. In the deformable porous layer, it is perceived that the fluid velocity, solid displacement, and fluid temperature profiles decrease with an increase in suction/injection parameter values. The present physical model finds applications in geomechanics (Coussy in Mechanics of porous continua, Wiley, New York, 1995; Biot in J Appl Phys 12(2):155–164, 1941) and biomedical engineering (Mow et al. in J Biomech 17(5):377–394, 1984; Barry et al. in J Appl Math Phys 42:633–648, 1991; Lai et al. in J Biomech Eng 131:245-258, 1991).

MHD mixed convection on an inclined stretching plate in Darcy porous medium with Soret effect and variable surface conditions

AbstractThis work is concerned with a steady 2D laminar MHD mixed convective flow of an electrically conducting Newtonian fluid with low electrical conductivity along with heat and mass transfer on an isothermal stretching semi-infinite inclined plate embedded in a Darcy porous medium. Along with a strong uniform transverse external magnetic field, the Soret effect is considered. The temperature and concentration at the wall are varying with distance from the edge along the plate, but it is uniform at far away from the plate. The governing equations with necessary flow conditions are formulated under boundary layer approximations. Then a continuous group of symmetry transformations are employed to the governing equations and boundary conditions which determine a set of self-similar equations with necessary scaling laws. These equations are solved numerically and similar velocity, concentration, and temperature for various values of involved parameters are obtained and presented through graphs. The momentum boundary layer thickness becomes larger with increasing thermal and concentration buoyancy forces. The flow boundary layer thickness decreases with the angle of inclination of the stretching plate. The concentration increases considerably for larger values of the Soret number and it decreases with Lewis number. The skin friction coefficient increases for increasing angle of inclination of the plate, magnetic and porosity parameters, however it decreases for rise of thermal and solutal buoyancy parameters. In this double diffusive boundary layer flow, Nusselt and Sherweed numbers increase for rise of thermal and solutal buoyancy parameters, Prandtl number, but they behave opposite nature in case of angle of inclination of the plate, magnetic and porosity parameters. The Sherwood number increases for increasing Lewis number but it decreases for increasing Soret number.

Unsteady solute dispersion in two-fluid flowing through narrow tubes: A temperature-dependent viscosity approach

The drug delivery or transportation of nutrients to our body involves the solute dispersion process through physiological systems and hence affected by the varying nature of viscosity, heat transfer and other factors. The majority of the previous works involving the solute dispersion in fluid flow through microvessels assumed the constant blood viscosity but in treatments involving temperature variations, the blood viscosity will be affected by the change in temperature and hence it is interesting to analyze its effect on the diffusion process. The motivation of the present work is to analyze the simultaneous impact of temperature-dependent viscosity and heat transfer on the solute dispersion in a two-fluid model of blood flow through narrow tubes by adopting the solution technique proposed by Sankarasubramanian and Gill (1973). Blood is considered as Herschel-Bulkley fluid with temperature-dependent viscosity filled up in a central region of the blood vessel and an outer cell free layer of plasma encircled over the central region consists of Newtonian fluid with constant viscosity. The desired flow related information using heat transfer aspect are obtained analytically for varying viscosity model and these expressions for velocity are then used to compute the diffusion coefficients and mean concentration. The entire dispersion process described by the three main diffusion coefficients known as exchange, convective and dispersion coefficients. An important observation is that the whole diffusion process (asymptotic convection, asymptotic dispersion coefficients and mean concentration) isaffected by the temperature-dependent viscosity with temperature parameters and same observation persist for three different types of fluids like Newtonian fluid (NF), Bingham-plastic fluid (BP), Power-law fluid (PL) which are specific cases of our model. A noteworthy observation is that an enhancement in viscosity index (and hence decay in viscosity of the core region fluid) affects the fluid flow velocity and hence affects the diffusion coefficients. Further, the dominance of thermal buoyancy forces expedite the diffusion process. The outcome of the results reveal the dependence of the solute dispersion on temperature-dependent viscosity and heat transfer. The study may be applicable to drug delivery through bloodstreams in the treatments involving the temperature variations such as chemotherapy.