Effects Of Buoyancy Forces Research Articles

Exact solutions of Stokes' second problem for hybrid nanofluid flow with a heat source

In this study, Stokes' second problem for Cu-Al2O3/water hybrid nanofluid is considered along with the effects of buoyancy force and a heat source. Using Laplace transforms, transient velocity, skin friction coefficient, and local Nusselt number are established in closed forms involving exponentials and error functions. The exact solutions have been compared with the numerical solutions as well as with available exact solutions, which show excellent agreement. It is found that the temperature, skin friction coefficient, and local Nusselt number are strongly affected and increased owing to the increase in the volume fractions of copper and alumina nanoparticles and heat source parameter. On the other hand, the mixed convection parameter noticeably enhances the flow velocity. When the heat source is absent, the skin friction coefficients are oscillating and the heat transfer approaches an asymptotic value. However, for a higher heat source parameter, when time increases, the amplitude of oscillation of the skin friction coefficients gradually increases and the magnitude of heat transfer exponentially increases. Both eventually go to infinity after a long period of time.

Mixed Convection of a Radiating Magnetic Nanofluid past a Heated Permeable Stretching/Shrinking Sheet in a Porous Medium

This paper analyzes the collective effects of buoyancy force, thermal radiation, convective heating, and magnetic field on stagnation point flow of an electrically conducting nanofluid past a permeable stretching/shrinking sheet in a porous medium. Similarity transformations are used on the resulting nonlinear partial differential equations to transfer into a system of coupled nonlinear ordinary differential equations. The fourth-fifth-order Runge–Kutta–Fehlberg method with shooting technique is applied to solve numerically. Results are obtained for dimensionless velocity, temperature, and nanoparticle volume fraction as well as the skin friction and local Nusselt and Sherwood numbers. The results indicate the existence of two real solutions for the shrinking sheet in the range of λ c < λ < 0 . The fluid flow stability is maintained by increasing the magnetic field effect, whereas the porous medium parameter inflates the flow stability. It is also noted that both the skin friction coefficient and the local Sherwood number approximately decline with the intensification of thermal radiation within the range from 9.83% to 14% and the range from 48.86% to 78.66%, respectively. It is also evident in the present work that the local Nusselt number upsurges with the porous and suction/injection parameters.

Optimal Homotopy Asymptotic Method for Investigation of Effects of Thermal Radiation, Internal Heat Generation, and Buoyancy on Velocity and Heat Transfer in the Blasius Flow

In this study, analytical examination of effects of internal heat generation, thermal radiation, and buoyancy force on flow and heat transfer in the Blasius flow over flat plate has been presented. The governing nonlinear partial differential equations of the problem are transformed into a set of coupled nonlinear third-order ordinary differential equations by the similarity variable method and have been systematically solved using the optimal homotopy asymptotic method. The main aim of the present study is to inspect the effects of various physical parameters in the flow model on velocity and heat transfer in steady two-dimensional laminar boundary layer flow with convective boundary conditions. The influences of the Grashof number, internal heat generation, the Biot number, radiation parameter, and the Prandtl number on the skin-friction coefficient, the fluid velocity profile, and temperature distribution have been determined and discussed in detail through several plots. The finding revealed that the fluid velocity and temperature delivery upsurge with snowballing in the values of the Biot number and internal heat generation parameters. The temperature profile of the fluid declines contrary to the value of the Grashof number and the Prandtl number but increases with thermal radiation. Moreover, it is found that the skin-friction coefficient and the rate of heat intensify with the Grashof number, internal heat generation, the Biot number, and thermal radiation parameter. The obtained result is likened with the previously published numerical results in a limited case of the problem and shows an excellent agreement.

Irreversibility analysis in natural bio-convective flow of Eyring-Powell nanofluid subject to activation energy and gyrotactic microorganisms

The developing interest in thermal engineering and nano-technology presented the idea of nanoparticles with enhanced thermal mechanisms and attained convinced novel applications in heat transportation systems, solar energy, micromechanics, air conditioning systems, cooling and heating facilities, bio-medical applications like cancer treatment, artificial heart surgery etc. Beside this, the phenomenon of entropy generation is another fascinating research area which used to improve the assessment of heat transportation with optimized procedure. The entropy generation in bio-convective flow of Eyring-Powell nanofluid over permeable stretched surface of cylinder is scrutinized in this research. The effects of magnetic field, thermal radiation and viscous dissipation are considered. Concentration communication is obtained in view of activation energy associated with binary chemical reaction. Furthermore, properties of Brownian diffusion and thermophoresis of nanoparticles are accounted. Suspended nanoparticles are made stable through mutual effects of bioconvection and buoyancy forces. Total entropy generation rate is modeled through second thermodynamics law. The governing flow model is obtained with the help of boundary layer approximations. Dimensional model is transformed into non-dimensional one by transformations and then tackled by Newton built-in shooting procedure. Impact of different influential variables on entropy generation, velocity, temperature, concentration, Bejan number and motile density of microorganisms are analyzed via graphs. Numerical values of skin friction coefficient, density, Sherwood and Nusselt numbers are tabulated and examined. Major findings are listed at the end. Since this analysis is based on theoretical flow assumptions, therefore the flow parameters specify the constant range like 0.0⩽Γ⩽6.0, 1.0⩽γ⩽4.0, 0.1⩽Ha⩽1.2, 0.2⩽λ⩽0.6,0.2⩽Rd⩽1.7, 0.1⩽K⩽3.0, 0.1⩽Pr⩽4.5, 0.3⩽Nb⩽1.8, 0.2⩽Nt⩽1.7, 0.0⩽E1⩽1.0, 1.0⩽Ec⩽4.0, 0.2⩽σ⩽1.4, 0.4⩽Sc⩽1.7, 1.0⩽δ⩽2.5, 0.5⩽Pe⩽2.0, 0.5⩽Ω°⩽2.0, 0.1⩽Br⩽1.0,0.1⩽Lb⩽1.5. The results show that fluid velocity decreases with curvature parameter and porosity constant. A decreasing variation in nanofluid temperature due to curvature parameter is examined. The entropy generation and Bejan number decline Brinkman number, motile density diffusion parameter and mass concentration diffusion variable. Furthermore, it is observed that skin friction coefficient increases with curvature parameter and porosity constant.

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.

Influence of buoyancy force on Ag-MgO/water hybrid nanofluid flow in an inclined permeable stretching/shrinking sheet

The present work explored the heat transfer and boundary layer flow of a hybrid nanofluid past an inclined stretching/shrinking sheet with suction and buoyancy force effects. Silver (Ag) and magnesium oxide (MgO) are considered as the hybrid nanoparticles and suspended in water to form Ag-MgO/water hybrid nanofluid. The partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs) by employing appropriate similarity transformation. The simplified mathematical model is then solved numerically using the bvp4c solver in the MATLAB software. The effects of governing parameters, namely the inclination angle, suction, stretching/shrinking, buoyancy or mixed convection and nanoparticle volume fraction parameters on the velocity and temperature profiles as well as skin friction coefficient and local Nusselt number are examined and presented graphically. The results are proven to have two solutions for both stretching and shrinking case, which consequently lead to the implementation of a stability analysis, hence confirming that only the first solution is stable. In addition, the local Nusselt number increases when the angle of inclination and suction parameters increase. The results also reveal that increasing values of Ag nanoparticle volume fraction in MgO/water nanofluid declines the local Nusselt number.

Effects of Variable Transport Properties on Heat and Mass Transfer in MHD Bioconvective Nanofluid Rheology with Gyrotactic Microorganisms: Numerical Approach

Rheology of MHD bioconvective nanofluid containing motile microorganisms is inspected numerically in order to analyze heat and mass transfer characteristics. Bioconvection is implemented by combined effects of magnetic field and buoyancy force. Gyrotactic microorganisms enhance the heat and transfer as well as perk up the nanomaterials’ stability. Variable transport properties along with assisting and opposing flow situations are taken into account. The significant influences of thermophoresis and Brownian motion have also been taken by employing Buongiorno’s model of nanofluid. Lie group analysis approach is utilized in order to compute the absolute invariants for the system of differential equations, which are solved numerically using Adams-Bashforth technique. Validity of results is confirmed by performing error analysis. Graphical and numerical illustrations are prepared in order to get the physical insight of the considered analysis. It is observed that for controlling parameters corresponding to variable transport properties c2, c4, c6, and c8, the velocity, temperature, concentration, and bioconvection density distributions accelerates, respectively. While heat and mass transfer rates increases for convection parameter and bioconvection Rayleigh number, respectively.

Mixed Convection Flow of Powell–Eyring Nanofluid near a Stagnation Point along a Vertical Stretching Sheet

A stagnation-point flow of a Powell–Eyring nanofluid along a vertical stretching surface is examined. The buoyancy force effect due to mixed convection is taken into consideration along with the Brownian motion and thermophoresis effect. The flow is investigated under active and passive controls of nanoparticles at the surface. The associating partial differential equations are converted into a set of nonlinear, ordinary differential equations using similarity conversions. Then, the equations are reduced to first-order differential equations before further being solved using the shooting method and bvp4c function in MATLAB. All results are presented in graphical and tabular forms. The buoyancy parameter causes the skin friction coefficient to increase in opposing flows but to decrease in assisting flows. In the absence of buoyancy force, there is no difference in the magnitude of the skin friction coefficient between active and passive controls of the nanoparticles. Stagnation has a bigger influence under passive control in enhancing the heat transfer rate as compared to when the fluid is under active control. Assisting flows have better heat and mass transfer rates with a lower magnitude of skin friction coefficient as compared to opposing flows. In this case, the nanofluid parameters, the Brownian motion, and thermophoresis altogether reduce the overall heat transfer rates of the non-Newtonian nanofluid.

Flow structure with mixed turbulent flow of supercritical CO2 heated in helically coiled tube

The mixed turbulent convection heat-transfer characteristics of supercritical CO2 (S-CO2) heated in both vertical and horizontal oriented helically coiled tube (HC-tube) is investigated via experimental and numerical methods. Firstly, the coupled equations of flow direction, buoyancy force and centrifugal force in HC-tube are established. Then, the influence of the three factors on axial and radial heat transfer coefficient (HTC) performance are discussed. In vertical oriented HC-tube, the HTC first increases progressively and then drop swiftly, presenting a peak value at the pseudo-critical point. But, in horizontal oriented HC-tube, due to buoyancy force effects, the HTC oscillates dramatically which indicates the poor heat-transfer stability. Meanwhile, the numerical simulation, corresponding to the experiment condition, is carried out. To capture the flow structures, 6 characteristic lines on each cross-section are selected and the corresponding velocity and the turbulent kinetic energy distributions are comparative analyzed. The results showed that the coupling effects of centrifugal force and buoyancy force mainly affect heat-transfer on the inside of a cross-section. In addition, different from the M-type velocity in straight tube, the salient point of M-type velocity in HC-tube always locate at the outer side of the buffer-layer and the heat-transfer is slightly affected. The local heat-transfer deterioration mainly occurs at inside of a cross section where the velocity is obviously suppressed.

Influence of heat transfer on MHD Carreau fluid flow due to motile cilia in a channel

Mucus transport mediated by motile cilia in the airway is an important defense mechanism for prevention of respiratory infections. Cilia motility can be affected by temperature difference and magnetic field. In this research, we investigate the combined effects of magnetic field and buoyancy force due to temperature difference. In the present study, mixed convective flow of a Carreau fluid model through a ciliated channel is modeled and analyzed by a symplectic metachoronal wave. The momentum and energy equations for the Carreau fluid are modeled and simplified by the stream function and small Reynold’s number approximation. The influence of magnetic parameter, Carreau fluid parameter, Brinkmann number and Weissenberg number on velocity, temperature and pressure gradient are presented via graphs. It is observed that Hartmann number helps to decelerate the flow, whereas Weissenberg number, Grashof number and Carreau fluid parameter are responsible for the accelerated flow. The heat transfer rate rises by increasing the values of Hartmann number, Weissenberg number, Carreau fluid parameter and Brinkmann number.

Suggestions for the Proper Treatment of Buoyancy Force Effect on Single Phase Thermal Stratification Phenomenon

In the operating nuclear power plants, piping and components installed in the in-service testing systems connected to the reactor coolant system are potentially exposed to fatigue caused by thermally stratified flow, possibly threatening its integrity. The emergency core cooling system (ECCS) is one of candidates for which the thermal stratification phenomenon can occur. Because temperature difference between the hot coolant in the cold leg and the cold cooling water injected from the ECCS line is 200 K or more, buoyancy due to density difference may have significant influence on thermal-hydraulic characteristics of the mixing flow. Therefore, in this study, the need to consider proper buoyancy models in governing equations, especially turbulence transport equations, for accurate prediction of single phase thermal stratification in the cold leg and downcomer by ECCS injection is numerically studied using ANSYS CFX R17.2.

MHD effects of partition plates on thermofluid performance of Indian variant LLCB TBM for ITER

Abstract Liquid metal Lead-Lithium (PbLi) flow channels in Indian LLCB (lead lithium cooled ceramic breeder) Test Blanket Module consist of a sequence of parallel channels which are fed from a common inlet header. Thin radial-toroidal vertical plates known as partition plates at the central plane perpendicular to the applied magnetic field are primarily envisaged to enhance the mechanical strength of high aspect ratio electrically coupled parallel poloidal channels. In that case the partition plates are acting as an internal Hartmann wall and they have significant effects on velocity profile, pressure drop and heat transfer characteristics at ITER relevant applied magnetic field (B0 = 4 T). Three dimensional numerical simulation is performed in a model of full scale LLCB variant to study the effects of these partition plates on various flow field variables. Axial velocity near the thin partition wall and side wall jet structures are found to get significantly. Magneto-hydraulic pressure drop and redistribution of flow rates due to the presence of partition plates are assessed by comparing the results with no partition wall. Thermofluid simulation is carried out to obtain the temperature distribution of various structures for a given heat load profile based on neutronic estimation. The effects of buoyancy force on thermofluid flow profile in channels with high temperature gradient are also presented.

Ultra-Lean Gaseous Flames in Terrestrial Gravity Conditions

Development of the combustion process in the gaseous mixtures of near-limit composition is of great interest for fundamental aspects of combustion theory and fire-safety applications. The dynamics of ultra-lean gaseous flames in near-limit mixtures is governed by many effects, such as buoyancy, preferential diffusion, radiation, and instability development. Though ultra-lean combustion was extensively studied in microgravity conditions, the influence of gravity on the ultra-lean flame structure and stability is still poorly understood. The paper is devoted to deepening the knowledge of ultra-lean flame dynamics in hydrogen-air mixtures under terrestrial gravity conditions. The spatial structures of the flame developing under the effect of buoyancy forces are investigated employing detailed numerical analysis. Different modes of near-limit flame evolution are observed depending on the mixture concentration. In particular, we registered and described three distinct spatial structures: individual kernels tending to extinguish in leanest compounds, complex multi-kernel structures in marginal compositions, and stable cap-shaped flames in more chemically active mixtures. We apply the flame-bubble analogy to interpret flame dynamics. On this basis, the diagram in the Re-Fr plane is developed. That allows classifying the emerging flame structures and determine flame stability. Additionally, different ignition modes are studied, and the mechanisms determining the impact of ignition mode on the flammability limits are distinguished. Obtained results provide useful insights into the processes of flame quenching and development in near-limit hydrogen-air mixtures under real gravity conditions and can be applied in the design of contemporary fire-safety systems.

Unsteady free convection flow of water-based carbon nanotubes due to non-coaxial rotations of moving disk

ABSTRACT Nanofluid is one of the significant developments for having an efficient heat transport process. Its implementation in a non-coaxial rotating system has benefited from designing a mixer machine with two stirrer blades, cooling fan, and jet engines. This study analytically investigates the free convection of unsteady non-coaxial rotating nanofluid flow through a moving disk. The suspension of single-wall or multi-wall carbon nanotubes in water is known as the nanofluid in this study. The fluid motion is affected by the effects of rotation and buoyancy forces. Using suitable dimensionless variables, the dimensional coupled partial differential of momentum and energy equations along with their initial and moving boundary conditions are converted into the dimensionless form. The expressions for temperature and velocity profiles are obtained by solving governing equations using Laplace transform method. The validity of obtained solution is confirmed by having a good agreement when comparing present results with the published result. The results show that the insertion of CNTs particles into the rotating water causes the temperature and velocity profiles to increase. The amount of heat transferred by SWCNTs is greater than MWCNTs. Increasing CNTs particles has descended both primary and secondary skin friction but increase Nusselt number. Further analysis with the help of pictorial discussion for the fluid flows and heat transfer under the influences of nanoparticle volume fraction, Grashof number, the amplitude of disk, and time is carried out.

Analyzing bulk density and void fraction: A. the effect of archimedes number

This paper presents an analysis of all forces affecting the void fraction (VF) and density of a particulate bed. The bulk density of many materials, both spherical and non-spherical, with a variety of properties, including particle size and density, were measured in air and various liquids. The Archimedes number (Ar) was found to be an appropriate representation of the particle behavior that considered the van der Waals forces. The effects of buoyancy and viscous forces, as components of Ar, on the VF were shown by experiments in various liquids. Additional forces, such as friction, impact, and tapping were discussed quantitatively and qualitatively. Furthermore, the effect of the particle shape on the VF was considered. Finally, general equations for VF and density were developed for practical use. The major effects of the moisture content and compression pressure on the VF will be discussed in a following paper.

Numerical Investigation on Conjugate Heat Transfer in Helical Coiled Tube under Vertical Placement

Conjugate heat transfer of supercritical CO2 inside helical coiled tube under vertical placement was investigated numerically in the present study. It can be concluded that the flow field of supercritical fluid is affected by both the buoyancy force and centrifugal force in conjugate heat transfer process. The dual effects of buoyancy force and centrifugal force lead to the deflection of second flow direction for the vertical placement, and further results in the heat transfer deterioration region on top generatrix wall for the downward flow larger than that for the upward flow. However, the overall heat transfer performance is slightly better than that in the upward flow in tube side.

MHD variable viscosity mixed convection of nanofluid in a microchannel with permeable walls

In this study, we examine the combined effects of buoyancy forces, pressure gradient, thermophoresis, Brownian motion, variable viscosity of nanofluid flow in a microchannel with suction and injection in the presence of uniform magnetic field imposed in cross-wise direction. It is assumed that the dynamic viscosity of the nanofluid is related with temperature exponentially and that the vertical parallel-plates temperature is held asymmetrically. Applying similarity transformation, the governing system of partial differential equations (PDEs) are transformed into a set of non-dimensional nonlinear partial differential equations whose solutions are obtained numerically by semi-discretization centered finite difference method along with Runge-Kutta Fehlberg integration technique scheme. Qualitative description of graphical results depicting the effect of thermophysical parameters on the dimensionless velocity, temperature, nanoparticles concentration, skin friction, Nusselt number and Sherwood number are presented.

Analytical Analysis of Effects of Buoyancy, Internal Heat Generation, Magnetic Field, and Thermal Radiation on a Boundary Layer over a Vertical Plate with a Convective Surface Boundary Condition

In this paper, the effects of magnetic field, thermal radiation, buoyancy force, and internal heat generation on the laminar boundary layer flow about a vertical plate in the presence of a convective surface boundary condition have been investigated. In the analysis, it is assumed that the left surface of the plate is in contact with a hot fluid, whereas a stream of cold fluid flows steadily over the right surface, and the heat source decays exponentially outwards from the surface of the plate. The governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations with the help of similarity transformation which were solved analytically by applying the optimal homotopy asymptotic method. The variations of fluid velocity and surface temperature for different values of the Grashof number, magnetic parameter, Prandtl number, internal heat generation parameter, Biot number, and radiation absorption parameter are tabulated, graphed, and interpreted in physical terms. A comparison with previously published results on similar special cases of the problem shows an excellent agreement.

Multifield Coupled Dynamics of Power Supply Arc Based on Image 3D Reconstruction Mathematical Model

During the conversion process of the short-circuit arc to the submerged power supply arc, because the short-circuit arc diameter is much larger than the submerged power supply arc, the specific position of the submerged power supply arc cannot be determined, and the initial position of the submerged power supply arc has a certain randomness. The purpose of this paper is to try to use the binocular stereo vision method to reconstruct the submerged arc image in three dimensions, obtain the moving image of the arc, obtain more comprehensive information than the two-dimensional image, and multi-field coupling dynamics of the power supply arc. In this paper, the multi-field coupling effects of electromagnetic force, thermal buoyancy, wind load and air resistance of the submerged arc of the half-wavelength transmission line are considered comprehensively, and the chain arc model is incorporated into the force equation and motion model of the submerged arc. By deeply analyzing the formation and motion mechanism of the arc root, the arc root model of the submerged power arc is established, and the optimal selection method of the current element length is proposed. The physical simulation experiment of the half-wavelength submerged arc is carried out, and the simulation results are compared with the experimental results to verify the effectiveness of the simulation model. By comparing the trajectory and self-extinguishing time of different submerged currents, wind speeds and winds to the submerged power supply arc, the effects of wind load, thermal buoyancy and electromagnetic force on the arc are analyzed, which indicates that the built arc model can effectively account for the wind load. The influence of submarine power arc motion and self-extinguishing characteristics. The results show that the submarine power arc image is acquired by constructing a binocular stereo vision system, and the obtained submersible arc image is reconstructed three-dimensionally. The three-dimensional image of the arc is obtained and compared with the actual image. The result shows that the three-dimensional reconstruction The result is effective, and the exploration study provides a new method for further obtaining the multiple variations of the true arc length of the arc with the arcing time.

Entropy generation of mixed convection of SWCNT–water nanofluid filled an annulus with a rotating cylinder and porous lining under LTNE

PurposeThe purpose of this study is to numerically analyze the mixed convection and entropy generation in an annulus with a rotating heated inner cylinder for single-wall carbon nanotube (SWCNT)–water nanofluid flow using local thermal nonequilibrium (LTNE) model. An examination of the system behavior is presented considering the heat-generating solid phase inside the porous layer partly filled at the inner surface of the outer cylinder.Design/methodology/approachThe discretized governing equations for nanofluid and porous layer by means of the finite volume method are solved by using the SIMPLE algorithm.FindingsIt is found that the buoyancy force and rotational effect have an important impact on the change of the strength of streamlines and isotherms for nanofluid flow. The minimum average Nusselt number on the inner cylinder is obtained at Ra$_E$ = 10$^4$, and the minimum total entropy generation is found at Re = 400 for given parameters. The entropy generation minimization is determined in case of different nanoparticle volume fractions. It is observed that at the same external Rayleigh numbers, the LTNE condition obtained with internal heat generation is very different from that without heat generation.Originality/valueTo the best of the authors’ knowledge, there is no previous paper presenting mixed convection and entropy generation of SWCNT–water nanofluid in a porous annulus under LTNE condition. The addition of nanoparticles to based fluid leads to a decrease in the value of minimum total entropy generation. Thus, using nanofluid has a significant role in the thermal design and optimization of heat transfer applications.