Three-dimensional Convection Flow Research Articles

3D-Numerical simulation of free convection inside a cubical cavity filled with non-Newtonian-Bingham fluid

This work focuses on a numerical study of the natural convection of a non-Newtonian viscoplastic fluid within a cubic enclosure. The viscoplastic behavior is described by the Bingham model. The considered three-dimensional convective flow is confined within a cavity, subjected to a horizontal temperature gradient, where the vertical walls have two imposed temperatures while the rest of the walls are adiabatic. The Navier-Stokes equations, along with the mass and energy conservation equations, are numerically solved. Fluid flow and heat transfer characteristics are systematically studied over a wide range of Rayleigh numbers Ra (103 - 106) and Bingham number Bn (0 - 20). Finally, comparisons were made with previous results obtained in two dimensions in order to analyze the existence of a three-dimensional effect on the flow of the Bingham fluid. The results show that the Nusselt number decreases with the increase of the Bingham number, and for the large values ​​of the latter the heat transfer is done by conduction. It is also noteworthy that the critical Bn of the 2D model is higher than that of the 3D model, which confirms the existence of the three-dimensional effect. This is attributed to the presence of a wall along the Z axis which hinders and limits the flow of fluid within the enclosure.

Impact of activation energy and cross-diffusion effects on 3D convective rotating nanoliquid flow in a non-Darcy porous medium

PurposeThis study aims to investigate numerically the impact of the three-dimensional convective nanoliquid flow on a rotating frame embedded in the non-Darcy porous medium in the presence of activation energy. The cross-diffusion effects, i.e. Soret and Dufour effects, and heat generation are included in the study. The convective heating condition is applied on the bounding surface.Design/methodology/approachThe control model consisted of a system of partial differential equations (PDE) with boundary constraints. Using suitable similarity transformation, the PDE transformed into an ordinary differential equation and solved numerically by the Runge–Kutta–Fehlberg method. The obtained results of velocity, temperature and solute concentration characteristics plotted to show the impact of the pertinent parameters. The heat and mass transfer rate and skin friction are also calculated.FindingsIt is found that both Biot numbers enhance the heat and mass distribution inside the boundary layer region. The temperature increases by increasing the Dufour number, while concentration decreases by increasing the Dufour number. The heat transfer is increased up to 8.1% in the presence of activation energy parameter (E). But, mass transfer rate declines up to 16.6% in the presence of E.Practical implicationsThe applications of combined Dufour and Soret effects are in separation of isotopes in mixture of gases, oil reservoirs and binary alloys solidification. The nanofluid with porous medium can be used in chemical engineering, heat exchangers and nuclear reactor.Social implicationsThis study is mainly useful for thermal sciences and chemical engineering.Originality/valueThe uniqueness in this research is the study of the impact of activation energy and cross-diffusion on rotating nanoliquid flow with heat generation and convective heating condition. The obtained results are unique and valuable, and it can be used in various fields of science and technology.

APPLICATION OF AN EXACT SOLUTION OF SPECIAL TYPE OF THERMOSOLUTAL CONVECTION EQUATIONS FOR THE INVESTIGATION OF EVAPORATIVE THREE-DIMENSIONAL FLOWS

The characteristics of gas-liquid flows with evaporation at the thermocapillary interface in an infinite rectangular duct, with a linearly distributed thermal load being applied on the upper and lower walls, are studied. The theoretical research of the three-dimensional convective flows is carried out within the framework of a two-sided model of evaporative convection based on the Navier-Stokes equations in the Oberbeck-Boussinesq approximation. A solution of a special type of governing stationary equations is used for describing the heat and mass transfer in a system of two immiscible fluids. We investigate the influence of the working (equilibrium) temperature of the system and intensity of the external thermal load on the structure of the velocity and temperature fields, as well as on changes in the evaporation mass flow rate and vapor content in the gas phase. The simulations are performed for the ethanol-air system. Based on the comparison of the calculated and experimental data, an effective way of nondimensionalization is proposed that allows one to consistently take into account the impact of the gas pumping velocity being a controlled parameter in experiments. It provides correct matching of the mathematical model to the experiment conditions, as well as a better qualitative and quantitative agreement between theoretical and measured values of evaporative mass flow rate. The results of the present study can aid in developing a theoretical basis for experimental research methods of evaporative convection and also in designing equipment for thermal coating or drying.

Heat and Mass Transfer Analysis of a Three-Dimensional MHD Convective Flow with Sinusoidal Suction in the Presence of Radiation Absorption and Diffusion Thermo Effect

Heat and Mass Transfer Analysis of a Three-Dimensional MHD Convective Flow with Sinusoidal Suction in the Presence of Radiation Absorption and Diffusion Thermo Effect

A revised model on three-dimensional hydromagnetic convective flow of nanofluids over a nonlinearly inclined stretching sheet

Theoretical research has been done on the hydromagnetic three-dimensional nanofluid flow across an inclined stretching sheet in the presence of Brownian motion and thermophoresis. It is taken into account that there are two different kinds of water-based nanofluids that contain copper and alumina. Three-dimensional nonlinear-type similarity transformations are used to convert the governing boundary-layer equations into a collection of similarity equations, which are then numerically solved by MATLAB. Further, results obtained in some limiting cases are compared to some results that have already been published, and it is found that there is good agreement. The problem is controlled by a number of physical factors, and the impact of these factors on different flow distributions is thoroughly examined with the help of graphs and tables. It has been observed that the nanofluid has better heat transfer conductivity than the ordinary base fluid.

Inverse cascades of kinetic energy and thermal variance in three-dimensional horizontally extended turbulent convection

Inverse cascades of kinetic energy and thermal variance in the subset of vertically homogeneous modes in spectral space are found to cause a slow aggregation to a pair of convective supergranules that eventually fill the whole horizontally extended, three-dimensional, turbulent Rayleigh-B\'{e}nard convection layer when a heat flux is prescribed at the top and bottom. An additional weak rotation of the layer around the vertical axis stops this aggregation at a scale that is smaller than the lateral domain extension and ceases the inverse cascade for the thermal variance. The inverse cascade for the kinetic energy remains intact, even for times at which the root mean square values of temperature and velocity have reached the statistically steady state. This kinetic energy inverse cascade sustains the horizontally extended convection patterns which are best visible in the temperature field. The resulting characteristic length of the aggregated convection patterns depends on the thermal driving and linearly on the strength of rotation. Our study demonstrates the importance of inverse energy cascades beyond the two-dimensional turbulence case in a three-dimensional convection flow that is subject to a multi-scale energy injection by thermal plumes and driven by boundary heat fluxes as typically present in natural geo- and astrophysical systems, such as solar convection.

Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh-Bénard convection flows.

We explore the transport mechanisms of heat in two- and three-dimensional turbulent convection flows by means of the long-term evolution of Lagrangian coherent sets. They are obtained from the spectral clustering of trajectories of massless fluid tracers that are advected in the flow. Coherent sets result from trajectories that stay closely together under the dynamics of the turbulent flow. For longer times, they are always destroyed by the intrinsic turbulent dispersion of material transport. Here, this constraint is overcome by the application of evolutionary clustering algorithms that add a time memory to the coherent set detection and allows individual trajectories to leak in or out of evolving clusters. Evolutionary clustering thus also opens the possibility to monitor the splits and mergers of coherent sets. These rare dynamic events leave clear footprints in the evolving eigenvalue spectrum of the Laplacian matrix of the trajectory network in both convection flows. The Lagrangian trajectories reveal the individual pathways of convective heat transfer across the fluid layer. We identify the long-term coherent sets as those fluid flow regions that contribute least to heat transfer. Thus, our evolutionary framework defines a complementary perspective on the slow dynamics of turbulent superstructure patterns in convection flows that were recently discussed in the Eulerian frame of reference. The presented framework might be well suited for studies in natural flows, which are typically based on sparse information from drifters and probes.

Bioconvection in Magneto Hydrodynamics Casson Nanoliquid (Fe3O4-Sodium Alginate) With Gyrotactic Microorganisms Over an Exponential Stretching Sheet

The present investigation focuses on the influence of motile gyrotactic microorganisms and thermal heat flux on three-dimensional convective flow of a Casson nanoliquid over an elongated surface. The flow equations are modelled by using Tiwari-Das nanofluid model. Sodium alginate (SA) is considered as the base fluid together with Ferromagnetic oxide (Fe3O4) nanoparticles. The governing flow equations are changed into a system of ODEs with the aid of similarity variables and are then addressed computationally. Influence of various pertinent parameters on different physical quantities is examined graphically. The outcomes of present investigation is validated through comparison study and is found to be in good arrangement. It is noticed that the coefficient of heat transfer rises with growing radiation and Biot numbers. Also the mass transfer coefficient surges for higher values of Schmidt number and generative chemical reaction parameter.

On the forced convective flow inside thermal collectors enhanced by porous media: from macro to micro-channels

PurposeAiming at finding the velocity distribution profile and other flow characteristic parameters such as the Poiseuille (Po) number, this study aims to focus on the three-dimensional forced convective flow inside rectangular ducts filled with porous media commonly used in air-based solar thermal collectors to enhance the thermal performance. The most general model for the fluid flow (i.e. the non-linear Darcy–Brinkman–Forchheimer partial differential equation subjected to slip and no-slip boundary conditions) is considered.Design/methodology/approachThe general governing equations are solved analytically based on the perturbation technique and the results are validated against numerical simulation study based on a finite-difference solution over a non-uniform but structured grid.FindingsThe analytical velocity distribution profile based on exponential functions for the above-mentioned general case is obtained, and accordingly, expressions for the Po are introduced. It is found that the velocity distribution tends to be uniform by increasing the aspect ratio of the duct. Moreover, a criterion for considering/neglecting the nonlinear drag term in the momentum equation (i.e. the Forchheimer term) is proposed. According to the sensitivity analysis, results show that the nonlinear drag term effects on the Nusselt number are important only in porous media with high Darcy numbers.Originality/valueA general analytic solution for three-dimensional forced convection flows through rectangular ducts filled with porous media for the general model of Darcy–Brinkman–Forchheimer and the general boundary condition including both no-slip and slip-flow regimes is obtained. An analytic expression to calculate Po number is obtained which can be practical for engineering estimations and a basis for validation of numerical simulations. A criterion for considering/neglecting the nonlinear drag term in the momentum equation is also introduced.

Three-dimensional magneto convective flows in geometries relevant for DCLL blankets

Abstract The dual coolant lead lithium (DCLL) blanket is one of the liquid metal blanket concepts investigated within the framework of the EUROfusion Consortium. In the proposed design, the liquid metal serves as tritium breeder, neutron multiplier, and as coolant for the breeding zone. Magnetohydrodynamic (MHD) effects resulting from the interaction of the moving liquid metal with the magnetic field that confines the fusion plasma are coupled with thermal phenomena. Induced electromagnetic forces lead to significant modifications of the hydrodynamic flow and affect in turn heat and mass transfer. The presence of a high-intensity neutron flux in the liquid metal yields volumetric heating and associated buoyant forces that drive complex flow patterns in the blanket. The resulting convective motions cause strong thermal mixing, and an increment in the effective heat transfer coefficient that may increase heat losses from the liquid metal into the helium coolant. This could deteriorate the thermal efficiency of the blanket. Buoyant MHD phenomena may also result in reversed flow and closed recirculations where tritium accumulates and temperature locally increases. The aim of the present investigation is to address by means of 3D numerical simulations the main features of magneto-convective flows in a geometry typical for DCLL blankets, in which PbLi moves upwards in a poloidal duct that faces the first wall and, after making a U-turn, flows downwards at the back of the blanket module. The liquid metal enters and leaves the model geometry by flowing radially in rectangular channels. It is found that in the front duct the velocity is characterized by jets in the boundary layers along walls parallel to the magnetic field, as expected in case of electrically conducting ducts. In the rear channel, along the wall that separates the two poloidal ducts, a downward flow occurs with much higher velocities than in the rest of the channel. The influence of the magnetic field on these flow features is investigated.

Natural convective three-dimensional flow structure in a cylindrical container

Experimental observations of steady-state natural convection of water inside a cylinder with an aspect ratio (height/diameter) of 1.33 are presented. The lower horizontal wall of the cylinder is at high temperature while the upper surface of the fluid is kept at a low temperature. The working fluid is water (Prandtl number 6.6) and the Rayleigh number is Ra = 6.5 × 105. The three-dimensional flow pattern is resolved using a scanning, stereoscopic PIV system that captures the three components of the velocity field in the whole volume occupied by the fluid. The experimental observations are compared with numerical results obtained through the solution of the conservation equations obtaining an excellent agreement. The flow observed is dominated by a non-axisymmetric natural convective cell that fills most of the volume, but in a particular plane the flow displays four symmetrically located vortical structures. Other geometrical properties of the flow include a specific vertical plane with zero normal velocity that divides the volume in two halves. Critical points and the structure of the vortex core are also identified.

Heat Transfer Analysis of Three-Dimensional Mixed Convective Flow of an Oldroyd-B Nanoliquid over a Slippery Stretching Surface

The present article examines Soret and Dufour effects on the three-dimensional mixed convective flow of an Oldroyd-B nanoliquid. The flow is caused due to bidirectional stretching of the surface in the presence of an induced magnetic field and heat generation/absorption. Besides, concentration and thermal buoyancy impacts are inspected. The velocity slip, convective and zero nanoparticle mass flux boundary condition at the surface are taken into account. Nonlinear system of equations which are highly coupled is solved via optimal homotopy algorithm. The influence of pertinent parameters on velocity, temperature, and concentration are analyzed graphically. The impact of Dufour number is quite substantial on temperature whereas Soret number increases the concentration. To see the legitimacy of the present work, the present results are compared with the results available in the literature and noted an excellent agreement for the limiting cases.

Numerical study on convective flow and heat transfer in 3D inclined enclosure with hot solid body and discrete cooling

Purpose This study aims to deal the numerical simulation on buoyant convection and energy transport in an inclined cubic box with diverse locations of the heater and coolers. Design/methodology/approach The left/right walls are cooled partially whereas the other walls are kept adiabatic. In the left/right walls, three different locations of the cooler are examined, whereas heater moves in three locations in the middle of the enclosed box. The governing models are numerically solved using the finite-element method. Findings The simulations are done on several values of the Rayleigh number and cavity inclination angles and different locations of the heater and coolers. The results are presented in the form of streamlines, isosurfaces and Nusselt numbers for different values of parameter involved here. It is recognized that the inclination of the box and the locations of the coolers strongly influence the stream and energy transport inside the enclosed domain. Research limitations/implications The present investigation is conducted for steady, laminar, three-dimensional natural convective flow in a box for different locations of cooler and tilting angles of a cavity. The study might be useful to the design of solar collectors, room ventilation systems and electronic cooling systems. Originality/value This work examines the effects of different locations of cooler and tilting angles of a cavity on convective heat transfer in a 3D cavity. The study is useful for thermal engineering applications.

Two-Phase Microscopic Heat Transfer Model for Three-Dimensional Stagnation Boundary-Layer Flow in a Porous Medium

Abstract This work examines the steady three-dimensional forced convective thermal boundary-layer flow of laminar and incompressible fluid in a porous medium. In this analysis, it is assumed that the solid phase and the fluid phase, which is immersed in a porous medium are subjected to local thermal nonequilibrium (LTNE) conditions, which essentially leads to one thermal boundary-layer equation for each phase. Suitable similarity transformations are introduced to reduce the boundary-layer equations into system of nonlinear ordinary differential equations, which are analyzed numerically using an implicit finite difference-based Keller-box method. The numerical results are further confirmed by the asymptotic solution of the same system for large three-dimensionality parameter, and the corresponding results agree well. Our results show that the thickness of boundary layer is always thinner for all permeability parameters tested when compared to the nonporous case. Also, it is noticed that the temperature of solid phase is found to be higher than the corresponding fluid phase for any set of parameters. There is a visible temperature difference in the two phases when the microscopic interphase rate is quite large. The physical hydrodynamics to these parameters is studied in some detail.

Two- and three-dimensional simulation of natural convection flow of CuO-water in a horizontal concentric annulus considering nanoparticles’ Brownian motion

A numerical study of two- and three-dimensional natural convection flows of copper oxide water-based nanofluid in a horizontal concentric annulus has been conducted to investigate the influence of Rayleigh number () and nanoparticles volume fraction () on both hydrodynamic and thermal behaviors, and further to examine the difference between two- and three-dimensional simulations. The Brownian motion of nanoparticles is considered in evaluating the effective thermal conductivity and dynamic viscosity of nanofluid. The mass, momentum and energy conservation equations are solved numerically by the finite volume method together with the artificial compressibility algorithm for pressure-velocity coupling. The obtained results indicate that the addition of nanoparticles in water leads to an existence of the general flow structure, but causes more complicated changes in flow intensity. The thermal performance of the nanofluid increases with increment of nanoparticles volume fraction up to a critical particle loading at which the maximum heat transfer occurs. The corresponding maximum heat transfer enhancement, at three different Rayleigh numbers (), is approximately 17.2% (19.0%), 11.2% (11.1%), and 13.6% (12.8%) for 2-D (3-D) configuration.

Polar waves and chaotic flows in thin rotating spherical shells

Convection in rotating spherical geometries is an important physical process in planetary and stellar systems. Using continuation methods at low Prandtl number, we find both strong equatorially asymmetric and symmetric polar nonlinear rotating waves in a model of thermal convection in thin rotating spherical shells with stress-free boundary conditions. For the symmetric waves convection is confined to high latitude in both hemispheres but is only restricted to one hemisphere close to the pole in the case of asymmetric waves. This is in contrast to what is previously known from studies in the field. These periodic flows, in which the pattern is rotating steadily in the azimuthal direction, develop a strong axisymmetric component very close to onset. Using stability analysis of periodic orbits the regions of stability are determined and the topology of the stable/unstable oscillatory flows bifurcated from the branches of rotating waves is described. By means of direct numerical simulations of these oscillatory chaotic flows, we show that these three-dimensional convective polar flows exhibit characteristics, such as force balance or mean physical properties, which are similar to flows occuring in planetary atmospheres. We show that these results may open a route to understanding unexplained features of gas giant atmospheres, in particular for the case of Jupiter. These include the observed equatorial asymmetry with a pronounced decrease at the equator (the so-called dimple), and the coherent vortices surrounding the poles recently observed by the Juno mission.

Lattice Boltzmann simulations of three-dimensional thermal convective flows at high Rayleigh number

We present numerical simulations of three-dimensional thermal convective flows in a cubic cell at high Rayleigh number using thermal lattice Boltzmann (LB) method. The thermal LB model is based on double distribution function approach, which consists of a D3Q19 model for the Navier-Stokes equations to simulate fluid flows and a D3Q7 model for the convection-diffusion equation to simulate heat transfer. Relaxation parameters are adjusted to achieve the isotropy of the fourth-order error term in the thermal LB model. Two types of thermal convective flows are considered: one is laminar thermal convection in side-heated convection cell, which is heated from one vertical side and cooled from the other vertical side; while the other is turbulent thermal convection in Rayleigh-Bénard convection cell, which is heated from the bottom and cooled from the top. In side-heated convection cell, steady results of hydrodynamic quantities and Nusselt numbers are presented at Rayleigh numbers of 106 and 107, and Prandtl number of 0.71, where the mesh sizes are up to 2573; in Rayleigh-Bénard convection cell, statistical averaged results of Reynolds and Nusselt numbers, as well as kinetic and thermal energy dissipation rates are presented at Rayleigh numbers of 106,3×106, and 107, and Prandtl numbers of 0.7 and 7, where the nodes within thermal boundary layer are around 8. Compared with existing benchmark data obtained by other methods, the present LB model can give consistent results.

Numerical study on convective flow in a three-dimensional enclosure with hot solid body and discrete cooling

The aim of the present numerical study is to analyze the effect of cooler location and aspect ratio and position of the hot solid body inside the enclosure on three-dimensional natural convection flow in a cubical enclosure. The cooler and heater positions and aspect ratio of the heater in a cavity are examined under different combinations of partially cooling vertical sidewalls and, hot solid body in the cubical cavity. That is, (i) different cooler locations with a fixed size of the hot solid body, and, (ii) centrally located hot solid body with different aspect ratio. The three-dimensional convective flow and thermal arrangements in the enclosure are analyzed using the distribution of streamlines, isosurfaces, and Nusselt number. It is found that the cooler location and aspect ratio of hot solid body play a key role on convective cooling and energy transport inside the enclosure. The unit aspect ratio of hot solid body provides higher energy transport inside the enclosure for all cooler positions.

Three-dimensional free convective flow of a second-grade fluid through a porous medium with periodic permeability and heat transfer

In this study, we model and theoretically analyze a free convective three-dimensional flow of an incompressible second-grade fluid through a highly porous medium bounded by an infinite vertical porous plate subjected to a constant suction. We assume the permeability of the medium to be periodic and the free stream velocity to be uniform. The assumption of either constant or time-dependent permeability of a porous medium leads to two-dimensional flows; however, the flow becomes three-dimensional due to variable permeability of the porous medium. We obtain analytic solutions for velocity field, pressure, skin friction components, temperature distribution, and discuss and graphically visualize effects of physical parameters emerging in the mathematical model of the physical phenomenon on these physical quantities. We note that the main flow velocity component decreases due to enhancement in non-Newtonian parameter; however, the pressure rises due to thickening of the fluid.

Dual solutions for three-dimensional magnetohydrodynamic nanofluid flow with entropy generation

Abstract This paper presents a formulation for simulating magnetohydrodynamic three-dimensional convective flow and heat transfer in a nanofluid by incorporating the complete viscous dissipation function in the energy equation. A novel feature of this investigation of entropy generation and dual solutions is the use of the spectral quasilinearization method to solve the conservation equations. The results are compared with exact solutions or higher order solutions and a good agreement is achieved. The accuracy is determined by calculation of residual errors and the method of solution is shown to produce smaller residual errors than those achieved by the fifth-order Runge-Kutta Fehlberg method for nonlinear differential equations. The dual solutions for different Prandtl number, and Brownian motion and thermophoresis parameters are shown graphically and discussed. It is found that the temperature profiles as well as thermal boundary layer thickness increase with the Brownian motion parameter for first and the second solutions. The temperature profiles increase with the thermophoresis parameter for the first and second solutions. The entropy generation increases with the Reynolds number. Highlights Combined effects of entropy generation and MHD nanofluid are proposed. Spectral quasi-linearization method (SQLM) is used for computer simulations. Use axisymmetric stretching/shrinking sheet for dual solution. Validate the accuracy and convergence using residual error analysis.