Fluids

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14 pages, 647 KiB

Open AccessArticle

Note on the Early Thermoelastic Stage Preceding Rayleigh–Bénard Convection in Soft Materials

by Rachid Rahouadj, Chérif Nouar and Antonio Pereira

Fluids 2022, 7(7), 231; https://doi.org/10.3390/fluids7070231 - 8 Jul 2022

Viewed by 1367

In this paper, we focus on the first stage of transition to Rayleigh–Bénard convection in soft-jammed systems (yield stress fluids) confined in a parallelepiped box heated from the bottom. Up to yielding, the material is in a solid-state with a constant elastic modulus. [...] Read more.

In this paper, we focus on the first stage of transition to Rayleigh–Bénard convection in soft-jammed systems (yield stress fluids) confined in a parallelepiped box heated from the bottom. Up to yielding, the material is in a solid-state with a constant elastic modulus. By means of a linear thermoelastic model, an analytical solution for stresses and strains induced by the gravity and the temperature gradient is derived. The analytical solution allows us to emphasize the appropriate dimensionless parameters. The onset of plastic deformation is then investigated using the classical yield criteria (Tresca, von Mises and Drucker–Prager). This analysis is subsequently applied to experimental data of the literature dealing with Rayleigh–Bénard convection in Carbopol micro gels. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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27 pages, 5001 KiB

Open AccessArticle

Analysis and Computations of Optimal Control Problems for Boussinesq Equations

by Andrea Chierici, Valentina Giovacchini and Sandro Manservisi

Fluids 2022, 7(6), 203; https://doi.org/10.3390/fluids7060203 - 14 Jun 2022

Cited by 6 | Viewed by 2227

Abstract

The main purpose of engineering applications for fluid with natural and mixed convection is to control or enhance the flow motion and the heat transfer. In this paper, we use mathematical tools based on optimal control theory to show the possibility of systematically [...] Read more.

The main purpose of engineering applications for fluid with natural and mixed convection is to control or enhance the flow motion and the heat transfer. In this paper, we use mathematical tools based on optimal control theory to show the possibility of systematically controlling natural and mixed convection flows. We consider different control mechanisms such as distributed, Dirichlet, and Neumann boundary controls. We introduce mathematical tools such as functional spaces and their norms together with bilinear and trilinear forms that are used to express the weak formulation of the partial differential equations. For each of the three different control mechanisms, we aim to study the optimal control problem from a mathematical and numerical point of view. To do so, we present the weak form of the boundary value problem in order to assure the existence of solutions. We state the optimization problem using the method of Lagrange multipliers. In this paper, we show and compare the numerical results obtained by considering these different control mechanisms with different objectives. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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13 pages, 431 KiB

Open AccessArticle

On Mixed Convection in a Horizontal Channel, Viscous Dissipation and Flow Duality

by Antonio Barletta, Michele Celli and Pedro Vayssière Brandão

Fluids 2022, 7(5), 170; https://doi.org/10.3390/fluids7050170 - 13 May 2022

Cited by 4 | Viewed by 1889

Abstract

The conditions defining a stationary fluid flow may lead to a multiplicity of solutions. This circumstance is widely documented in the literature when mixed convection in a vertical channel or duct is accompanied by an important effect of viscous dissipation. Usually, there are [...] Read more.

The conditions defining a stationary fluid flow may lead to a multiplicity of solutions. This circumstance is widely documented in the literature when mixed convection in a vertical channel or duct is accompanied by an important effect of viscous dissipation. Usually, there are double stationary solutions with a parallel velocity field which satisfy given temperature boundary conditions and with a prescribed mass flow rate. However, in a vertical internal flow, the dual solutions can be determined only numerically as they do not have a closed analytical form. This study shows that, in a horizontal channel, stationary mixed convection with viscous dissipation shows up dual flow branches whose mathematical expressions can be determined analytically. The features of these dual flows are discussed. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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20 pages, 7347 KiB

Open AccessArticle

The Emergence and Identification of Large-Scale Coherent Structures in Free Convective Flows of the Rayleigh-Bénard Type

by Sergei Smirnov, Alexander Smirnovsky and Sergey Bogdanov

Fluids 2021, 6(12), 431; https://doi.org/10.3390/fluids6120431 - 29 Nov 2021

Cited by 5 | Viewed by 2771

Abstract

The revealing of the turbulence archetypes is one of the fundamental problems in the study of turbulence, which is important not only from the fundamental point of view but also for practical applications, e.g., in geophysics of ocean and lakes. The paper is [...] Read more.

The revealing of the turbulence archetypes is one of the fundamental problems in the study of turbulence, which is important not only from the fundamental point of view but also for practical applications, e.g., in geophysics of ocean and lakes. The paper is devoted to the study of the emergence of coherent structures and the identification of their turbulent archetypes, typical for the free convective flows of the Rayleigh-Bénard type. Using Direct Numerical Simulation, we perform a numerical study of two refined convective flows: convection in a cylinder heated from below and internally heated convection in a layer. The main purpose of the study is identifying coherent structures (CS), investigating its main features and properties, and determining the turbulence archetypes using the anisotropy invariant map (AIM). We show that, in both configurations considered, CS takes place. In a cylinder, CS is a single large-scale vortex that can rotate azimuthally in non-titled container, but is almost “fixed” in the case of slightly tilted cylinder; in a layer, CS is a quasi-2D vortex, which can arise, exist for some time, disrupt, and then re-emerge again in the orthogonal direction. Nevertheless, the turbulence archetypes represented by the AIM are quite similar for both cases, and there are the distinct CS fingerprints on AIM. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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17 pages, 503 KiB

Open AccessArticle

Two-Dimensional Steady Boussinesq Convection: Existence, Computation and Scaling

by Jeremiah S. Lane and Benjamin F. Akers

Fluids 2021, 6(12), 425; https://doi.org/10.3390/fluids6120425 - 25 Nov 2021

Cited by 4 | Viewed by 2434

Abstract

This research investigates laser-induced convection through a stream function-vorticity formulation. Specifically, this paper considers a solution to the steady Boussinesq Navier–Stokes equations in two dimensions with a slip boundary condition on a finite box. A fixed-point algorithm is introduced in stream function-vorticity variables, [...] Read more.

This research investigates laser-induced convection through a stream function-vorticity formulation. Specifically, this paper considers a solution to the steady Boussinesq Navier–Stokes equations in two dimensions with a slip boundary condition on a finite box. A fixed-point algorithm is introduced in stream function-vorticity variables, followed by a proof of the existence of steady solutions for small laser amplitudes. From this analysis, an asymptotic relationship is demonstrated between the nondimensional fluid parameters and least upper bounds for laser amplitudes that guarantee existence, which accords with numerical results implementing the algorithm in a finite difference scheme. The findings indicate that the upper bound for laser amplitude scales by

O ({Re}^{- 2} {Pe}^{- 1} {Ri}^{- 1})

when

Re ≫ Pe

, and by

O ({Re}^{- 1} {Pe}^{- 2} {Ri}^{- 1})

when

Pe ≫ Re

. These results suggest that the existence of steady solutions is heavily dependent on the size of the Reynolds (Re) and Peclet (Pe) numbers, as noted in previous studies. The simulations of steady solutions indicate the presence of symmetric vortex rings, which agrees with experimental results described in the literature. From these results, relevant implications to thermal blooming in laser propagation simulations are discussed. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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14 pages, 3831 KiB

Open AccessArticle

Parametric Study of Unsteady Flow and Heat Transfer of Compressible Helium–Xenon Binary Gas through a Porous Channel Subjected to a Magnetic Field

by Pornthep Pattanavanitkul and Watit Pakdee

Fluids 2021, 6(11), 392; https://doi.org/10.3390/fluids6110392 - 1 Nov 2021

Cited by 1 | Viewed by 1533

Abstract

A numerical analysis of unsteady fluid and heat transport of compressible Helium–Xenon binary gas through a rectangular porous channel subjected to a transverse magnetic field is herein presented. The binary gas mixture consists of Helium (He) and Xenon (Xe). In addition, the compressible [...] Read more.

A numerical analysis of unsteady fluid and heat transport of compressible Helium–Xenon binary gas through a rectangular porous channel subjected to a transverse magnetic field is herein presented. The binary gas mixture consists of Helium (He) and Xenon (Xe). In addition, the compressible gas properties are temperature-dependent. The set of governing equations are nondimensionalized via appropriate dimensionless parameters. The dimensionless equations involve a number of dimensionless groups employed for detailed parametric study. Consequently, the set of equations is discretized using a compact finite difference scheme and solved by using the 3rd-order Runge–Kutta method. The model’s computed results are compared with data from past literature, and very favorable agreement is achieved. The results show that the magnetic field, compressibility and variable fluid properties profoundly affect heat and fluid transport. Variations of density with temperature as well as pressure result in an asymmetric mass flow profile. Furthermore, the friction coefficient is greater for the upper wall than for the lower wall due to larger velocity gradients along the top wall. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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13 pages, 5939 KiB

Open AccessArticle

Parameter Variability in Viscous Convection

by Ekkehard Holzbecher

Fluids 2021, 6(11), 376; https://doi.org/10.3390/fluids6110376 - 22 Oct 2021

Viewed by 1341

Abstract

For the optimal design of cooling and heating devices, the properties of the included fluids are crucial. The temperature dependence of viscosity deserves attention, as changes can be one order of magnitude or more. Here we examine the influence on convective motions by [...] Read more.

For the optimal design of cooling and heating devices, the properties of the included fluids are crucial. The temperature dependence of viscosity deserves attention, as changes can be one order of magnitude or more. Here we examine the influence on convective motions by simulating a heating and cooling experiment with a vertical cylinder by finite element computational fluid dynamics (CFD) models. Such an experimental setup in which flow patterns are determined by transient viscous convection has not been simulated before. Evaluating the general behavior of the experiment in 2D, we find a dynamic phase after and before phases with moderate changes. Flow patterns in the dynamic phase change significantly with the temperature range of the experiment. We compare the outcome of the numerical models with results from laboratory experiments, finding major discrepancies concerning the flow patterns in the dynamic phase. 3D modeling shows weaker dynamics but does not show good timing with the experiment. The study depicts the importance of parameter dependencies for convective motions and demonstrates the capabilities and limitations of models to reproduce details of viscous convection. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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10 pages, 3210 KiB

Open AccessArticle

Numerical and Analytical Studies of Soret-Driven Convection Flow Inside an Annular Horizontal Porous Cavity

by Abdelkader Mojtabi, Khairi Sioud, Alain Bergeon and Marie Catherine Charrier-Mojtabi

Fluids 2021, 6(10), 357; https://doi.org/10.3390/fluids6100357 - 11 Oct 2021

Cited by 4 | Viewed by 1908

Abstract

This paper studies the species separation of a binary fluid in a porous cavity between two horizontal concentric cylinders, submitted to a temperature gradient. The thickness of the cavity is

e = R_{o} - R_{i}

, where

R_{i}

and [...] Read more.

This paper studies the species separation of a binary fluid in a porous cavity between two horizontal concentric cylinders, submitted to a temperature gradient. The thickness of the cavity is

e = R_{o} - R_{i}

, where

R_{i}

and

R_{o}

are the internal and external radius, respectively. The numerous previous experiments performed in thermogravitational vertical columns (TGCs) showed that in order to obtain a significant separation, the thickness of the cell must be very small, compared with its height. Therefore, in our configuration, we considered

e ≪ R_{i}

. The solution is assumed to be axisymmetric. Under the assumptions of parallel flow and forgotten effect, an analytical solution is obtained using Maple software, and the results are compared with those found numerically using Comsol Multiphysics. In natural convection, our results are in very good agreement with those evaluated with a regular perturbation method in powers of the dimensionless gap width

ε = \frac{e}{R_{i}}

of order 15, and with the Galerkin method. The species separation calculated for our configuration is very close to the one obtained in a TGC column of height:

H = π R_{i} .

One of the main interests of the analytical solution presented here is that it can be used as a basic solution for a stability study analysis. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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13 pages, 465 KiB

Open AccessArticle

Linear Stability of a Steady Convective Flow between Permeable Cylinders

by Maksims Zigunovs, Andrei Kolyshkin and Ilmars Iltins

Fluids 2021, 6(10), 342; https://doi.org/10.3390/fluids6100342 - 28 Sep 2021

Cited by 1 | Viewed by 1557

Abstract

Linear stability analysis of a steady convective flow in a tall vertical annulus caused by nonlinear heat sources is conducted in the paper. Heat sources are generated as a result of a chemical reaction. The effect of radial cross-flow through permeable porous walls [...] Read more.

Linear stability analysis of a steady convective flow in a tall vertical annulus caused by nonlinear heat sources is conducted in the paper. Heat sources are generated as a result of a chemical reaction. The effect of radial cross-flow through permeable porous walls of the annulus is analyzed. The problem is relevant to biomass thermal conversion. The base flow solution is obtained by solving nonlinear boundary value problem. Linear stability analysis is performed, using collocation method. The calculations show that radial inward or outward flow has a stabilizing effect on the flow, while the increase in the Frank–Kamenetskii parameter (proportional to the intensity of the chemical reaction) destabilizes the flow. The increase in the Reynolds number based on the radial velocity leads to the appearance of the second minimum on the marginal stability curves. The rate of increase in the critical Grashof number with respect to the Reynolds number is different for inward and outward radial flows. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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16 pages, 3415 KiB

Open AccessArticle

Analysis of Temperature Anomalies during Thermal Monitoring of Frozen Wall Formation

by Mikhail Semin, Ivan Golovatyi and Aleksei Pugin

Fluids 2021, 6(8), 297; https://doi.org/10.3390/fluids6080297 - 22 Aug 2021

Cited by 10 | Viewed by 2339

Abstract

The paper describes a distributed temperature sensing system that was used to monitor the artificial freezing of soils during the construction of a potash mine shaft. The technique of reconstructing the temperature field by solving the inverse problem in the entire volume of [...] Read more.

The paper describes a distributed temperature sensing system that was used to monitor the artificial freezing of soils during the construction of a potash mine shaft. The technique of reconstructing the temperature field by solving the inverse problem in the entire volume of frozen soils using the measured temperatures in four thermal monitoring (TM) wells is described. Two local anomalies in temperature distributions in TM wells are described and analyzed theoretically using thermo-hydraulic modeling. The first anomaly concerns the asymmetric temperature distribution in one of the soil layers and is associated with the influence of natural groundwater flow in the horizontal direction. The second anomaly consists of a sharp decrease in water temperature in the section of the TM well located inside the freezing contour. Calculations showed that it is most likely associated with the entry of cold groundwater from the overlying layers of soils through a well filter at a depth of 160 m and the subsequent movement of the water up the well. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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37 pages, 7503 KiB

Open AccessArticle

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

by Amel Bouachir, Mahmoud Mamou, Redha Rebhi and Smail Benissaad

Fluids 2021, 6(8), 292; https://doi.org/10.3390/fluids6080292 - 20 Aug 2021

Cited by 3 | Viewed by 2268

Abstract

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 [...] Read more.

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,

R_{T C}^{s u p}

, and overstable,

R_{T C}^{o v e r}

, 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,

R_{T C}^{H o p f}

, 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. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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17 pages, 2871 KiB

Open AccessArticle

Passive Flow Control for Drag Reduction on a Cylinder in Cross-Flow Using Leeward Partial Porous Coatings

by Imogen Guinness and Tim Persoons

Fluids 2021, 6(8), 289; https://doi.org/10.3390/fluids6080289 - 17 Aug 2021

Cited by 4 | Viewed by 3075

Abstract

This paper presents a numerical study on the impact of partial leeward porous coatings on the drag of circular cylinders in cross-flow. Porous coatings are receiving increasing attention for their potential in passive flow control. An unsteady Reynolds-averaged Navier–Stokes model was developed that [...] Read more.

This paper presents a numerical study on the impact of partial leeward porous coatings on the drag of circular cylinders in cross-flow. Porous coatings are receiving increasing attention for their potential in passive flow control. An unsteady Reynolds-averaged Navier–Stokes model was developed that agreed well with the numerical and experimental literature. Using the two-equation shear stress transport

k - ω

turbulence model, 2D flow around a circular cylinder was simulated at

R e

=

4.2 \times 10^{4}

with five different angles of partial leeward porous coatings and a full porous coating. For coating angles below

130^{\circ}

, the coating resulted in an increase in pressure on the leeward side of the cylinder. There was a significant reduction in the fluctuation of the pressure and aerodynamic forces and a damping effect on vortex shedding. Flow separation occurred earlier; the wake was widened; and there was a decrease in turbulence intensity at the outlet. A reduction of drag between 5 and 16% was measured, with the maximum at a 70

^{\circ}

coating angle. The results differed greatly for a full porous coating and a 160

^{\circ}

coating, which were found to cause an increase in drag of 42% and 43%, respectively. The results showed that leeward porous coatings have a clear drag-reducing potential, with possibilities for further research into the optimum configuration. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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27 pages, 7264 KiB

Open AccessArticle

Onset of Linear and Nonlinear Thermosolutal Convection with Soret and Dufour Effects in a Porous Collector under a Uniform Magnetic Field

by Redha Rebhi, Mahmoud Mamou and Noureddine Hadidi

Fluids 2021, 6(7), 243; https://doi.org/10.3390/fluids6070243 - 3 Jul 2021

Cited by 4 | Viewed by 2271

Abstract

The present paper reports on an analytical and numerical study of combined Soret and Dufour effects on thermosolutal convection in a horizontal porous cavity saturated with an electrically conducting binary fluid under a magnetic field. The horizontal walls of the system are subject [...] Read more.

The present paper reports on an analytical and numerical study of combined Soret and Dufour effects on thermosolutal convection in a horizontal porous cavity saturated with an electrically conducting binary fluid under a magnetic field. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The main governing parameters of the problem are the Rayleigh, the Hartmann, the Soret, the Dufour and the Lewis numbers, the buoyancy ratio, the enclosure aspect ratio, and the normalized porosity of the porous medium. An asymptotic parallel flow approximation is applied to determine the onset of subcritical nonlinear convection. In addition, a linear stability analysis is performed to predict explicitly the thresholds for the onset of stationary, overstable and oscillatory convection, and the Hopf bifurcation as functions of the governing parameters. The combined effect of a magnetic field, Soret and Dufour parameters have a noticeable influence on the intensity of the convective flow, the heat and mass transfer rates, and the thresholds of linear convection. It is found that the imposition of a magnetic field delays the onset of convection and its intensification can lead to the total suppression of the convective currents. The heat transfer rate increases with the Dufour number and decreases with the Soret number and vice versa for the mass transfer rate. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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16 pages, 4625 KiB

Open AccessArticle

Heat Enhancement Effectiveness Using Multiple Twisted Tape in Rectangular Channels

by M. Ziad Saghir, Ayman Bayomy and Md Abdur Rahman

Fluids 2021, 6(5), 188; https://doi.org/10.3390/fluids6050188 - 14 May 2021

Cited by 1 | Viewed by 2141

Abstract

Heat enhancement and heat removal have been the subject of considerable research in the energy system field. Flow-through channels and pipes have received much attention from engineers involved in heat exchanger design and construction. The use of insert tape is one of many [...] Read more.

Heat enhancement and heat removal have been the subject of considerable research in the energy system field. Flow-through channels and pipes have received much attention from engineers involved in heat exchanger design and construction. The use of insert tape is one of many ways to mix fluids, even in a laminar flow regime. The present study focused on the use of different twisted tapes with different pitch-to-pitch distances and lengths to determine the optimum design for the best possible performance energy coefficient. The results revealed that twisted tape of one revolution represented the optimal design configuration and provided the largest Nusselt number. The length of the tape played a major role in the pressure drop. The results revealed that the insertion of a shorter twisted tape can create mixing while minimizing the changes in the pressure drop. In particular, the best performance evaluation criterion is found for a short tape located towards the exit of the channel. The highest performance energy coefficient was obtained for the half-twisted tape for a Reynolds number varying between 200 and 600. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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22 pages, 406 KiB

Open AccessArticle

Cross Diffusion Effect on Linear and Nonlinear Double Diffusive Convection in a Viscoelastic Fluid Saturated Porous Layer with Internal Heat Source

by A.A. Altawallbeh

Fluids 2021, 6(5), 182; https://doi.org/10.3390/fluids6050182 - 12 May 2021

Cited by 11 | Viewed by 2451

Abstract

Double diffusive convection in a binary viscoelastic fluid saturated porous layer in the presence of a cross diffusion effect and an internal heat source is studied analytically using linear and nonlinear stability analysis. The linear stability theory is based on the normal mode [...] Read more.

Double diffusive convection in a binary viscoelastic fluid saturated porous layer in the presence of a cross diffusion effect and an internal heat source is studied analytically using linear and nonlinear stability analysis. The linear stability theory is based on the normal mode technique, while the nonlinear theory is based on a minimal representation of truncated double Fourier series. The modified Darcy law for the viscoelastic fluid of the Oldroyd type is considered to model the momentum equation. The onset criterion for stationary and oscillatory convection and steady heat and mass transfer have been obtained analytically using linear and nonlinear theory, respectively. The combined effect of an internal heat source and cross diffusion is investigated. The effects of Dufour, Soret, internal heat, relaxation and retardation time, Lewis number and concentration Rayleigh number on stationary, oscillatory, and heat and mass transport are depicted graphically. Heat and mass transfer are presented graphically in terms of Nusselt and Sherwood numbers, respectively. It is reported that the stationary and oscillatory convection are significantly influenced with variation of Soret and Defour parameters. An increment of the internal heat parameter has a destabilizing effect as well as enhancing the heat transfer process. On the other hand, an increment of internal heat parameter has a variable effect on mass transfer. It is found that there is a critical value for the thermal Rayleigh number, below which increasing internal heat decreases the Sherwood number, while above it increasing the internal heat increases the Sherwood number. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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20 pages, 3515 KiB

Open AccessArticle

A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

by Seyed Amin Nabavizadeh, Himel Barua, Mohsen Eshraghi and Sergio D. Felicelli

Fluids 2021, 6(4), 148; https://doi.org/10.3390/fluids6040148 - 8 Apr 2021

Cited by 6 | Viewed by 2594

Abstract

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow [...] Read more.

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations. Full article

(This article belongs to the Special Issue Convection in Fluid and Porous Media)

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