Double-diffusive Natural Convection Research Articles

Numerical investigation of double-diffusive natural convection in a staggered cavity with two triangular obstacles

Numerical investigation of double-diffusive natural convection in a staggered cavity with two triangular obstacles

Thermosolutal natural convection in a partly porous cavity with sinusoidal wall heating and cooling

PurposeThis paper aims to consider numerical analysis of laminar double-diffusive natural convection inside a non-homogeneous closed medium composed of a saturated porous matrix and a clear binary fluid under spatial sinusoidal heating/cooling on one side wall and uniform salting.Design/methodology/approachThe domain of interest is a partially square porous enclosure with sinusoidal wall heating and cooling. The fluid flow, heat and mass transfer dimensionless governing equations associated with the corresponding boundary conditions are discretized using the finite volume method. The resulting algebraic equations are solved by an in-house FORTRAN code and the SIMPLE algorithm to handle the non-linear character of conservation equations. The validity of the in-house FORTRAN code is checked by comparing the current results with previously published experimental and numerical works. The effect of the porous layer thickness, the spatial frequency of heating and cooling, the Darcy number, the Rayleigh number and the porous to fluid thermal conductivity ratio is analyzed.FindingsThe results demonstrate that for high values of the spatial frequency of heating and cooling (f = 7), temperature contours show periodic variations with positive and negative values providing higher temperature gradient near the thermally active wall. In this case, the temperature variation is mainly in the porous layer, while the temperature of the clear fluid region is practically the same as that imposed on the left vertical wall. This aspect can have a beneficial impact on thermal insulation. Besides, the porous to fluid thermal conductivity ratio, , has practically no effect on , contrary to where a strong increase is observed as is increased from 0.1 to 100, and much heat transfer from the hot wall to the clear fluid via the porous media is obtained.Practical implicationsThe findings are useful for devices working on double-diffusive natural convection inside non-homogenous cavities.Originality/valueThe authors believe that the presented results are original and have not been published elsewhere.

Analysis of Double-diffusive natural convection in a solar distiller embedded with PCM and cooled with external water stream

BackgroundThe increase demand of water for irrigation and human activities leads to a global development of alternative methods to produce distillate water especially from sea. In this context, the use of solar distiller instead of the classic distillation process is a good solution to preserve environment and reduce the use of fuel. This study explores the advantages of the classic solar still by studying the effect of the PCM-RT42. Hence, a detailed investigation of the heat and mass transfer of a single slope solar still incorporation PCM-RT42 as heat storage system will be presented. MethodsThe governing equations are solved numerically with employing the finite volume method. The next scopes of parameters are utilized in the computations: dimensionless time (τ = 4.2×10–3, 25.2×10–3, and 50.4×10–3), Rayleigh number (104 ≤ Ra ≤ 106), buoyancy ratio (1 ≤ N ≤ 5). Mixture Prandtl number (Prm), Schmidt number (Sc) and Lewis number (Le) are presumed as fixed to 0.705, 0.613 and 0.869, respectively. Significant FindingsThe results show the good effect of the PCM-RT42 on the transfer of heat and mass compared to the initial time for low Ra. However, for Ra=105 and 106, a reduction in the efficiency of condensation and the performance of the solar distiller is observed.

Numerical simulation on double diffusion natural convection of a power-law nanofluid within double wavy cavity

In the present paper, the effect of double diffusion natural convection fluid flow inside the double wavy enclosure using the mesh-free method is investigated. The enclosure is filled with nanofluid whose base fluid is non-Newtonian. The results are obtained for the variation in Brownian motion parameter (0.2–0.8), buoyancy ratio parameter (0.2–1), power-law index (0.2–1), thermophoresis parameter (0.2–0.8), Rayleigh number (103–105), and Lewis number (1–5) on mass and heat transfer. It is explored that the mass and heat transfer rate increases with increase in the Rayleigh number and buoyancy ratio. Heat transfer rate decreases with increase in the thermophoresis parameter, Lewis number, Brownian motion, and power-law index, whereas mass transfer rate increases. Such type of enclosure has direct application in heat exchanger devices, the double-wall thermal insulation system, and microelectronic devices. Parallel implementation with the hybrid [EFGM (element free Galerkin method)/FEM (finite element method)] method has been used for the reduction of the running cost to ensure efficiency, which is the novel contribution of the author.

MHD Double-Diffusive Natural Convection in a Closed Space Filled with Liquid Metal: Mesoscopic Analysis

In this paper, the lattice Boltzmann approach is carried out to study the double-diffusive natural convection in a space encapsulating liquid metal is presented. The Uniform magnetic field is applied horizontally at the square domain and an insulated rectangular block is kept stationary at the center of the cavity. The linear increment of temperature and concentration is used at the left wall and cold temperature is applied at the right wall. Horizontal walls are adiabatic conditions. Horizontal walls are adiabatic conditions. The numerical analysis is performed at the range of Rayleigh number (103 ≤ Ra ≤ 105), Lewis number (2 ≤ Le ≤ 10), buoyancy ratio (-2 ≤ N ≤ 2), Hartmann number (0 ≤ Ha ≤ 50) with Prandtl number (Pr) = 0.054. Results show that the increase in Ra tends to maximize heat and mass transfer rate while increasing Ha, decreases the same. The rise in Le diminishes heat transfer marginally but increasing the mass transfer significantly. The effect of N differs with different operating conditions, in general, the rate of heat and mass transfer is found to decrease with a decrease of N value.

Influence of porous circular cylinder on MHD double-diffusive natural convection and entropy generation

In this study, the significance of porous circular cylinder and magnetic field on the double-diffusive natural convection and entropy generation in an enclosure is analysed using lattice Boltzmann method. Prime objective of this study is to assess the impression of permeability, buoyancy force variation, magnetic field and its direction on the thermo-solutal convection around a porous zone. The parametric study concentrates on the effects of Buoyancy ratio (BR=−5 to 5), Darcy number (Da=10−5, 10−4, & 10−3), Hartmann number (Ha=0, 25, & 50), and magnetic field angle (γM=0∘, 45∘, & 90∘) on the flow, heat and concentration transfer, and the variation in irreversibilities in and around the porous circular cylinder with high temperature and concentration. The Darcy-Brinkman-Forchheimer model is coupled with LB flow evolution equation to acquire flow features in the porous cylinder. Results indicate that Da, BR, and γM increment improves the heat and concentration transfers. Permeability increment significantly enhances the flow-field intensity around the cylinder. Effect of Ha on the reduction in mean Nusselt number and Sherwood number can be significantly controlled by the direction of magnetic field. However, magnetic field influences trivially on the flow field in the porous cylinder. Besides, the amalgamation of Da and γM induces unsteady characteristics in the enclosure. Also, γM increment widens the range of BR for the production of unsteady traits. The entropy generation augments with Ha, when the magnetic field direction is aligned with the fluid flow. Further, the irreversibilities due to concentration transfer is observed to be higher than that of other associated irreversibilities in the enclosure. The increment in BR (positive values) tends to suppress the fluid-friction and magnetic irreversibilities.

Conjugate fluid, heat and species transports inside an enclosure containing miscellaneous solid arrays: General models of electronic cooling and pollutant removals

Double-diffusive natural convection in a vertical enclosure containing various solid block arrays is numerically and analytically investigated in present work, where heat and species source and sink are simultaneously attached on the walls. Rayleigh number, buoyancy force ratio, number of inner solid blocks, solid thermal conductivity and mass diffusion coefficient have been varied to observe inherent flow structures and mechanism of thermal and mass transports, regarding of different levels of solid-to-fluid volume ratios. Correlations have been presented for different flow regimes, namely thermal buoyancy driven flow and solutal buoyancy driven flow. Simulation and correlation results demonstrate that influences of thermal conductivity and mass diffusion coefficient of the solid block arrays on average Nusselt and Sherwood numbers are not evident compared with that of Rayleigh number. Furthermore, there is a positive correlation between average Nusselt number and Sherwood number. In addition, under certain values of Rayleigh number, absolute values of buoyancy force ratio close to unity will cause multiple steady solutions in pure natural convection. This research could benefit the future thermal and species management for electronics and built environment.

A mesoscopic model for thermal–solutal problems of power-law fluids through porous media

A mesoscopic method based on the lattice Boltzmann method for thermal–solutal incompressible non-Newtonian power-law fluids through porous media is introduced. The macroscopic equations of different representative element volume (REV) models of porous media are presented, and the equations of power-law fluids through porous media for various REV models reported. The general mesoscopic model for two- and three-dimensional cases are presented, and their derivations shown. To demonstrate the ability of the proposed method, natural convection and double-diffusive natural convection of Newtonian and power-law fluids in porous cavities are studied, and the results are validated against previous findings. Finally, double-diffusive natural convection in a porous cubic cavity filled with a non-Newtonian power-law fluid is simulated by the proposed method.

A lattice Boltzmann model for the coupled cross-diffusion-fluid system

In this paper, we propose a lattice Boltzmann (LB) model for the generalized coupled cross-diffusion-fluid system. Through the direct Taylor expansion method, the proposed LB model can correctly recover the macroscopic equations. The cross diffusion terms in the coupled system are modeled by introducing additional collision operators, which can be used to avoid special treatments for the gradient terms. In addition, the auxiliary source terms are constructed properly such that the numerical diffusion caused by the convection can be eliminated. We adopt the developed LB model to study two important systems, i.e., the coupled chemotaxis-fluid system and the double-diffusive convection system with Soret and Dufour effects. We first test the present LB model through considering a steady-state case of coupled chemotaxis-fluid system, then we analyze the influences of some physical parameters on the formation of sinking plumes. Finally, the double-diffusive natural convection system with Soret and Dufour effects is also studied, and the numerical results agree well with some previous works.

Thermal radiation and double diffusive effects on bioconvection flow of a nanofluid past an inclined wavy surface

In this article, the influence of thermal radiation on double-diffusive natural convection of a nanofluid past an inclined wavy surface in the presence of gyrotactic microorganisms is analysed. A coordinate transformation is used to transform the complex wavy surface to a smooth surface. Using the pseudo-similarity variables, the governing non-linear differential equations and their associate boundary stipulations are non-dimensionalized. The resulting system of non-linear partial differential equations is linearized using a local linearization method. The obtained linear system of partial differential equations is solved using the bivariate Chebyshev pseudo-spectral collocation method. The effect of pertinent physical and geometrical parameters on the physical quantities of the flow are illustrated through graphs and analyzed.

On the performance of curvature stabilization time stepping methods for double-diffusive natural convection flows in the presence of magnetic field

This paper considers analytically and numerically the curvature-based stabilization method for double-diffusive natural convection flows in the presence of magnetic field. Unconditionally stable and optimally accurate second-order approximations are obtained. The impact of curvature stabilization on different flow fields are presented for several numerical test problems.

A Note on the Significance of Entropy Generation and Work Fluxes on Humid Air Inside a Solar Still Due to Double-Diffusive Natural Convection

The motion of the humid air inside a solar still is due to double-diffusive natural convection, where convective heat and mass transfer phenomena are encountered. The humid air, an intermediate medium between the evaporating and the condensing surfaces of the solar still, is regarded as a heat engine that absorbs heat from the free surface of the warmed brackish or saline water and converts it into work to carry up the water vapor molecules to the inner surface of the glass cover. Like all heat engines, the humid air work is accompanied by a degraded energy due to the presence of irreversibilities. The aim of the present study is to give answers about the internal irreversibility origins and the associated work fluxes of the humid air inside the solar still due to double-diffusive natural convection. It is for the first time that the internal entropy generation and the work fluxes formulations are developed and investigated for the humid air inside a solar still. It is found that the irreversibility rate due to fluid friction is the major contributor of the total entropy generation for N > 0.3. The increase in the temperature and the concentration gradients enhances the augmentation of all irreversibility rates. The second law efficiency is an important parameter that should be evaluated to assess the system performance. The mean value of the irreversibility percentage is found equal to 6.83%. The reversible and the lost work fluxes increase with the increase in the humid air temperature.

Double-diffusive natural convection in a trapezoidal solar pond with discrete heat boundary conditions: Effects on non-convective zones

A three-dimensional numerical study is conducted to investigate the double-diffusive natural convection inside a trapezoidal solar pond filled with water and salt solution and subjected to discrete heat boundary conditions. It investigates the effect of stored thermal extraction on the non-convective zone (NCZ) of the solar pond. The heat extraction from the middle region on the lower convective zone (LCZ) is modeled as a discrete thermal boundary condition in the NCZ-LCZ. The governing equations are developed using the three-dimensional potential-vorticity formulation and solved using the finite volume method. The numerical computations are performed for the following parameter ranges: Rayleigh number 103 ≤ Ra ≤ 105 and buoyancy ratio－10≤ N ≤0. Two different cases related to the thermal boundary conditions are investigated. The most important results that are drawn from this study are: (i) the non-uniform heat extraction from the LCZ increased due to vortex formation which disturbed the structure of the flow, and (ii) the three-dimensional effects become more pronounced that caused a decrease in the efficiency of the solar pond. Therefore, when extracting the stored heat from the LCZ layer, it is imperative to maintain the surface temperature as constant as possible and to avoid getting discrete heat surfaces.

Double-diffusive natural convection study in a shallow horizontal porous layer filled with a binary fluid and submitted to destabilized conditions in the presence of Soret effect

This paper reports an analytical and numerical study of thermosolutal convection in a Brinkman horizontal porous layer saturated with a binary mixture, destabilized by submitting it either to both heat and mass fluxes (a=0, with Soret effect) or only to a heat flux to recover the case of pure Soret effect (a=1). The analytical solution is derived based on the parallel flow approximation and validated numerically using a finite difference method. A good agreement is found between the predictions of the parallel flow approximation and the numerical results obtained by solving the full governing equations. The governing parameters of this study are the Lewis number, Le, the Rayleigh thermal, RT, the Soret number, Sr, and the buoyancy ratio, φ. The thresholds for the onset of convection and the generated heat and mass transfer rates are examined both in the presence (a=0) and in the absence (a=1) of an external mass flux. The influence of the governing parameters on the onset of motion and the resulting fluid flow, temperature and concentration fields is discussed. It was found that the onset of convection for a=0 and positive values of Sr is delayed compared to the case a=1 (pure Soret effect) and, for the latter case, the onset of convection is delayed compared to a=0 and negative values of the Soret number.

Non-Darcian effect on double-diffusive natural convection inside aninclined square Dupuit-Darcy porous cavity under a magnetic field

This paper presents a numerical study of a double diffusive convection in an inclined square porous cavity filled with an electrically conducting binary mixture. The upper and bottom walls are maintained at a constant temperatures and concentrations whereas the left and right walls are assumed to be adiabatic and impermeable. A uniform and tilted magnetic field is applied at an angle, ?, about the horizontal, it is obvious that this is related to the orientation of the magnetic force that can help or oppose the buoyant force. The Dupuit-Darcy flow model, which includes effects of the inertial parameter, with the Boussinesq approximation, energy, and species transport equations are solved numerically using the classical finite difference method. Governing parameters of the problem under study are the thermal Rayleigh number, Hartmann number, Lewis number, the buoyancy ratio, inclination angle, and tilting angle of the magnetic field. The numerical results are reported on the contours of streamline, temperature, and concentration and for the average Nusselt and Sherwood numbers for various parametric conditions. It is demonstrated that both the inertial effect parameter and the magnetic field, have a strong influence on the strength of the natural convection heat and mass transfer within the porous layer.

Effects of buoyancy ratio on diffusion of solid particles inside a pipe during double diffusive flow of a nanofluid

PurposeThe purpose of this study is to use an incompressible smoothed particle hydrodynamics (ISPH) method for simulating buoyancy ratio and magnetic field effects on double diffusive natural convection of a cooper-water nanofluid in a cavity. An open pipe is embedded inside the center of a cavity, and it is occupied by solid particles.Design/methodology/approachThe dimensionless governing equations in Lagrangian form were solved by ISPH method. Two different thermal conditions were considered for the solid particles. The actions of the solid particles were tracked inside a cavity. The effects of Hartman parameter, Rayleigh number, nanoparticles volume fraction and Lewis number on features of heat and mass transfer and flow field were tested.FindingsThe results showed that the buoyancy ratio changes the directions of the solid particles diffusion in a cavity. The hot solid particles were raised upwards at aiding mode (N > 0) and downwards at an opposing mode (N < 0). A comparison is made with experimental and numerical simulation results, and it showed a well agreement.Originality/valueNovel studies for the impacts of buoyancy ratio on the diffusion of solid particles embedded in an open pipe during double-diffusive flow were conducted.

Magnetic field effect on double-diffusion with magnetic and non-magnetic nanofluids

Magnetic nanofluids also are known as ferrofluids behave differently under magnetic field effect in comparison to non-magnetic nanofluids. The inclusion of magnetic forces term into the governing equations of magnetic media gives rise to the magnetohydrodynamics of magnetic nanofluids, also named as ferrohydrodynamics. This ferrohydrodynaimcs claims promising applications Rosensweig (1985)[1] with the field of new phenomena Berkovsky and Bashtovoy (1996)[2]. In the present numerical study, 2D laminar steady governing equations for double-diffusive natural convection with inclined magnetic forces for magnetic nanofluid Fe3O4/H2O and non-magnetic nanofluid Cu/H2O inside an exponentially heated and concentrated enclosure have been solved via finite-difference based stream-vorticity approach. Further, a comparative study has been conducted to analyze the impact of the magnetic field upon magnetic nanofluid Fe3O4/H2O and non-magnetic nanofluid Cu/H2O. Influence of various parameters namely; Rayleigh number (Ra), Lewis number (Le), buoyancy ratio (N), Hartmann number (Ha), nanoparticle volume fraction (ϕ), and magnetic field inclination angle (γ) on heat and mass transfer has been studied in detail. Heat and mass lines visualization techniques have been used for better insight of heat and mass transfer. The present work validates against experimental and numerical benchmark results and found to be in satisfactory acceptance. Total heat and mass transfers strengthen with the rise in inclination angle (γ) of magnetic field. It concludes that the effect of the magnetic field at lower value of Rayleigh number on overall heat transfer utilizing magnetic nanofluid Fe3O4/H2O is more effective than non-magnetic nanofluid Cu/H2O. Whereas magnetic field effect on mass transfer is more effective at a higher value of Rayleigh number. Percentage reduction in mass transfer is 10% has been found for Fe3O4/H2O, which is less than 12% of Cu/H2O nanofluid at higher value of volume concentration of nanoparticle.

Lattice Boltzmann simulation of magneto-hydrodynamic double-diffusive natural convection in an enclosure with internal heat and solute source using nanofluids

Magneto-hydrodynamic double-diffusive natural convection in a cavity is numerically investigated in the present work. Al2O3, Cu, and Ag based nanofluids in a square cavity with a thermal and solute source in the center, and uniform magnetic field are considered. The Patel model is employed to estimate the thermal conductivity of applied nanofluids, and the numerical calculation is based on the implementation of the lattice Boltzmann method and utilizing the standard $$D_{2} Q_{9}$$ model to study the heat transfer, and also species concentration. A parametric study is carried out to observe the influence of the type, the volume fraction of nanoparticle ( $$\phi = 0 - 5\%$$ ), Rayleigh ( $$Ra = 10^{4} - 10^{5} - 10^{6} )$$ , Lewis $$\left( {0.1 - 2 - 10} \right)$$ , and Hartmann number $$\left( {10 - 20 - 100} \right)$$ on average Nusselt and Sherwood numbers, flow fields, temperature, and concentration distribution. The results show that an augment in nanoparticle volume fraction and Rayleigh number increased the average Nusselt and Sherwood numbers. Lewis number showed a significant impact on mass transfer rate. However, it did not affect the heat transfer rate remarkably. Applying a magnetic field caused a reduction in flow circulation which resulted in a decline in heat and mass transfer. A comparison of the simulation outcome with the available data shows that the generated code perfectly captures the fluid flow behavior and heat transfer process as a function of the affecting parameters.

Uncertainty quantification and global sensitivity analysis of double-diffusive natural convection in a porous enclosure

In this paper, detailed uncertainty propagation analysis (UPA) and variance-based global sensitivity analysis (GSA) are performed on the widely adopted double-diffuse convection (DDC) benchmark problem of a square porous cavity with horizontal temperature and concentration gradients. The objective is to understand the impact of uncertainties related to model parameters on metrics characterizing flow, heat and mass transfer processes, and to derive spatial maps of uncertainty and sensitivity indices which can provide physical insights and a better understanding of DDC processes in porous media. DDC simulations are computationally expensive and UPA and GSA require large number of simulations, so an appropriate strategy is developed to reduce the computational burden. The approach is built on two pillars: (a) an efficient numerical simulator based on the Fourier series method that generates training data, and (b) polynomial chaos expansion (PCE) meta-models that are trained using the simulator data, and then replace the numerical model in UPA and GSA. Assuming that the Rayleigh number (Ra), the solutal to thermal buoyancy ratio (Nb) and the Lewis number (Le) are the uncertain input variables, the results of UPA show that the zones of high temperature and concentration variability are located in the regions where the flow is mainly driven by the buoyancy effects. GSA indicates that Nb is the most influential parameter affecting the temperature and concentration fields, followed respectively by Ra and Le. For the heat-driven flow case (Nb>−1), the concentration field is more influenced by Le than Ra. For deeper understanding of uncertainty propagation, we estimate the bias introduced by replacing uncertain parameters by deterministic values. The resulting spatial maps of the difference between deterministic output and stochastic mean show that a deterministic approach leads to different zones where the temperature, concentration and velocity fields can be either overestimated or underestimated. The conclusions drawn in this work are likely to be helpful in different applications involving DDC in porous enclosures leading to convective circulation cells.

Three-Dimensional Numerical Analysis on Performance Enhancement of Micropolar Hybrid Nanofluid in Comparison with Simple Nanofluid

The objectives of the present research work are the three-dimensional computational analysis and predictions on double-diffusive natural convection in a cubic cavity filled with Cu–Al2O3/water micropolar hybrid nanofluid. The governing equations are carefully modified employing vorticity–vector potential formulation and are solved by the finite volume method. Performance enhancement of Cu–Al2O3/water micropolar hybrid nanofluid is judiciously compared with the Cu/water simple nanofluid. Besides, the influences of concentration of nanoparticles, Rayleigh number, buoyancy ratio, and micropolar vortex parameter on the flow field and heat transfer are critically analyzed. The results show that heat and mass transfer rates are lower for a micropolar nanofluid model when compared to the pure nanofluid model. The hybrid micropolar nanofluid displays more heat and mass transfer rates for thermal buoyancy-dominated zones when compared with traditional nanofluid. Conversely, the heat and mass transfer rates are decreased when using micropolar hybrid nanofluid for the solutal-dominated regime. The enhancement of micropolar viscosity parameter results in a decrease of average Nusselt and Sherwood numbers which are more perceptible in the thermal buoyancy-dominated flow.