Effects Of Buoyancy Ratio Research Articles

Impact of thermal and solute source-sink combination on thermosolutal convection in a partially active porous annulus

The objective of the current paper is to investigate the thermosolutal flow along with heat and mass dissipation rates in an upright porous annular space subjected to discrete heating and salting along the vertical boundaries with insulated and impermeable horizontal boundaries. To solve the model equations, an implicit finite difference scheme with over relaxation technique has been implemented. The numerical predictions focus specifically on the effect of buoyancy ratio, Lewis number, Darcy number and source-sink arrangements on fluid flow behavior, thermal and solutal characteristics, average Nusselt and Sherwood numbers. The simulations were performed for an extensive range of dimensionless parameters (−10 ≤ N ≤ 10, 0.1 ≤ Le ≤ 1, 10−5 ≤ Da ≤ 10−1) by considering two different types of source-sink arrangements and found that the flow circulation strength is maximum with in-line arrangement of source and sink compared to alternative arrangement. Also, we found that in case-I, regardless of Lewis number, the maximum heat and mass dissipation rates takes place through top source during opposing flow, and through bottom source for aided flow. However, in case-II arrangement, irrespective to type of flow, the greater amount of heat and mass transport is found through the bottom source at the inner cylinder compared to top source placed at outer cylinder.

Numerical framework for unsteady bioconvection flow of third-grade nanofluid over a porous Riga surface with convective Nield approach

The ultra-high significances of thermal radiation, magnetic field and activation energy in thermal enhancement processes allow significant applications in chemical and mechanical engineering, modern technology and various thermal engineering eras. The improvement in energy resources and production became one of the major challenges for researchers and scientists for sustained development in industrial growths. Beside this, the bioconvection assessment in nanomaterials conveys prestigious applications in biotechnology like bio-sensors, enzymes, petroleum industry, bio-fuels and many more. In view of such renewable applications, present exploration discloses unsteady two-dimensional flow of third-grade nanomaterial accommodating gyrotactic microorganisms induced by unsteady stretched Riga sheet in porous medium. The formulated flow problem is further scrutinized by utilizing the chemical reaction, activation energy, thermal radiation and magnetic aspects. The convective Nield constraints are further subjected in the current investigation. Apposite transformations are used to condense the nonlinear developed problem into dimensionless ordinary form. The numerical solution of such similar flow problem is presented via shooting technique. The detailed graphical illustrations of the dimensionless temperature, nanoparticles concentration, velocity and motile microorganisms for physical significance of diverse relevant parameters are deliberated. Furthermore, numerical data of local Sherwood, Nusselt and motile density numbers is designated in tabular form. Study accentuated that velocity increases for higher modified Hartmann and material constants, while the effects of buoyancy ratio and bioconvected Rayleigh numbers are rather opposite. The temperature, microorganism and concentration distributions were enhanced for unsteady parameter. It is also acknowledged that the concentration distribution is enhanced for activating the energy number. Moreover, the microorganism distribution enhances for concentration difference and magneto-porous constants, while bioconvected Lewis and Peclet numbers show conflicting trend.

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.

Heat and Mass Transfer in an Inclined Bi-L-Shaped Layered Porous Media: Effect of Buoyancy Ration

The effect of buoyancy ratio on the two dimensional natural convection heat and mass transfer generated in an inclined square bi-L-shaped layered porous cavity filled with Newtonian fluid has been investigated numerically. Each porous layer is considered isotropic, homogeneous and saturated with the same fluid. The cavity is heated and salted from below where as the vertical walls are assumed to be adiabatic and impermeable. The physical model for the momentum conservation equation makes use of the Darcy-Brinkman-Forcheimer model, and the set of coupled equations is solved using a finite volume approach. The power-law scheme is used to evaluate the flow, heat and mass fluxes across each of the control volume boundaries. Tri diagonal matrix algorithm with under-relaxation is used in conjunction with iterations to solve the nonlinear discretized equations. An in-house code developed for this study is validated using previous studies. The results are presented graphically in terms of streamlines, isotherms and iso-concentrations. In addition, the heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers.

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.

Two Modes of Vibrational Double-Diffusive Instability in a Superposed Fluid-Porous Layer Heated from Below: The Effect of Buoyancy Ratio

The convective double-diffusive instability in a two-layer system consisting of a binary fluid layer overlaying a fluid-saturated porous layer is investigated numerically. The system moves periodically in a vertical direction under the conditions of gravity field. The layers are heated from below and oscillate with high frequency and small amplitude. The instability threshold for the convection onset and the wavelength of convective rolls, which induce as soon as the fluid equilibrium state has lost its stability, are found. The buoyancy ratio and vibrational parameter effects are studied. A region of parameters for the bimodal marginal stability curves is obtained and divided it into parts for the local and large-scale convection onset values. It is revealed that wavelength of stationary convection rolls varies non-monotonically as the buoyancy ratio decreases. The longitudinal scale of rolls reduces sharply at first and then increases gradually. Vibration produces the greatest stabilizing effect on the fluid equilibrium state in a narrow range of small negative and positive buoyancy ratios, which are responsible for a considerable change in the wavelength of rolls. The buoyancy ratio effect on the oscillatory convection rolls is rather weak. The vibration effect on their marginal stability threshold and wavelength is more pronounced.

Influence of density inversion and sinusoidal heating on dual diffusive convection in a water saturated square porous box

The motive of the present numerical study is to analyze the density maximum effect of double diffusive buoyancy-driven convection in a square porous box. The horizontal walls are treated as adiabatic and the vertical walls are maintained with different temperatures. The right wall is heated sinusoidally while the left wall kept with constant temperature. The concentration on the left and right walls of the box are Cl and Ch, respectively, with Ch> Cl. The present study uses finite volume method to solve the governing equations. The effects of buoyancy ratio, density inversion parameter, Darcy number and porosity are studied by using the Brinkmann-Forchheimer extended Darcy model. It is observed that the bicellular structure is formed due to density inversion. When Tm =1, the average mass and thermal energy transfer rates are high for every values of buoyancy ratio. When Tm =0.4, the average mass and thermal energy transfer rates are low for all values of N due to density maximum of water.

Modified Lewis Number and Buoyancy Ratio Effects on Turbulent Double-Diffusive Convection in Porous Media Using the Thermal Nonequilibrium Model

This work presents a study of double-diffusive free convection in a porous square cavity under turbulent flow regime and with aiding drive. The thermal nonequilibrium model was employed to analyze the energy and mass transport across the enclosure. Governing equations were time- and volume-averaged according to the double-decomposition concept. Analysis of a modified Lewis number, Lem, showed that for porous media, this parameter presents opposite behavior when varying the thermal conductivity ratio or the Schmidt number, while maintaining the same value for Lem. Differently form free flow, the existence of the porous matrix contributes to the overall thermal diffusivity of the medium, whereas mass diffusivity is only effective within the fluid phase for an inert medium. Results indicated that increasing Lem through an increase in Sc reduces flow circulation inside porous cavities, reducing Nuw and increasing Shw. Results further indicate that increasing the buoyancy ratio N promotes circulation within the porous cavity, leading to an increase in turbulence levels within the boundary layers. Partial contributions of each phase of the porous cavity (solid and fluid) to the overall average Nusselt number become independent of n for higher values of the thermal conductivity ratio, ks/kf. Further, for high values of ks/kf, the average Nusselt number drops as N increases.

Some Insights on Unsteady Double Diffusive Natural Convection of Porous Medium in Vertical Open-Ended Cylinder

The work presented in this paper deals with combined heat and mass transfer by natural convection in porous media. The aim is to investigate numerically the effect of control parameters on the flow behavior as well as the enhancement of heat transfer in vertical porous enclosure. The side wall temperature is periodic function of time which is the case in several physical problems. The Darcy’s flow model coupled with the energy and mass equations is considered. The numerical results show that the flow’s behavior is strongly dependent on the buoyancy ratio values. Three types of flows take place: chimney, reversal and top aspiration flow. Further, the effect of buoyancy ratio (N) at which the different flow types occur is significantly influenced by the values of control parameters. The relative heat transfer enhancement between constant and periodical wall temperature is profoundly affected by thermal Rayleigh number (Ra), buoyancy ratio and dimensionless amplitude (XA). In the case of opposing double diffusive flow, the relative difference becomes to the favor of the stationary case for high Ra and XA.

Fem Simulation of Triple Diffusive Natural Convection Along Inclined Plate in Porous Medium: Prescribed Surface Heat, Solute and Nanoparticles Flux

In this paper, triple diffusive natural convection under Darcy flow over an inclined plate embedded in a porous medium saturated with a binary base fluid containing nanoparticles and two salts is studied. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. The vertical surface has the heat, mass and nanoparticle fluxes each prescribed as a power law function of the distance along the wall. The boundary layer equations are transformed into a set of ordinary differential equations with the help of group theory transformations. A wide range of parameter values are chosen to bring out the effect of buoyancy ratio, regular Lewis number and modified Dufour parameters of both salts and nanofluid parameters with varying angle of inclinations. The effects of parameters on the velocity, temperature, solutal and nanoparticles volume fraction profiles, as well as on the important parameters of heat and mass transfer, i.e., the reduced Nusselt, regular and nanofluid Sherwood numbers, are discussed. Such problems find application in extrusion of metals, polymers and ceramics, production of plastic films, insulation of wires and liquid packaging.

Numerical Investigations on the Advantage of Nanofluids under DDMC in a Lid‐Driven Cavity

AbstractDouble diffusive mixed convection in a lid‐driven cavity filled with Cu–water nanofluid is studied in detail. Various numerical experiments are conducted under horizontal thermal and concentration gradients. Flow equations were solved in velocity vorticity form using Galerkin's weighted residual finite element method. The Maxwell‐Garnett model and Brinkman models are applied to predict the thermal conductivity and dynamic viscosity of the nanofluid, respectively. The effectiveness of a nanofluid on heat transfer enhancement with respect to change in Richardson number has been studied at different Reynolds numbers for variation in particle volume fraction from 0 to 0.05. Similarly, the effect of buoyancy ratio on heat and mass transfer is presented for buoyancy ratio in the range of −25 to 25. Detailed contour plots comparing the streamlines, temperature, concentration with and without nanoparticles were presented for all the range of parameters considered. The role of particle concentration and change in type of nanofluid has been reported. The average Nusselt number has increased in all the cases where as the Sherwood number slightly decreased with an increase in particle volume fraction. The Ag–water nanofluid showed better improvement in heat transfer characteristics compared to other nanofluids for all Reynolds numbers and particle volume fractions.

Unsteady double diffusive convection in an inclined rectangular lid-driven enclosure with different magnetic field angles and non-uniform boundary conditions

The effect of buoyancy ratio on an unsteady double diffusive natural convection flow in an inclined lid-driven enclosure with different magnetic field angles is studied. The enclosure is non-uniformly heated and concentrated from the bottom side and uniformly heated and concentrated from the left vertical side. The right vertical wall is insulated and the top wall is cooled. The top wall moves in the positive direction with a constant speed from left to right. The governing equations have been solved numerically using the staggered grid finite-difference method to obtain streamlines, isotherms, iso-concentrations, average Nusselt and Sherwood numbers for various values of the buoyancy ratio and different magnetic field angles for three different cavity inclination angles. The results indicate that the flow pattern, temperature and concentration fields are significantly depend on the magnetic field and cavity inclination angles. It was found that different angles of the magnetic field may suppress the convection flow and that the direction of the magnetic field influences the flow pattern. Computations of the average Nusselt numbers at the left hot wall are made and these compare favorably with previously published results. The change in streamline, isotherm and iso-concentration patterns with time is described here.

Combined effect of variable viscosity and thermal conductivity on free convection flow of a viscous fluid in a vertical channel using DTM

An analysis is performed for fully developed free convection flow of a viscous fluid in a vertical channel including the effect of viscous dissipation for the cases of separated effect of variable viscosity, variable thermal conductivity and combined effect of variable viscosity and variable thermal conductivity. The viscosity of the fluid is assumed to depend on the temperature and the thermal conductivity is assumed to vary linearly with temperature. Flow governing motion and energy balance equations are solved using semi-analytical–numerical method called differential transform method (DTM). The principle of differential transformation is briefly introduced, and then applied for the aforementioned problem. Effect of variable viscosity and variable thermal conductivity as well as the effect of buoyancy ratio and wall temperature ratio on the velocity and temperature fields are presented. Effects of the above parameters on volumetric flow rate, skin friction and Nusselt number are also calculated. The current results are then compared with those derived from the Runge–Kutta shooting method (RKSM) in order to verify the accuracy of the proposed method. The findings reveal that DTM and RKSM agree to the order of 10−6.

Effect of Buoyancy Ratio on Double-Diffusive Natural Convection in a Porous Rhombic Annulus

This paper reports on the effect of buoyancy ratio due to both heat and mass transfer on natural convection in a porous enclosure between two isothermal concentric cylinders of rhombic cross sections. For negative values of the buoyancy ratio, buoyancy forces due to heat and mass transfer are in opposite directions (opposing mode), while for positive values they are in the same direction (aiding mode). Numerical results demonstrate that the flow strength increases as the absolute value of the buoyancy ratio increases. In the opposing mode, the eye of the vortex flow is located in the lower half of the enclosure, while in the aiding mode it is positioned in the upper part of the annulus. The average Nusselt and Sherwood number values increase as the absolute value of the buoyancy ratio moves away from 1, with values obtained in the aiding mode being higher than corresponding values achieved in the opposing mode. A comparison is also made between the computed average Nusselt and Sherwood number values and similar ones obtained in a circular annulus having the same inner and outer perimeters as the rhombic enclosure. Predictions indicate large percent difference in values, demonstrating that circular geometries cannot be exploited to accurately predict heat and mass transfer in complex geometries.

Effect of buoyancy ratio on unsteady thermosolutal combined convection in a lid driven trapezoidal enclosure in the presence of magnetic field

In this paper we concentrate to investigate the double diffusive unsteady mixed convection flow in a trapezoidal enclosure in presence of magnetic field. The bottom wall of the enclosure is heated and concentrated uniformly (case-I) and non-uniformly (case-II) while the top wall is cooled and moved uniformly with a constant velocity. Both side walls are adiabatic and impermeable. The coupled governing equations for this phenomenon is solved numerically using weighted residual based Galerkin technique of finite element method (FEM) for Richardson’s number (Ri=0.1–100) and Buoyancy ratio (Br=−10 to 10) at time τ=1.0. Reynolds number, Prandtl number and Lewis number are fixed at 100, 0.71 and 10 respectively. Streamlines, isotherm lines and iso-concentration lines are used to show the result graphically for velocity, temperature and mass distribution respectively. Nusselt and Sherwood number values are presented graphically to show the heat and mass transfer rate from the bottom surface of the cavity.

Effects of buoyancy ratio on unsteady double-diffusive natural convection in a cavity filled with porous medium with non-uniform boundary conditions

The effects of buoyancy ratio on unsteady double-diffusive natural convection in a cavity filled with porous medium with uniform and non-uniform boundary conditions are analyzed in this paper. It is assumed that the left vertical wall and bottom wall are heated and concentrated (uniformly and non-uniformly), while the right vertical wall is maintained at a constant cold temperature, and the top wall is well insulated. The governing equations are solved numerically using a staggered grid finite-difference method to determine the streamlines, isotherms, isoconcentrations, local Nusselt number, local Sherwood number, average Nusselt number and average Sherwood number for various values of buoyancy ratio and Rayleigh number. The change of flow patterns with respect to time depicted and described here. The results are compared with previously published work and excellent agreement has been obtained.

Effects of buoyancy ratio on double-diffusive natural convection in a lid-driven cavity

The effects of uniform and non-uniform heating of wall(s) on double-diffusive natural convection in a lid-driven square enclosure are analyzed. It is assumed that the left vertical wall and bottom wall are heated and concentrated (uniformly or non-uniformly), while the other vertical wall is maintained at a constant cold temperature and the top wall is well insulated which moves with a constant speed. The governing equations are solved numerically using staggered grid finite-difference method. Streamlines, isotherms, local Nusselt number, local Sherwood number, average Nusselt number and average Sherwood number for various values of buoyancy ratio and thermal Rayleigh number are obtained. The results are compared with previously published work and excellent agreement has been obtained.

Effect of Buoyancy Ratio on Non-Darcy Mixed Convection in a Vertical Channel: A Thermal Non-equilibrium Approach

This article presents a numerical study of the doublediffusive mixed convection in a vertical channel filled with porous medium by using non-equilibrium model. The flow is assumed fully developed, uni-directional and steady state. The controlling parameters are thermal Rayleigh number (RaT ), Darcy number (Da), Forchheimer number (F), buoyancy ratio (N), inter phase heat transfer coefficient (H), and porosity scaled thermal conductivity ratio (γ). The Brinkman-extended non-Darcy model is considered. The governing equations are solved by spectral collocation method. The main emphasize is given on flow profiles as well as heat and solute transfer rates, when two diffusive components in terms of buoyancy ratio are in favor (against) of each other and solid matrix and fluid are thermally non-equilibrium. The results show that, for aiding flow (RaT = 1000), the heat transfer rate of fluid (Nuf ) increases upto a certain value of H, beyond that decreases smoothly and converges to a constant, whereas in case of opposing flow (RaT = -1000), the result is same for N = 0 and 1. The variation of Nuf in (N, Nuf )-plane shows sinusoidal pattern for RaT = -1000. For both cases (aiding and opposing) the flow destabilize on increasing N by inviting point of inflection or flow separation on the velocity profile. Overall, the buoyancy force have significant impact on the non-Darcy mixed convection under LTNE conditions. Keywords—buoyancy ratio, mixed convection, non-Darcy model, thermal non-equilibrium

Combined heat and moisture convective transport in a partial enclosure with multiple free ports

Combined heat and moisture transport in an enclosure with free ports has been investigated numerically. Enclosed moist air interacts with the surrounding air through these free-vented ports. The governing conservation equations were solved numerically using a control volume-based finite difference technique. Appropriate velocity boundary conditions at each ports are imposed to achieve overall mass conservation across this system. Air, heat and moisture transport structures are visualized respectively by streamlines, heatlines and masslines. Effects of buoyancy ratio, thermal Rayleigh number on convective heat/moisture transfer rate and flow rate across each free-vented port are discussed. Particularly, Numerical results demonstrate that the convective heat and moisture transport patterns and transport rates on horizontal ports greatly depend on properties of porous medium, while the air exchange rate on vertical port is almost unaffected by the buoyancy ratios for most situations.

Numerical Simulation of Double Diffusive Mixed Convection in a Lid-Driven Square Cavity Using Velocity-Vorticity Formulation

In this article, convection driven by combined thermal and solutal concentration buoyancy effects in a lid-driven square cavity is examined using velocity-vorticity form of Navier-Stokes equations. The governing equations consist of vorticity transport equation, velocity Poisson equations, energy equation, and concentration equation. Validation results are discussed for convection due to heat and mass transfer in a lid-driven square cavity at Re = 500, Le = 2, and GRT = GRS = 100. These results indicate that the present velocity-vorticity formulation could predict the characteristic parameters of flow, temperature, and solutal concentration fields using a much coarser mesh compared to the mesh used in a stream function-vorticity formulation. The capability of the proposed algorithm to handle complex geometry is demonstrated by application to mixed convection in a lid-driven square cavity with a square blockage. The effect of buoyancy ratio on the convection phenomenon is discussed for buoyancy ratio varying from − 100 to 100 at Re = 100. Under opposing temperature and concentration gradients along the vertical direction, the negative buoyancy ratios give rise to aiding flows.