Showing papers on "Rayleigh number published in 2020"

Conjugate natural convection flow of Ag–MgO/water hybrid nanofluid in a square cavity

Abstract: The conjugate natural convection of a new type of hybrid nanofluid (Ag–MgO/water hybrid nanofluid) inside a square cavity is addressed. A thick layer of conductive solid is considered over the hot wall. The governing partial differential equations (PDEs) representing the physical model of the natural convection of the hybrid nanofluid along with the boundary conditions are reported. The thermophysical properties of the nanofluid are directly calculated using experimental data. The governing PDEs are transformed into a dimensionless form and solved by the finite element method. The effect of the variation of key parameters, such as the volume fraction of nanoparticles, Rayleigh number, and the ratio between the thermal conductivity of the wall and the thermal conductivity of the hybrid nanofluid (Rk), is studied. Furthermore, the effects of the key parameters are investigated on the temperature distribution, local Nusselt number, and average Nusselt number. The results of this study show that the heat transfer rate increases by adding hybrid nanoparticles for a conduction-dominant regime (low Rayleigh number). The heat transfer rate is an increasing function of both the Rayleigh number and the thermal conductivity ratio (Rk). In the case of a convective-dominant flow (high Rayleigh number flow) and an excellent thermally conductive wall, the local Nusselt number at the surface of the conjugate wall decreases substantially by moving from the bottom of the cavity toward the top.

Entropy generation analysis due to MHD natural convection flow in a cavity occupied with hybrid nanofluid and equipped with a conducting hollow cylinder

Abstract: The main objective of this numerical investigation was to analyze the entropy generation and natural convection flow under magnetic field in a square enclosure filled with Cu–Al2O3/water hybrid nanofluid. The enclosure is equipped with a conducting hollow cylinder. The free convective flow in the enclosure is created by a horizontal temperature difference between the vertical left hot wall and the right cold wall under the Boussinesq approximation. The dimensionless equations of steady laminar natural convection flow for Newtonian and incompressible mixture are discretized using the finite volume method. The effective thermal conductivity and viscosity of the hybrid nanofluid are calculated using Corcione correlations taking into consideration the Brownian motion of nanoparticles. Numerical solutions were performed for different values of the nanoparticles volumic concentration, Hartmann number, Rayleigh number, radius ratio, and solid–fluid thermal conductivity ratio. The analyzed results show that inserting a hollow conducting cylinder plays an important role in controlling flow characteristic and heat transfer rate as well as irreversibilities within the cavity.

Natural convection analysis in a square enclosure with a wavy circular heater under magnetic field and nanoparticles

Abstract: The aim of the current study is to investigate the natural convection heat transfer in a square enclosure with a wavy circular heater under magnetic field and nanoparticles. The governing equations that are expressed in dimensionless form are solved by means of control volume finite element method employing a validated FORTRAN code. The dimensionless controlling parameters of the present investigation are shape factor of nanoparticles (m), Hartmann number (Ha), Rayleigh number (Ra), and nanoparticle volume fraction (ϕ). In this study, the amplitude A and number of undulations N are fixed at a constant value of 0.2 and 8, respectively. The obtained results portray that in the presence of waves on the inner wall of the annulus, the heat transfer rate is an ascending function of Rayleigh number, nanoparticle volume fraction and less obvious function of their shape factor, while it is a descending function of the Hartmann number.

Numerical simulation of hydrothermal features of Cu–H2O nanofluid natural convection within a porous annulus considering diverse configurations of heater

Abstract: The purpose of the current study is to numerically investigate the effects of shape factors of nanoparticles on natural convection in a fluid-saturated porous annulus developed between the elliptical cylinder and square enclosure. A numerical method called the control volume-based finite element method is implemented for solving the governing equations. The modified flow and thermal structures and corresponding heat transfer features are investigated. Numerical outcomes reveal very good grid independency and excellent agreement with the existing studies. The obtained results convey that at a certain aspect ratio, an increment in Rayleigh and Darcy numbers significantly augments the heat transfer and average Nusselt number. Further, enhancement of Rayleigh number increases the velocity of nanofluid, while that of aspect ratio of the elliptical cylinder shows the opposite trend.

Magnetohydrodynamic natural convection and entropy generation analyses inside a nanofluid-filled incinerator-shaped porous cavity with wavy heater block

Abstract: The aim of the current study is natural convection analysis conjugated with entropy generation analysis in an incinerator shaped permeable enclosure loaded with Al2O3–H2O nanofluid subjected to the magnetic field with a rectangular wavy heater block positioned on the bottom of the cavity wall. The bottom and top horizontal walls are adiabatic; the inclined and vertical walls are thought to be cooled. Firstly, the governing expressions and standard k–e turbulence model are rewritten from dimensional form to non-dimensional form using dimensionless parameters such as vorticity and stream function. In the next step, the equation of entropy generation is written in dimensionless form. Then, the system of non-dimensional governing equations is solved by the finite volume method (FVM) conjugated with a non-dimensionalization scheme using ANSYS Fluent. Fine grids (wall y+ < 2) with inflated layers have been used for the higher Rayleigh number. The effects of the Rayleigh number in the laminar region (Ra = 103, 104, and 105) and turbulent region (Ra = 108, 0.5 × 109, and 109), Darcy number (Da = 0.01 and 100), Hartmann number (Ha = 0 and 40), and the nanoparticles ( $$ \phi = 2{{\% }} $$ ) on the entropy generation number and natural convection are investigated. The validation results were in good agreement with those of the literature. The results demonstrate that for the laminar region, the Nusselt number and entropy generation number increase as the Rayleigh number and the Darcy number grow, whereas both of them abate as Hartmann number increases. In the turbulent region, the average Nusselt number decreases by ascending the Darcy number. Also, for turbulent region (Ra = 109), convection flow strength decreases 6.28% when Hartmann number increases from 0 to 40, whereas the entropy generation number increases 31.5% at Da = 0.01.

Natural convection and entropy production in hybrid nanofluid filled-annular elliptical cavity with internal heat generation or absorption

Abstract: This study is an attempt to understand the characteristics of heat transfer by natural convection, flow, and entropy generation of Cu-Al2O3/H2O based hybrid nanoliquid filled-annulus delimited by two elliptic cylinders considering internal heat generation or absorption (IHG/A) phenomenon The buoyancy-driven flow is induced by a thermal gradient between isothermal and differentially heated inner and outer cylinders A numerical solution of the governing equations in the dimensionless and non-primitive form is performed using the technique of finite volume discretization Impacts of diverse parameters of the study such as copper-alumina nanoparticles volumic concentration, Rayleigh number, and dimensionless internal heat generation or absorption parameter on the thermohydrodynamic characteristic and entropy generation are examined An analysis of the results showed that the combined effects of internal heat generation/absorption and hybrid nanoliquid significantly alter the hydrothermal characteristics, heat transfer rate, and entropy generation within the annulus

Significance of bioconvection in chemical reactive flow of magnetized Carreau–Yasuda nanofluid with thermal radiation and second-order slip

Abstract: Several non-Newtonian fluids are of practical interest, and it is fascinating to examine the rheology of such fluids with various flow features. In this study, the flow of Carreau–Yasuda nanofluid has been analyzed in the presence of gyrotactic microorganisms. The impressive features of nanofluid are displayed by abiding the thermophoresis and Brownian motion aspects. The second-order velocity slip effects are decomposed in the mathematical simulations. Further, the governing flow problem governed the impact of thermal radiation, chemical reaction and convective Nield boundary conditions. Although some attempts are available in the literature which examines the rheological features of Carreau–Yasuda nanofluid, whereas the analysis for bioconvection of flow of this non-Newtonian fluid model in the presence of second-order slip features is not proposed yet. Further, it has been noticed that many investigators used first-order or partial slip effects associated with their flow problems. The flow problem becomes more realistic due to the interaction of second-order slip constrains and subsequently develops a more stable boundary layer. The governing equations for the formulated flow problem are partial differential equations. Standard dimensionless quantities are recommended to alter the flow equations in dimensionless forms. The solution of the locally similar problem has been computed numerically via shooting technique. All the computations are performed by using bvp4c with the help of MATLAB software. Following the iterative procedure, the solution is accurate up to convincing accuracy of $$ 10^{ - 4} . $$ The step size for the present simulation is taken as $$ \Delta \eta = 1 \times 10^{ - 4} . $$ The results are also verified by comparing with already reported numerical computation and found a convincible accuracy. The implication of each parameter is executed for velocity, temperature, concentration and microorganisms’ distributions. Moreover, the substantial quantities, namely skin friction coefficient, motile density number, local Nusselt number, and local Sherwood number numerically evaluated and are overviewed for various parameters. The study reveals that velocity distribution decays with the presence of first-order slip parameter and Rayleigh number, while an enhanced velocity profile has been noted for variation of Weissenberg number. An improved nanoparticle temperature and concentration distributions have been found with the utilization of the second-order slip factor and combine parameter. It is further observed that the density of motile microorganisms declined with Peclet number and bioconvection Lewis number. In recent days, a growing interest has been developed from scientists toward the significance of nanoparticles because of their diverse engineering, industrial and commercial applications. The proposed observations can be useful in extrusion systems applications, biomolecules, biomimetic systems, energy production improvement and enhancement of manufacturing processes.

Magnetohydrodynamic Natural Convection Heat Transfer of Hybrid Nanofluid in a Square Enclosure in the Presence of a Wavy Circular Conductive Cylinder

Abstract: In this paper, steady natural convective heat transfer and flow characteristics of Al2O3-Cu/water hybrid nanofluid filled square enclosure in the presence of magnetic field has been investigated numerically. The enclosure is equipped with a wavy circular conductive cylinder. The natural convection in the cavity is induced by a temperature difference between the vertical left hot wall and the other right cold wall. The steady 2-D equations of laminar natural convection problem for Newtonian and incompressible mixture are discretized using the finite volume method. The effective thermal conductivity and viscosity of the hybrid nanofluid are calculated using Corcione correlations taking into consideration the Brownian motion of the nanoparticles. A numerical parametric investigation is carried out for different values of the nanoparticles volumic concentration, Hartmann number, Rayleigh number, and the ratio of fluid to solid thermal conductivities. According to the results, the corrugated conductive block plays an important role in controlling the convective flow characteristic and the heat transfer rate within the system.

Second Grade Bioconvective Nanofluid Flow with Buoyancy Effect and Chemical Reaction

Abstract: This study mainly concerns with the examination of heat transfer rate, mass and motile micro-organisms for convective second grade nanofluid flow. The considered model comprises of both nanoparticles as well as gyrotactic micro-organisms. Microorganisms stabilize the suspension of nanoparticles by bio-convective flow which is generated by the combined effects of nanoparticles and buoyancy forces. The Brownian motion and thermophoretic mechanisms along with Newtonian heating are also considered. Appropriately modified transformations are invoked to get a non-linear system of differential equations. The resulting problems are solved using a numerical scheme. Velocity field, thermal and solute distributions and motile micro-organism density are discussed graphically. Wall-drag (skin-friction) coefficient, Nusselt, Sherwood and motile micro-organisms are numerically examined for various parameters. The outcomes indicate that for a larger Rayleigh number, the bio-convection restricts the upward movement of nanoparticles that are involved in nanofluid for the given buoyancy effect. Furthermore, larger buoyancy is instigated which certainly opposes the fluid flow and affects the concentration. For a larger values of fluid parameter, the fluid viscosity faces a decline and certainly less restriction is faced by the fluid. In both assisting and opposing cases, we notice a certain rise in fluid motion. Thermal layer receives enhancement for larger values of Brownian diffusion parameter. The random motion for stronger Brownian impact suddenly raises which improves the heat convection and consequently thermal distribution receives enhancement. Thermal distribution receives enhancement for a larger Lewis number whereas the decline is noticed in concentration distribution. The larger Rayleigh number results in a strong buoyancy force that effectively increases the fluid temperature. This also increases the concentration difference, thus more nanoparticles transport between surface and micro-organisms. Furthermore, for larger (Nb), the thermal state of fluid receives enhancement while a decline in motile density is observed. Numerical results show that mass flux is an enhancing function of both the (Le) and (Nb).

Magnetohydrodynamic natural convection of hybrid nanofluid in a porous enclosure: numerical analysis of the entropy generation

Abstract: The effect on the entropy production and MHD convection of the hybrid nanofluid Al2O3–Cu/water (water with Cu and Al2O3 nanoparticles) in a porous square enclosure is studied numerically via Galerkin finite element method. The enclosure used for flow and natural convection analysis is subjected to sinusoidal varying temperatures at the boundaries. Calculations were performed for specific parameters of the Rayleigh number (Ra = 103–106), porosity ratio (e = 0.1–0.9), Darcy number (Da = 10−5–10−2), Hartmann number (Ha = 0–100) and nanoparticles concentration (φ = 0–0.08). The numerical results are presented by velocity profiles, isotherms, streamlines, and Nusselt number. They indicate that the isotherms subject to estimation variations under Ha boost from 0 to 100 as Ra enhances. At high Ha, the conduction transfer mechanism is more obvious. Also, it is seen that the convective heat transfer becomes stronger with the enhancement of the Ra while it detracts with the rise in Ha. Due to the Ra increase, the flow cell becomes stronger. For Ra = 106 and higher Hartmann numbers, the isotherms remain constant which is an indication of convection predominance.

Classical 1/3 scaling of convection holds up to Ra = 1015.

Abstract: The global transport of heat and momentum in turbulent convection is constrained by thin thermal and viscous boundary layers at the heated and cooled boundaries of the system. This bottleneck is thought to be lifted once the boundary layers themselves become fully turbulent at very high values of the Rayleigh number R a —the dimensionless parameter that describes the vigor of convective turbulence. Laboratory experiments in cylindrical cells for R a ≳ 1 0 12 have reported different outcomes on the putative heat transport law. Here we show, by direct numerical simulations of three-dimensional turbulent Rayleigh–Benard convection flows in a slender cylindrical cell of aspect ratio 1 / 10 , that the Nusselt number—the dimensionless measure of heat transport—follows the classical power law of N u = ( 0.0525 ± 0.006 ) × R a 0.331 ± 0.002 up to R a = 1 0 15 . Intermittent fluctuations in the wall stress, a blueprint of turbulence in the vicinity of the boundaries, manifest at all R a considered here, increasing with increasing R a , and suggest that an abrupt transition of the boundary layer to turbulence does not take place.

The influence of different shapes of nanoparticle on Cu–H2O nanofluids in a partially heated irregular wavy enclosure

Abstract: In this work, a complex nature structure is presented to deal with the flow and heat transfer characteristics of Cu–H 2 O nanofluid within the irregular triangular enclosure. Influences of the various shape of Cu nanoparticles are also considered to deal with this mechanism. The irregular side (sinusoidal) of the triangular cavity is partially heated from the bottom. A fixed magnetic field is horizontally applied to the enclosure. The governing equations are derived in the form of nonlinear coupled partial differential equations comprising energy, momentum, and continuity equations. These equations are firstly nondimensionalized before being numerically simulated via Control Volume based Finite Element Method (CVFEM). The relation among the diverse parameters is defined in the form of correlation for Nusselt number. The study concludes that the heat transfer rate is ascended owing to the ascendant in Rayleigh number and descended owing to the ascendant in Hartmann number. Particle shape factor also plays a crucial role in the heat transfer rate within and at the surface of the enclosure.

Prediction of MHD flow and entropy generation by Artificial Neural Network in square cavity with heater-sink for nanomaterial

Abstract: Numerical analysis of magneto-hydrodynamic flow has been a matter of concern for research engineers and scientists. In this paper, magneto-hydrodynamic convection in square tank occupied with Cu-H 2 O nanomaterial is investigated for different configurations of heater-sink, in which Artificial Neural Network (ANN) model was used as an advanced predictive tool. The active semi-circular thermal location (heater and sink) at the left- right vertical sides are kept constantly at high and low temperatures respectively, whereas other walls are kept adiabatic. To reach the solution, Galerkin residual finite element analysis has been implemented. The investigation has been done for Hartmann number (Ha = 0 – 100), Rayleigh number (Ra = 103-107) and nanomaterial concentration ( φ = 0 – 0.05) and finally, streamlines, isotherm contours and entropy generation contours are discussed thoroughly. The overall heat transfer and generation entropy are quantitatively investigated by overall Nusselt number (Nu) and Bejan number (Be), respectively. Existence of external Lorentz forces affects on both non-dimensional performance parameters, Nu and Be. Finally, the higher heat transfer is found for middle–middle configuration of heater-sink walls. The impact of Ha and φ on Nu and Be found from the numerical heat transfer analysis has been predicted and compared with ANN prediction model. To be noted, ANN is widely used technique to compare and predict different experimental and numerical data accurately in many engineering applications.

Effects of conductive curved partition and magnetic field on natural convection and entropy generation in an inclined cavity filled with nanofluid

Abstract: In this study, natural convection and entropy generation analysis of nanofluid in an inclined cavity including a curved shaped conductive partition are performed under the impact of inclined magnetic field by using Galerkin weighted residual finite element method. Numerical simulations are performed for various values of Rayleigh number (between 10 4 and 10 6 ), inclination angle of the cavity (between 0 o and 180 o ), Hartmann number (between 0 and 50), orientation angle of the magnetic field (between 0 o and 90 o ), curvatures of the conductive partition (between 0.01 and 0.1), conductivity ratio (between 0.01 and 100) and solid nanoparticle volume fraction (between 0 and 0.03). The average Nusselt number increases with higher values of Rayleigh number, inclusion of nano sized particles whereas it is reduced with higher values of Hartmann number. When the value of Hartmann number is increased from 0 to 50, 32% and 34% of average Nusselt number reduction is obtained for water and nanofluid. The cavity inclination angle has significant effects on the convective heat transfer characteristics. When the radii of the vertical and horizontal elliptic curved partitions are increased to 0.3H, 23% and 3.8% deterioration of average Nusselt number is obtained while significant enhancement in the heat transfer is observed when the conductivity of the partition is increased. The second law analysis was included in the study and entropy generation rate was found to vary with different parameters. Contributions of solid and fluid domains to the entropy generation rate were determined.