Increasing Rayleigh Number Research Articles

Conjugate natural convection in a vertically divided square enclosure by a corrugated solid partition into air and water regions

The purpose of this study is to investigate conjugate natural convection inside a partitioned differentially heated square enclosure. A corrugated heat-conducting solid partition of three different values of thickness and three different materials is selected. The partition divides the empty spaces of the enclosure into two fluid zones and those zones are filled with air and water, respectively. The governing Navier-Stokes and energy equations are numerically solved by means of the finite element method. The effects of corrugation amplitude, corrugation frequency, thermal conductivity, position and thickness of the corrugated solid partition along with the variation of Rayleigh numbers based on the properties of air on thermal and flow fields have been depicted through contour plots of temperature and stream function, respectively. The average Nusselt number along the hot wall and the average temperatures of both air and water in their respective domains have also been examined to observe the influence of the above variations. The change of corrugation amplitude, thermal conductivity, position and thickness of the corrugated solid partition has considerable effects on heat transfer performance with increasing Rayleigh number. Out of those controlling parameters, it is found that increasing partition thermal conductivity enhances thermal performance by up to 25%. However, the variation of corrugation frequency of the partition as a function of Rayleigh number does not seem to be significant for heat transfer enhancement.

Mixed convection of a nanofluid past an inclined wavy surface in the presence of gyrotactic microorganisms

AbstractThe mixed convection of a nanofluid flow past an inclined wavy surface in the existence of gyrotactic microbes is considered. To convert the wavy surface to a plane surface, a transformation of coordinates is applied. The governing equations that are nonlinear and the accompanying boundary conditions are converted into a dimensionless form using pseudo‐similarity variables. Using a local linearization process, the system of nonlinear partial differential equations is linearized. The resulting system is solved using the Bivariate Chebyshev pseudo‐spectral collocation method. The influence of different physical and geometrical factors on the parameters of engineering importance of the flow is analyzed and illustrated graphically. It is observed that the skin friction, the density of motile microorganisms, and nanoparticle mass transfer rate are increasing with an increase in the bioconvection Peclet and Schmidt numbers whereas these quantities are decreasing with an increase in Rayleigh number. The local Nusselt number, nanoparticle Sherwood number, and density number of microbes increases with an increase in the Brownian motion and thermophoresis parameter. These physical quantities are increasing when the surface changes from horizontal to vertical.

Magnetized bioconvection flow of Sutterby fluid characterized by the suspension of nanoparticles across a wedge with activation energy

AbstractNanofluids are playing a vital part in advancing practical life. The potential application of nanomaterials in a multitude of scenarios, such oil recovery, the melting of electronic systems in computers, cooling systems, the construction of fluid, cooling spirals, engineering and manufacturing, heat storage devices, and bioengineering. The microorganisms have a vital role to play in numerous applications, such as biological sciences, drugs, and biotechnology, biofuels processing, wastewater treatment, and food production. The current investigation exhibits a numerical model for Sutterby fluid with activation energy, thermal radiation, and bioconvection flowing past a stretching/shrinking wedge. The set of conservative governing partial differential equations (PDEs) is converted into a dimensionless ODEs system by using suitable similarity variables. The obtained new system of the model with dimensionless relative boundary conditions is tackled numerically by manipulating the famous shooting method through bvp4c solver in MATLAB coding. The physical and mathematical findings for profiles of velocity, temperature, concentration, and microbe dispersion owing to various controlling parameter inputs are displayed in tables and graphs. Flow velocity is shown to decrease as the bioconvection Rayleigh number increases. Moreover, the Prandtl number increases, the thermal field of the fluid decreases while it increases for the temperature ratio parameter. Furthermore, it is determined from this situation that the concentration field decreases as the Brownian motion parameter increases. The field of the microorganism decreases as the Peclet number increases.

A numerical technique and effect of magnetic field dependent (MFD) viscosity on thermal instability in a ferrofluid pores with Coriolis force for Darcy model

PurposeThe effect of magnetic field dependent (MFD) viscosity on the onset of convection in a ferromagnetic fluid layer heated from below saturating rotating porous medium in the presence of vertical magnetic field is investigated theoretically by using Darcy model. The resulting eigen value problem is solved using the regular perturbation technique. Both stationary and oscillatory instabilities have been obtained. It is found that increase in MFD viscosity and increase in magnetic Rayleigh number is to delay the onset of ferroconvection, while the nonlinearity of fluid magnetization has no influence on the stability of the system.Design/methodology/approachThe thermal perturbation method is employed for analytical solution. A theory of linear stability analysis and normal mode technique have been carried out to analyze the onset of convection for a fluid layer contained between two impermeable boundaries for which an exact solution is obtained.FindingsThe conditions for the system to stabilize both by stationary and oscillatory modes are studied. Even for the oscillatory system of particular frequency dictated by physical conditions, the critical Rayleigh numbers for oscillatory mode of the system were found to be greater than for the stationary mode. The system gets destabilized for various physical parameters only through stationary mode. Hence, the analysis is restricted to the stationary mode. To the Coriolis force, the Taylor number Ta is calculated to discuss the results. It is found that the system stabilizes through stationary mode for values of and for oscillatory instability is favored for Ta > 104. Therefore the Taylor number Ta leads to stability of the system. For larger rotation, magnetization leads to destabilization of the system. The MFD viscosity is found to stabilize the system.Originality/valueThis research paper is new and original.

Improved Energy Efficiency of Mixed Convection Heating Process in Eccentric Annulus

This paper deals with a numerical study of mixed convection heat transfer in horizontal eccentric annulus. The inner cylinder is supposed hot and rotating, however the outer one is kept cold and motionless. The numerical problem was solved using COMSOL Multiphysics® which is based on finite element method. The resolution of the partial differential equations was conducted through an implicit scheme with the use of the damped Newton’s method. The present numerical analysis concerns the effect of eccentricity, rotation speed and Rayleigh number on the flow patterns, heat transfer rate, and energy efficiency of the process. It was found that the heat transfer rate increases with the increase of Rayleigh number. In addition, the heat transfer rate drops with the increase of rotation speed. Finally, we have demonstrated that maximum energy efficiency is achieved not only with higher Rayleigh number but also it is maximum with small eccentricity.

Numerical simulation of thermal management during natural convection in a porous triangular cavity containing air and hot obstacles

A numerical study is presented of laminar viscous magnetohydrodynamic natural convection flow in a triangular-shaped porous enclosure filled with electrically conducting air and containing two hot obstacles. The mathematical model is formulated in terms of dimensional partial differential equations. The pressure gradient term is eliminated by using the vorticity–stream (\(\omega - \psi\)) function approach. The emerging dimensionless governing equations are employed by the regular finite difference scheme along with thermofluidic boundary conditions. The efficiency of the obtained computed results for isotherms and streamlines is validated via comparison with previously published work. The impact of physical parameters on streamlines and temperature contours for an extensive range of Rayleigh number (Ra = 103–105), Hartmann magnetohydrodynamic number (Ha = 5–30), Darcy parameter (Da = 0.0001–0.1) for fixed Prandtl number (Pr = 0.71) is considered. Numerical results are also presented for local and average Nusselt numbers along the hot base wall. Interesting features of the thermofluid behaviour are revealed. At lower Rayleigh number, the isotherms are generally parallel to the inclined wall and only distorted substantially near the obstacles at the left vertical adiabatic wall; however, with increasing Rayleigh number, this distortion is magnified in the core zone and simultaneously warmer zones expand towards the inclined cold wall. The simulations are relevant to magnetic materials processing and hybrid magnetic fuel cells.

Porous materials saturated with water-copper nanofluid for heat transfer improvement between vertical concentric cones

Water-Copper nanofluid saturated porous materials are used to improve cooling of a conical electronic component contained in another concentric cavity of the same shape maintained at low temperature. Ratio between thermal conductivity of the solid matrix of the porous materials and that of the base fluid (water) varies between 4 and 41.2 while the nanofluid's volume fraction varies between 0% (pure water) and 10%. Free convective heat transfer was determined by means of a numerical approach based on the volume control method using the SIMPLE algorithm. Results show improvement of heat transfer as thermal conductivity ratio, nanoparticles concentration and Rayleigh number increase. Improvement was quantified through specific functions. New correlation is proposed to determine the average Nusselt number for any combination of the thermal conductivity ratio and nanofluid volume fraction in the 3.32x105-6.74x107 Rayleigh number range.

Bioconvection flow of Casson nanofluid by rotating disk with motile microorganisms

This paper presents the bioconvection flow of Casson nanofluid by a rotating disk with gyrotactic microorganisms, multiple slips, and thermal radiation. The non-Newtonian fluid (Casson fluid) in the existence of thermophoretic and Brownian diffusion effects is incorporated. The research of rotatable disk has practical applications in numerous processes like rotating machinery, lubrication, computer storage devices, oceanography, crystal growth, etc. Using appropriate variables, a system of strongly non-linear PDEs is translated into a system of ODEs. To construct a numerical solution of nonlinear flow equations, the bvp4c technique is used. The impacts of various numbers on velocities, thermal field, the volumetric concentration of nanoparticles, and microorganism field are investigated. From the results, it can be noticed that radial velocity rises by varying values of mixed convection parameter. An increase in bioconvection Rayleigh number causes decays in velocity fields. A larger Prandtl number declines the temperature distribution. Furthermore, an increment in the estimations of thermophoresis parameter increases the thermal and solutal field of species. Significant heat transfer is acquired with higher radiation effects. Slip parameter for temperature and concentration decreased the thermal and solutal profiles. The microorganisms field is declined with greater microorganisms slip parameter.

Natural convection in a horizontal annular sector containing heat-generating porous medium

PurposeThe purpose of this work is to propose the generalized integral transform technique (GITT) for the investigation of two-dimensional steady-state natural convection in a horizontal annular sector containing heat-generating porous medium.Design/methodology/approachGITT was used to investigate steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. The governing equations in stream function formulation are integral transformed in the azimuthal direction, with the resulting system of nonlinear ordinary differential equations numerically solved by finite difference method. The GITT solutions are validated by comparison with fully numerical solutions by finite difference method, showing excellent agreement and convergence with low computational cost.FindingsThe effects of increasing Rayleigh number are more noticeable in stream function, whereas less significant for temperature. With decreasing annular sector angle from π to π/6, a reduction in the maximum temperature and stream function was noticed. While the two counter-rotating vortical structure is common for all annular sector angles investigated, the relative size of the two vortices varies with decreasing sector angle, with the vortex near the outer radius of the cavity becoming dominant. The annular sector angle affects strongly the maximum temperature and the partition of heat transfer on the inner and outer surfaces of the annular sector with heat-generating porous medium.Originality/valueThe strong effects of the annular sector angle on natural convection in annular sectors containing heat-generating porous medium are investigated for the first time. The proposed hybrid analytical–numerical approach can be applied in other convection problems in cylindrical or annular configurations, with or without porous medium. It shows potential for applications in practical convection problems in the nuclear and other industries.

Hydromagnetic natural convection in a wavy-walled enclosure equipped with hybrid nanofluid and heat generating cylinder

Flow and heat transfer components of buoyancy driven convection in a hybrid nanofluid filled wavy-walled cavity are numerically investigated in this study. A cylindrical heat generating blockage is placed at the center of the cavity. The cavity is partially heated from its bottom wall and cooled from wavy-walls while the remaining walls are adiabatic. The cavity is permeated by a transverse magnetic field. Thermal conductivity model of hybrid nanofluid is developed comprising Brownian motions of different nanoparticles. The non dimensional governing equations are solved by implementing finite element method. Obtained results demonstrate the intensification of fluid flow circulation for increasing Rayleigh number and heater length. The heat transfer rate is expeditiously augmented for increase in Rayleigh number and hybrid nanoparticles volume fraction but reverse trend is observed for higher Hartmann number. The flow circulation and temperature distribution are influenced with the presence of heat generating cylinder and roughness of the cavity walls. In addition, strength of fluid motion becomes higher for wavy cavity containing heat generating obstacle compared to smooth cavity without blockage. Maximum heat transfer is ensured at lower heater length and radius of the heat generating cylinder. Heat transfer rate also increases with the roughness of the cavity.

Studying the Internal Heat Transfer By Natural Convection Through an Inclined and a Modified Square Enclosure with a Triangular Top Wall.

A numerical analysis used to simulate laminar natural convective heat transfer in a two-dimensional inclined and a modified square enclosure having a triangular top wall has been performed. The model is applied to analyze natural convection in this enclosure where the left side wall is subjected to a constant heat flux while the other opposite wall is kept at isothermal cold temperature. The other enclosure walls are considered adiabatic. The enclosure under study is filled with air with Prandtl number is taken as 0.71. The two-dimensional flow is solved numerically by using the Finite Volume Method (FVM).The computations are carried out at different heights of triangular top wall. The Rayleigh numbers considered ranging from 103 to 106. The effect of inclination angle of the enclosure on the resulting convection process is investigated for inclination angles ranging from 0o to 60o. The results of the present investigation show that the convective phenomenon is greatly influenced by the inclined top wall height and the dominance of the convective currents with the increase of Rayleigh number and inclination angle. The streamline and isotherm plots and the variation of the average Nusselt number at the hot left side wall are also presented. The results showed a good agreement with another published results.

Lattice Boltzmann modeling of double-diffusive convection of dielectric liquid in rectangular cavity subjected to unipolar injection

The lattice Boltzmann method is used to study the double-diffusive convection caused by the simultaneous effect of the temperature gradient and concentration gradient of the dielectric liquid in a rectangular cavity in the case of unipolar injection of ions. Considering that the physical model in this article is a complex dynamic system, we first conducted a linear stability analysis and obtained a neutral stability curve. Then we made a series of simulations to determine the influence of different dimensionless parameters on the movement of dielectric liquids and the distribution of charge density, temperature field, and concentration field. The variation range of the parameters is as follows: thermal Rayleigh number (1000≤Ra≤20000), electric Rayleigh number (100≤T≤800), Lewis number (1.0≤Le≤50.0), and buoyancy ratio (−2≤Nc≤0.5). The results show that the increase in electric Rayleigh number and thermal Rayleigh number will enhance the intensity of heat and mass transfer. Compared with pure electric convection, the existence of temperature field and concentration field have increased the instability of the dielectric fluid flow. When the Lewis number increases, the average Nusselt number will decrease but the average Sherwood number will increase. In addition, we noticed that the heat and mass transfer intensities have increased with the increase of the buoyancy ratio. When the buoyancy rate gradually increases from –2.0, we observe a bifurcation structure, and as the electric Rayleigh number increases, the critical value Ncc that causes convection will decrease.

Evolution of solid–liquid interface in bottom heated cavity for low Prandtl number using lattice Boltzmann method

The influence of natural convection cells on heat transfer and the evolution of melt interface is studied for low Prandtl number fluid (Pr = 0.025) in phase-change Rayleigh–Benard convection using the lattice Boltzmann method. The thermal lattice Boltzmann model is used to evaluate the effect of Rayleigh number (Ra = 6708, 11 708, and 21 708) and cavity aspect ratio (γ = 0.062 5, 0.125, 0.25, 0.5, and 1) on the onset of convection, number of convection cells, and Nusselt number in the classical Rayleigh–Benard convection. The modified equilibrium distribution function-based thermal lattice Boltzmann model is applied to evaluate the effect of Stefan number (Ste = 0.025, 0.05, and 0.1) in the phase change Rayleigh–Benard convection. Distinct flow configurations depend on the Rayleigh number, aspect ratio, and Stefan number. The number of convection cells follows an inverse relation with the aspect ratio. Nusselt number increases with decreasing cavity aspect ratio and increasing Rayleigh number in the classical Rayleigh–Benard convection. With the variation in the aspect ratio based on the melt layer height during melting of phase change material, the number of convection cells changes resulting in the change in the evolution of the melt interface and convective heat transfer. Melting in a cavity of aspect ratio less than 0.5, the evolution of melt interface remains symmetrical. For an aspect ratio greater than 0.5, the interface evolution becomes unsymmetrical depending on the transition to single convection cell-dominated heat transfer.

Bio-convective and chemically reactive hybrid nanofluid flow upon a thin stirring needle with viscous dissipation

In this work, the thermal analysis for bio-convective hybrid nanofluid flowing upon a thin horizontally moving needle is carried out. The chemical reaction and viscous dissipation has also considered for flow system in the presence of microorganism. The hybrid nanoparticles comprising of Copper left( {Cu} right) and Alumina left( {Al_{2} O_{3} } right) are considered for current flow problem. Mathematically the flow problem is formulated by employing the famous Buongiorno’s model that will also investigate the consequences of thermophoretic forces and Brownian motion upon flow system. Group of similar variables is used to transform the model equations into dimensionless form and have then solved analytically by homotopy analysis method (HAM). It has established in this work that, flow of fluid declines due to increase in bioconvection Rayleigh number, buoyancy ratio and volume fractions of nanoparticles. Thermal flow grows due to rise in Eckert number, Brownian, thermophoresis parameters and volume fraction of nanoparticles. Concentration profiles increase due to growth in Brownian motion parameter and reduces due to increase in thermophoresis parameter and Lewis number. Motile microorganism profile declines due to augmentation in Peclet and bioconvection Lewis numbers. Moreover, the percentage enhancement in the drag force and rate of heat transfer using conventional nanofluid and hybrid nanofluid are observed and discussed. The hybrid nanofluid increases the skin friction and heat transfer rate more rapidly and efficiently as compared to other traditional fluids. A comparison of the present study with the existing literature is also conducted with a closed agreement between both results for variations in thickness of the needle.

CNT–water nanofluid magneto-convective heat transfer in a cubical cavity equipped with perforated partition

This paper discusses the magneto-hydrodynamic natural convection in a cubical cavity equipped with a perforated separation. Several situations related to the number of perforations, magnitude of magnetic field, nanoparticles concentration and Rayleigh number are studied. During this study, the CNT–water filled cavity is differentially heated and a uniform external magnetic field is imposed. Computations are performed for Hartmann (0 ≤ Ha ≤ 100), (103 ≤ Ra ≤ 105 ), (3 × 3 ≤ N ≤ 7 × 7) and (0 ≤ ϕ ≤ 0.02). The results indicate that, the heat transfer is enhanced when the CNT volume fraction and Rayleigh number increase and decrease when the magnitude of the magnetic field increases. Moreover, the average Nusselt number has its highest values of the solid volume fraction and the number of perforations (ϕ = 0.02 and N = 7 × 7). Furthermore, it was seen that the number of perforations is more effective on heat transfer for higher Rayleigh number values.

Natural convection of CuO-water nanofluid in a conventional oil/water separator cavity: Application to combined-cycle power plants

The oily water from various sources in combined cycle power plants is collected in oil/water separator in which the oil separates from water due to the density difference. The idea of the presented geometry is taken from conventional oil/water separators. This paper studies the natural convection of the CuO-water nanoliquid in a rectangular cavity with fins attached to the insulated wall and porous media. Discretion of Navier-Stokes equations is done by Finite Element Method and assumptions are laminar, steady and incompressible flow. Heat transfer performance and entropy generation are investigated for distinct Rayleigh numbers (103–105), Darcy numbers (10−2–10−4), and Hartmann numbers (0, 10, 20). Different sizes of the fins are also studied to show consequences of fin size on heat transfer in cavity. This is the first time that these parameters and their impacts on Nusselt number and entropy generation are studied for a conventional oil/water separator cavity. Corollaries demonstrate that increasing Rayleigh number and Darcy number improves heat transfer performance and average Nusselt number. Nevertheless, Hartmann number has a reverse effect with average Nusselt number. Finally, a new equation for average Nusselt number is developed with regard to Rayleigh number, Hartmann number, and Darcy number.

The onset of magnetic nanofluid convection because of selective absorption of radiation

This article reports a linear stability analysis of the onset of convection stimulated by selective absorption of radiation in a horizontal layer of magnetic nanofluid (MNF) under the impact of an external magnetic field. The Chebyshev pseudospectral method is utilized to obtain the numerical solution for water-based magnetic nanofluids (MNFs). The confining boundaries of the magnetic nanofluid layer are considered to be rigid–rigid, rigid–free, and free–free. The results are derived for two different conditions, viz., when the system is heated from the below and when the system is heated from the above. It is observed that an increase in the value of the Langevin parameter , diffusivity ratio and a decrease in the value of nanofluid Lewis number , the parameter which represents the impact of selective absorption of radiation and modified diffusivity ratio delays the onset of MNF convection for both the two configurations. Moreover, as the value of concentration Rayleigh number increases, the convection commences easily when the system is heated from the below, whereas the onset of MNF convection gets delayed as the system is heated from the above.

Convective heat transport in yield stress nanofluids in a differentially heated square enclosure

ABSTRACT In the present study, flow and heat transfer characteristics of some yield stress nanofluid filled in a differentially heated square enclosure are investigated. The rheology of the fluid is modeled by regularized Bingham model. The effects of Rayleigh number in the range of 5 × 103 to 5 × 106, Bingham number between 0 and 2, nanoparticle volume fraction varying between 0% and 5% and Prandtl number ranging 5 to 100 on the natural convection of yield stress nanofluid has been investigated. The phenomenon is explained through velocity, temperature distribution and contour plots of streamlines and isotherms. The rate of thermal transportation through test fluids rises with an increase in Rayleigh number and volume fraction, while it falls as yield stress and Prandtl number is increased. Dependency of mean Nusselt number is more pronounced on nanoparticle addition, rather than its yield stress. A correlation of mean Nu has been proposed. All predicted values of mean Nu are obtained to be within ±13% band.

Natural convection of nanofluids in solar energy collectors based on a two-phase lattice Boltzmann model

In order to improve the photothermal conversion efficiency of solar energy collectors, the laminar convection of nanofluids in five types of solar energy collectors was numerically studied with a two-phase lattice Boltzmann model. In the current simulation, Cu–water nanofluids (volume fraction φ = 0.3%) were chosen. The equilibrium distribution function with D2Q9 model and the boundary conditions of nonequilibrium extrapolation scheme were applied to establish the lattice Boltzmann model. The effects of different Rayleigh numbers (Ra = 104–106), structures (rectangle cavity, trapezoid cavity and parallelogram cavity) and aspect ratios (A = 2:1, 4:3 and 1:1) of solar energy collectors on the heat transfer were considered. The temperature distribution, streamline and entropy generation of nanofluids in the solar energy collectors were analyzed. Results demonstrated that the increase in Rayleigh number heightens the heat convection of nanofluids. The trapezoid cavity and parallelogram have a special structure, which will form a flow dead zone, weaken the heat transfer effect and determine the position of maximum entropy generation.

Mathematical Modelling of MHD Natural Convection in a Linearly Heated Porous Cavity

A linear increase in thermal boundaries towards the bottom of the porous cavity is considered for numerical flow analysis on MHD natural convection. The two-dimensional square shaped cavity is filled with the Cu-water nanofluid. The dimensionless equations are considered to interpret the fluid and heat flow inside the cavity with respect to the desired boundaries. The governing equations are solved using the finite difference techniques. The relevant dimensionless parameters used in the present study are Rayleigh number, Darcy number, solid volume fraction of the nanoparticles and Hartmann number to obtain the flow fields. Heatline flows picturization techniques involved in the study analyze the heat flow inside the cavity. As the Rayleigh number and Darcy number increases, an increase in streamlines flow velocity and convection heat transfer is observed. Convective heat transfer is interrupted by increasing the applied magnetic field effects. An improvement in the heat transfer is noticed by increasing the solid volume fraction of the particles.