Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field

In this study natural convection heat transfer of Cu–water nanofluid in a cold outer circular enclosure containing a hot inner sinusoidal circular cylinder in the presence of horizontal magnetic field is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both circular enclosure and inner cylinder are maintained at constant temperature. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations were performed for different governing parameters such as the Hartmann number, Rayleigh number, values of the number of undulations of the inner cylinder and nanoparticle volume fraction. The results indicate that in the absence of magnetic field, enhancement ratio decreases as Rayleigh number increases while an opposite trend is observed in the presence of magnetic field. Also it is found that the average Nusselt number is an increasing function of nanoparticle volume fraction, the number of undulations and Rayleigh numbers while it is a decreasing function of Hartmann number.     

Magnetohydrodynamic Natural Convection in a Square Enclosure with Four Circular Cylinders Positioned at Different Rectangular Locations

We deploy a finite volume numerical computation to investigate the two-dimensional hydromagnetic natural convection in a cooled square enclosure in the presence of four inner heated circular cylinders with identical shape. The inner circular cylinders are placed in a rectangular array with equal distance away from each other within the enclosure and moving along the diagonals of the enclosure. All the walls of the enclosure are kept isothermal with temperatures less than that of the cylinders. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. All solid walls are assumed electrically insulated. Simulations are performed for a range of the controlling parameters such as the Rayleigh number 10³ to 10⁶, Hartmann number 0 to 50, and the dimensionless horizontal and vertical distance from the center of a cylinder to center of another cylinder 0.3 to 0.7. The study specifically aims to understand the effects of the location of the cylinders in the enclosure on the magnetoconvective transport, when they moved along the diagonals of the enclosure. It is observed that the unsteady behavior of the flow and thermal fields at relatively larger Rayleigh numbers and for some cylinder position are suppressed by imposition of the magnetic field. The heat transfer strongly depends on the position of the cylinders and the strength of the magnetic field. Hence, by controlling the position of the objects and the magnetic field strength, a significant control on the hydrodynamic and thermal transport can be achieved.     

Simulating magnetohydrodynamic natural convection flow in a horizontal cylindrical annulus using the lattice Boltzmann method

A numerical study is presented about the effect of a uniform magnetic field on free convection in a horizontal cylindrical annulus using the lattice Boltzmann method. The inner and outer cylinders are maintained at uniform temperatures and it is assumed the walls are insulating with a magnetic field. Detailed numerical results of heat transfer rate, temperature, and velocity fields have been presented for Pr=0.7, Ra=10³ to 5 × 10⁴, and Ha=0 to 100. The computational results show that in a horizontal cylindrical annulus the flow and heat transfer are suppressed more effectively by a radial magnetic field. It is also found that the flow oscillations can be suppressed effectively by imposing an external radial magnetic field. The average Nusselt number increases by increasing the radius ratio while it decreases by increasing the Hartmann number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21008     

Hydromagnetic natural cooling of a triangular heat source in a triangular cavity with water–CuO nanofluid

This paper presents a numerical analysis of natural cooling of a right triangular heat source by a water–CuO nanofluid in a right triangular cavity that is under the influence of a horizontal magnetic field. A computational domain is defined and a numerical scheme based on the control volume formulation using the SIMPLE algorithm is developed. The convection–diffusion terms are discretised using a power-law scheme. The effects of the Rayleigh number, the solid volume fraction, the Hartmann number and the heat source position in the cavity on the heat transfer performance of the cavity are examined. The thermal performance of the cavity is enhanced as the Rayleigh number increases, the Hartmann number decreases and the distance of the heat source with the cold walls decreases. An optimum solid volume fraction is found that maximises the heat transfer at high Rayleigh numbers.     

Magnetohydrodynamic Natural Convection of Nanofluids in U-shaped Enclosures

This article presents the results of a numerical study of laminar natural convection in a U-shaped enclosure that is filled with a water-Cu nanofluid and is under the influence of a horizontal magnetic field. A computational domain was defined and a numerical scheme based on the control volume formulation using the SIMPLE algorithm was developed. The convection-diffusion terms were discretized using a power-law scheme. The effects of the Rayleigh number, the solid volume fraction, the Hartmann number, and the enclosure aspect ratio on the heat transfer performance of the enclosure were examined. The thermal performance of the enclosure was found to be a function of the enclosure aspect ratio. The results also showed that the heat transfer rate increased with an increase of the Rayleigh number and the solid volume fraction, but it decreased with an increase of the Hartmann number.     

Buoyancy Induced Heat Transfer Flow Inside a Tilted Square Enclosure Filled with Nanofluids in the Presence of Oriented Magnetic Field

This paper analyzes heat transfer and fluid flow of natural convection in an inclined square enclosure filled with different types of nanofluids having various shapes of nanoparticles in the presence of oriented magnetic field. The Galerkin weighted residual finite element method has been employed to solve the governing non-dimensional partial differential equations. In the numerical simulations, water, ethylene glycol, and engine oil containing copper, alumina, titanium dioxide nanoparticles are considered. The effects of model parameters such as Rayleigh number, Hartmann number, nanoparticles volume fraction, magnetic field inclination angle, geometry inclination angle on the fluid flow and heat transfer are investigated. The results indicate that increment of the Rayleigh number and nanoparticle volume fraction increase the heat transfer rate in a significant way, whereas, increment of the Hartmann number decreases the overall heat transfer rate. It is also observed that a blade shape nanoparticle gives higher heat transfer rate compared to other shapes of nanoparticles. The critical geometry inclination angle at which the maximum heat transfer rate is achieved depends on the nanoparticle volume fraction as well as on the magnetic field orientation. These results are new and have direct applications in solar thermal collectors and thermal insulator of buildings.     

Analytical investigation of polar fluid flow with induced magnetic field in concentric annular region

The influence of microrotational velocity on a fully developed laminar, natural convection flow in vertical concentric annuli in the presence of radial magnetic field between two nonconducting vertical concentric annuli is investigated in the present study. The induced magnetic field is generated due to the motion of an electrically conducting fluid in the annulus; the polar fluid has been considered in the present analysis. Transport equations such as momentum, energy, polar fluid, and induced magnetic field are solved analytically for the isothermal case. The effects of the different pertinent parameters of the present model are obtained and analyzed after verification of present methodology. The effects of the Hartmann number, the gap between two cylinders, and vertex viscosity parameters on velocity profiles, induced magnetic field, induced current density, and microrotational velocity profiles are studied. It is observed that the velocity profile and induced magnetic field decrease due to the vertex viscosity parameter; the Hartmann number accelerates the velocity of the microrotation; the induced current density profile decreases for both the Hartmann number and vertex viscosity parameter. The Hartmann number reduces the magnitude of mass flux and skin frictions at the inner and outer cylinder.     

Numerical Investigation of Transient Magnetohydrodynamic Mixed Convection in a Ventilated Cavity Containing Two Heated Circular Cylinders

A two-dimensional finite volume computation is performed to analyze the transient magnetoconvective transport in a ventilated cavity containing two inner heated circular cylinders with identical shape. An electrically conducting fluid (Prandtl number 0.01) enters the cavity through an opening at the middle of the left wall and is taken away by a similar opening at the middle of the right wall. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. Simulations are performed for the parameters, Richardson number (0, 0.25, 0.5, and 1), Reynolds number (380–550), Hartmann number (0, 10, 20, and 50) and dimensionless gap between the cylinders 0.1, 0.2, and 0.3. The analysis indicates that the transport process is a complex function of the magnetic field strength, mixed convective strength and the cylinder distance. Some typical combinations of these controlling parameters may produce three different transport characteristics such as the steady state, periodic oscillatory, and chaotic. With a lower cylinder distance and higher mixed convective strength, the flow instability increases causing periodic and even chaotic oscillations, whereas the magnetic field due to its damping nature imparts stability to the flow resulting in a steady state flow condition.     

A numerical study of laminar natural convective heat transfer around a horizontal cylinder inside a concentric air-filled triangular enclosure

A numerical investigation of steady-state laminar natural convective heat transfer around a horizontal cylinder to its concentric triangular enclosure was carried out. The enclosure was filled with air and both the inner and outer cylinders were maintained at uniform temperatures. The buoyancy effect was modeled by applying the Boussinesq approximation of density to the momentum equation and the governing equations were iteratively solved using the control volume approach. The effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively. Variations of the maximum value of the dimensionless stream function and the local and average Nusselt numbers were also presented. The average Nusselt number was correlated to the Rayleigh number based on curve-fitting for each aspect ratio. At the highest Rayleigh number studied, the effects of different inclination angles of the enclosure and various cross-section geometries of the inner cylinder were investigated. The computed results indicated that at constant aspect ratio, both the inclination angle and cross-section geometry have insignificant effects on the overall heat transfer rates though the flow patterns are significantly modified.     

MHD and Thermal Flow Between Isothermal Vertical Concentric Cylinders with the Rotation of the Inner Cylinder

A numerical analysis is performed to study the fully developed laminar flow of an electrically conducting liquid metal between two concentric cylinders in the presence of an external transverse magnetic field. The outer cylinder is constant, and the inner cylinder is constant or is rotating at a constant angular velocity about its axis. The cylinders are maintained at uniform temperatures. The temperature difference between the walls creates buoyancy force, due to the density variations. The CVP numerical variational method is used for the study. The obtained results are compared for various angular velocities, Reynolds, Grashof, Prandtl, and Hartmann numbers.     

Flow and convective heat transfer of a ferro-nanofluid in a double-sided lid-driven cavity with a wavy wall in the presence of a variable magnetic field

ABSTRACT

In this work, the effect of a variable spatial magnetic field on ferro-nanofluid flow and heat transfer in a double-sided lid-driven enclosure with a sinusoidal hot wall is investigated. The working fluid is a mixture of iron oxide (Fe₃O₄) nanoparticles and water and is referred to as a ferro-nanofluid. The control volume-based finite element method (CVFEM) is used to solve the governing equations in the stream function–vorticity formulation. In deriving the governing equations for this investigation, the effect of both ferro-hydrodynamics and magneto-hydrodynamics is taken into account. The numerical calculations are performed for different governing parameters namely; the Reynolds number, nanoparticle volume fraction, magnetic number (arising from Ferrohydrodynamics (FHD) consideration), and the Hartmann number (arising from Magnetohydrodynamics (MHD) consideration). The results show that an enhancement in heat transfer has a direct relationship with the Reynolds number and the Hartmann number, but it has an inverse relationship with the magnetic number. Also, it can be concluded that the Nusselt number increases with the increase of the nanoparticle volume fraction, magnetic number, and the Reynolds number while the opposite trend is observed for the Hartmann number.     

Numerical study of mixed convection nanofluid in an annulus enclosure between outer rotating cylinder and inner corrugation cylinder

Numerical investigations are presented for mixed convection problems in a concentric inner sinusoidal cylinder and an outer rotating circular cylinder, which were kept at constant hot and cold temperatures, respectively. The free space between the cylinders and the enclosure walls was filled with a water‐Cu nanofluid. The governing equations are formulated for velocity, pressure, and temperature formulation and are modeled in COMSOL5.2a, a partial differential equation solver based on the Galerkin finite element method. The governing parameters considered are the solid volume fraction, [0, 0.02, 0.04, and 0.06], Re (1, 25, 100, 200, and 300), and Ra (less than 10⁴), and the inner cylinder corrugation frequencies varied from (N = 3, 6, and 9). According to the calculations, the Reynolds number, the Rayleigh number, the nanoparticle volume fraction, and the number of corrugations play an important role of forming the stream and isothermal lines, the local and the average Nusselt number inside the annulus enclosure. The average Nusselt number decreases with increasing Reynolds number and the number of corrugations, while it increases as the Rayleigh number and the volume fraction increase.     

The effect of radial temperature gradient and axial magnetic field on the stability of couette flow: The narrow gap problem

A numerical solution to the MHD stability problem for dissipative Couette flow in a narrow gap is presented under the following conditions: (i) the inner cylinder rotating with the outer cylinder stationary, (ii) corotating cylinders, (iii) counter-rotating cylinders, (iv) an axially applied magnetic field, (v) conducting and nonconducting walls, and (vi) the presence of a radial temperature gradient. Results for the critical wave number a_c, and the critical Taylor number T_c, are presented. The variation of T_c is shown on graphs for both the conducting and nonconducting walls and for different values of ±μ (= Ω₂/Ω₁, where Ω₂ is the angular velocity of the outer cylinder, and Ω₁ is the angular velocity of the inner cylinder), the magnetic field parameter Q, which is the square of the Hartmann number and ± N (= Ra/Ta, where Ra is the Rayleigh number). The effects of ±μ, N and Q on the stability of flow are discussed. It is seen that the effect of the magnetic field is to inhibit the onset of instability, this being more so in the presence of conducting walls and a negative temperature gradient.     

MHD Mixed Convection in a Channel with a Triangular Cavity

A numerical study has been carried out in an open channel, which have a heated triangular cavity at the bottom wall. The remaining walls of the channel are adiabatic. Flow inlets to the channel with uniform velocity and fully developed flow are accepted at the exit of the channel. Steady state mixed convection by laminar flow has been studied by numerically solving governing equations to obtain flow field and temperature distribution under the magnetic field and Joule effect. Equations are solved via the Galerkin weighted residual finite element technique. Calculations are performed for different governing parameters such as Hartmann number (10 ≤ Ha ≤ 100), Reynolds number (100 ≤ Re ≤ 2,000), Rayleigh number (10³ ≤Ra ≤ 10⁵), Joule parameter (0 ≤ J ≤ 5), and Prandtl number (1 ≤ Pr ≤ 10). It is found that heat transfer decreases with an increasing of the Hartmann number especially at higher values of Rayleigh number. Fluid temperature at the exit of the channel also decreases with increasing of Hartmann number. Fluid temperature at the outlet of the channel becomes higher at low Reynolds number and higher Rayleigh number. However, it decreases with the decreasing of the Reynolds number.     

Magnetoconvection in a Square Enclosure with Sinusoidal Temperature Distributions on Both Side Walls

A computational study of convective flow and heat transfer in a cavity in the presence of uniform magnetic field is carried out. The side walls of the cavity have spatially varying sinusoidal temperature distributions. The horizontal walls are adiabatic. The governing equations are solved by the finite volume method. The results are discussed for different combinations of phase deviation, amplitude ratio, and Hartmann and Rayleigh numbers. It is observed that the heat transfer rate is increased with amplitude ratio. The heat transfer rate is increased first and then decreased on increasing the phase deviation. It is also found that the heat transfer rate is decreased with an increasing Hartmann number.     

Investigation of the effect of magnetic field on melting of solid gallium in a bottom-heated rectangular cavity using the lattice Boltzmann method

ABSTRACT

A numerical study is presented for two-dimensional convection melting of solid gallium in a rectangular cavity. The bottom wall of the cavity is uniformly heated and a uniform magnetic field is applied separately in both horizontal and vertical directions. The lattice Boltzmann (LB) method considering the magnetic field force is employed to solve the governing equations. The effects of magnetic field on flow and heat transfer during melting are presented and discussed at Rayleigh number Ra = 1 × 10⁵ and Hartmann number Ha = 0, 15, and 30. The results show that the magnetic field with an inclination angle has a significant impact on the flow and heat transfer in the melting process. For a small Hartmann number, similar melting characteristics are observed for both horizontally applied and vertically applied magnetic fields. For a high value of Hartmann number, it is found that in the earlier stage of melting process, the flow retardation effect caused by the horizontally applied magnetic field is less obvious than that caused by the vertically applied magnetic field. However, the opposite is true in the later stage.     

Influence of relative motion of magnetic field on time‐dependent MHD natural convection flow

The effects of relative motion of magnetic field on unsteady magnetohydrodynamic free convection flow with ramped motion and temperature‐dependent heat source/sink have been analyzed. The motion of the inner cylinder is ramped while the motion of the outer cylinder is fixed. The momentum and energy equations are solved using the well‐known Laplace transform. The time‐domain solution is obtained using the Riemann‐sum approximation method. The influence of the governing parameters on fluid velocity, fluid temperature, volume flow rate, and rate of heat transfer are discussed with the help of line graphs. It is found that Hartmann number has a retarding effect on fluid velocity, skin friction at the outer surface of the inner cylinder, and mass flow rate when the magnetic field is fixed with the fluid and when the velocity of the magnetic field is less than the velocity of the moving cylinder. Whereas, the reverse effect is noticed when the magnetic field is fixed with the moving cylinder.     

Natural convection in a concentric annulus with a porous sleeve

Analytical solutions obtained through perturbation method and Fourier transform are presented for natural convection in concentric cylinders with a porous sleeve. The porous sleeve is press-fitted to the inner surface of the outer cylinder. Both the inner and outer cylinders are kept at constant temperatures with the inner surface at a slightly higher temperature than that of the outer. The main objective of the present study is to investigate the buoyancy-induced flow as affected by the presence of the porous layer. A parametric study has been performed to investigate the effects of Rayleigh number, Darcy number, porous sleeve thickness, and relative thermal conductivity on the heat transfer results.     

Numerical study of MHD natural convection in a rectangular enclosure with an insulated block

The present study numerically investigates the two-dimensional laminar natural convection in a differently heated rectangular enclosure with an insulated square block, in the presence of a uniform magnetic field applied in the horizontal direction. Numerical simulations were performed for the conditions of different Rayleigh and Hartmann numbers with a fixed Prandtl number. The heat transfer rate decreases with the increase in the intensity of the magnetic field. It was found that the insertion of an insulated block contributes to the enhancement of the heat transfer rate in certain ranges of the block size and the Hartmann number.     

Natural Convection in a Square Enclosure with Two Horizontal Cylinders

This study investigates natural convection in a cooled square enclosure with two inner heated circular cylinders with the same diameter. The centers of two equidiameter cylinders are placed at those of the lower and upper half of the enclosure, respectively. The immersed boundary method (IBM) to model the inner circular cylinders based on the finite volume method is used to study a two-dimensional natural convection for different Rayleigh numbers varying in the range of 10³ ≤ Ra ≤ 10⁵. The effect of the radius of inner circular cylinders in an enclosure on heat transfer and fluid flow at different Rayleigh numbers has been examined. As the Rayleigh number increases, the horizontal symmetry is broken and the asymmetry occurred from the smaller radius. As the radius decreases, the dependence of the convection on the Rayleigh number is considerable. The dependence of the Nusselt number on the radius and the Rayleigh number is presented.