Ferrohydrodynamic and magnetohydrodynamic effects on ferrofluid flow and convective heat transfer
Introduction
The CVFEM (Control Volume based Finite Element Method) uses the benefits of both finite volume and finite element methods for simulation of multi-physics problems in complex geometries [1] and [2]. Sheikholeslami et al. [3] studied the problem of free convection between a circular enclosure and a sinusoidal cylinder. They concluded that streamlines, isotherms, the number, size and formation of the cells inside the enclosure strongly depend on the Rayleigh number, values of amplitude and the number of undulations of the enclosure. Sheikholeslami et al. [4] used heatline analysis to simulate two phase nanofluid flow and heat transfer. Their results indicated that the average Nusselt number decreases as buoyancy ratio number increases until it reaches a minimum value and then starts increasing. MHD (magnetohydrodynamic) effect on natural convection heat transfer in an enclosure filled with nanofluid was studied by Sheikholeslami et al. [5]. Their results indicated that Nusselt number is an increasing function of buoyancy ratio number but it is a decreasing function of Lewis number and Hartmann number. Sheikholeslami et al. [6] used CVFEM to simulate the effect of magnetic field on free convection in an inclined half-annulus enclosure filled with Cu–water nanofluid. Their results showed that Hartmann number and the inclination angle of the enclosure can be considered as control parameters at different Rayleigh number. Also this method is used in order to simulate different scientific problems [7], [8], [9], [10], [11], [12], [13], [14], [15].
Cooling capabilities of heat transfer equipments have been constrained because of the low thermal conductivity of conventional heat transfer fluids. However, it is well known that, metals in solid form heavy orders-of-magnitude higher thermal conductivities than those of fluids. Therefore, the thermal conductivities of fluids that contain suspended solid metallic particles could be expected to be significantly higher than those of conventional heat transfer fluids. The goal of nanofluid is to achieve the highest possible thermal properties at the smallest possible concentrations by uniform dispersion and stable suspension of nano particles (preferably <10 nm) in host fluids. Nanotechnology provides new area of research to process and produce materials with average crystallite sizes below 100 nm called nano materials. Sheikholeslami and Ganji [16] investigated two phase modeling of nanofluid in a rotating system with permeable sheet. They found that Nusselt number has direct relationship with Reynolds number and injection parameter while it has reverse relationship with Rotation parameter, Schmidt number, Thermophoretic parameter and Brownian parameter. Asymmetric laminar flow and heat transfer of nanofluid between contracting rotating disks was studied by Hatami et al. [17]. Their results indicated that temperature profile becomes more flat near the middle of two disks with increase of injection but opposite trend is observed with increase of expansion ratio. Nanofluid convective heat transfer becomes a popular topic in last decade [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38].
Magnetic nanofluid (Ferrofluid) is a magnetic colloidal suspension consisting of base liquid and magnetic nanoparticles with a size range of 5–15 nm in diameter coated with a surfactant layer. Jue [39] used semi implicit finite element method in order to simulate magnetic gradient and thermal buoyancy induced cavity ferrofluid flow. Their results showed the flow strength increases with the strengthening magnetic field. Numerical analysis of the heat transfer enhancement and fluid flow characteristics of a rotating cylinder under the influence of magnetic dipole in the backward facing step geometry was conducted by Selimefendigil and Oztop [40]. They found that the effect of cylinder rotation on the local Nusselt number distribution is more pronounced at low Reynolds number. Nanjundappa et al. [41] studied the effect of MFD (magnetic field dependent) viscosity on the onset of ferro convection in a ferrofluid saturated horizontal porous layer. They showed the nonlinearity of fluid magnetization has no influence on the stability of the system. The vortex dynamics behind various magnetic obstacles and characteristics of heat transfer were investigated by Zhang and Huang [42]. They found that the pressure drop penalty was not increasingly dependent on interaction parameter. Azizian et al. [43] studied the effect of an external magnetic field on the convective heat transfer and pressure drop of magnetite nanofluids under laminar flow regime conditions. They showed that the mechanisms for heat transfer enhancement are postulated to be accumulation of particles near the magnets. Natural convection in a rectangular enclosure containing an oval-shaped heat source and filled with Fe3O4/water nanofluid was investigated by Moraveji and Hejazian [44]. Free convection of ferrofluid in a cavity heated from below in the presence of magnetic field was studied by Sheikholeslami and Gorji [45]. They found that particles with a smaller size have better ability to dissipate heat, and a larger volume fraction would provide a stronger driving force which leads to increase in temperature profile.
Parametric analysis and optimization of entropy generation in unsteady MHD flow over a stretching rotating disk was investigated by Rashidi et al. [46]. Rahman et al. [47] studied the augmentation of natural convection heat transfer in triangular shape solar collector by utilizing water based nanofluids having a corrugated bottom wall. They found that both Grashof number and solid volume fraction have significant influence on streamlines and isotherms in the enclosure. The effects of using different geometrical parameters with the combination of nanofluid on heat transfer and fluid flow characteristics in a HCTHE (helically coiled tube heat exchanger) were numerically investigated by Mohammed and Narrein [48].They found that counter-flow configuration produced better results as compared to parallel-flow configuration. Free convection heat transfer in a concentric annulus between a cold square and heated elliptic cylinders in presence of magnetic field was investigated by Sheikholeslami et al. [49]. They found that the enhancement in heat transfer increases as Hartmann number increases but it decreases with increase of Rayleigh number. Rashidi et al. [50] studied the effects of magnetic interaction number, slip factor and relative temperature difference on velocity and temperature profiles as well as entropy generation in MHD (magnetohydrodynamic) flow of a fluid with variable properties over a rotating disk. Ellahi [51] studied the MHD flow of non-Newtonian nanofluid in a pipe. He observed that the MHD parameter decreases the fluid motion and the velocity profile is larger than that of temperature profile even in the presence of variable viscosities. Rashidi et al. [52] considered the analysis of the second law of thermodynamics applied to an electrically conducting incompressible nanofluid fluid flowing over a porous rotating disk. They concluded that using magnetic rotating disk drives has important applications in heat transfer enhancement in renewable energy systems. Sheikholeslami et al. [53] studied the magnetic field effect on CuO–water nanofluid flow and heat transfer in an enclosure which is heated from below. They showed that effect of Hartmann number and heat source length is more pronounced at high Rayleigh number. Sheikholeslami et al. [54] studied the problem of MHD free convection in an eccentric semi-annulus filled with nanofluid. They showed that Nusselt number decreases with increase of position of inner cylinder at high Rayleigh number. Lattice Boltzmann Method was used to investigate magnetohydrodynamic flow utilizing Cu–water nanofluid in a concentric annulus by Sheikholeslami et al. [55].Their results proved that enhancement ratio increases with decrease of Rayleigh number and it increases with augment of Hartmann number. Recently, effect of magnetic field on nanofluid flow and heat transfer has been investigated by several authors [56], [57], [58], [59], [60], [61].
The main purpose of the present work is to study ferrofluid flow and heat transfer in an enclosure with sinusoidal hot wall in presence of an external magnetic field. CVFEM is applied to solve this problem. The numerical investigation is carried out for different governing parameters such as the Rayleigh number, nanoparticle volume fraction, Magnetic number arising from FHD (Ferrohydrodynamics) and Hartmann number arising from MHD.
Section snippets
Geometry definition and boundary conditions
The physical model along with the important geometrical parameters and the mesh of the enclosure used in the present CVFEM program are shown in Fig. 1. The inner and outer walls are maintained at constant temperatures Th and Tc, respectively. The shape of inner cylinder profile is assumed to mimic the following pattern.
in which rin is the base circle radius, rout is the radius of outer cylinder, A and N are amplitude and number of undulations, respectively, ζ is the rotation
Problem formulation
The flow is steady, two-dimensional, laminar and incompressible. The magnetic Reynolds number is assumed to be small so that the induced magnetic field can be neglected compared to the applied magnetic field. Using the Boussinesq approximation, the governing equations of heat transfer and fluid flow for nanofluid can be obtained as follows:
Grid testing and code validation
A mesh testing procedure was conducted to guarantee the grid-independency of the present solution. Various mesh combinations were explored for the case of Ra = 105, ϕ = 0.04, MnF = 500, Ha = 5, Ec = 10−5, ε1 = 0 and Pr = 6.8 as shown in Table 2. The present code was tested for grid independence by calculating the average Nusselt number on the inner hot wall. In harmony with this, it was found that a grid size of 71 × 211 ensures a grid-independent solution. The convergence criterion for the
Results and discussion
Effect of an external magnetic field on ferrofluid flow and heat transfer in a semi-annulus enclosure with sinusoidal hot wall is studied. The mathematical model used for the formulation of the problem is consistent with the principles of FHD (Ferrohydrodynamics) and MHD (Magnetohydrodynamics). The thermo physical properties of Fe3O4 nanoparticles and based fluid (water) are shown in Table 1 [65]. Calculations are made for various values of volume fraction of nanoparticles (ϕ = 0% and 4%),
Conclusions
Ferrofluid flow and heat transfer in presence of magnetic field in a semi-annulus enclosure with sinusoidal hot wall is investigated. CVFEM is used to solve the governing equations in which both effects of FHD and MHD are considered. Numerical results are obtained for different values of Rayleigh number, nanoparticle volume fraction, Magnetic number arising from FHD and Hartmann number arising from MHD. Results show that effect of Kelvin forces is more sensible for low Rayleigh number. Also it
References (67)
- et al.
Numerical study of natural convection between a circular enclosure and a sinusoidal cylinder using control volume based finite element method
Int J Therm Sci
(2013) - et al.
Two phase simulation of nanofluid flow and heat transfer using heatline analysis
Int Commun Heat Mass Transf
(2013) - et al.
Magnetohydrodynamic free convection of Al2O3-water nanofluid considering thermophoresis and brownian motion effects
Comput Fluids
(2014) - et al.
Effect of a magnetic field on natural convection in an inclined half-annulus enclosure filled with Cu–water nanofluid using CVFEM
Adv Powder Technol
(2013) - et al.
Thermal management for free convection of nanofluid using two phase model
J Mol Liq
(2014) - et al.
Heat flux boundary condition for nanofluid filled enclosure in presence of magnetic field
J Mol Liq
(2014) - et al.
Magnetic field effect on nanofluid flow and heat transfer using KKL model
J Taiwan Inst Chem Eng
(2014) - et al.
Effects of MHD on Cu-water nanofluid flow and heat transfer by means of CVFEM
J Magnetism Magnetic Mater
(2014) - et al.
Natural convection heat transfer in a cavity with sinusoidal wall filled with CuO-water nanofluid in presence of magnetic field
J Taiwan Inst Chem Eng
(2014) - et al.
Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field
Int Commun Heat Mass Transf
(2012)