Effect of Magnetic Field on the Mixed Convection Ferrofluid Flow in A
Total Page：16
File Type：pdf, Size：1020Kb
Pramana – J. Phys. (2020) 94:156 © Indian Academy of Sciences https://doi.org/10.1007/s12043-020-02015-7 Effect of magnetic field on the mixed convection Fe3O4/water ferrofluid flow in a horizontal porous channel AMIRA JARRAY, ZOUHAIER MEHREZ∗ and AFIF EL CAFSI Laboratoire d’Energétique et des Transferts Thermique et Massique (LETTM), Département de Physique, Faculté des Sciences de Tunis, Université d’el Manar, Tunis, Tunisia ∗Corresponding author. E-mail: [email protected]; [email protected] MS received 7 May 2020; revised 11 July 2020; accepted 29 July 2020 Abstract. The effect of an external magnetic field on the mixed convection Fe3O4/water ferrofluid flow in a horizontal porous channel was studied numerically. The governing equations using the Darcy–Brinkman– Forchheimer formulation were solved by employing the finite volume method. The computations were carried out for a range of volume fractions of nanoparticles 0 ≤ ϕ ≤ 0.05, magnetic numbers 0 ≤ Mn ≤ 100, Reynolds numbers 100 ≤ Re ≤ 500, Darcy numbers 10−3 ≤ Da ≤ 10−1 and porosity parameters 0.7 ≤ ε ≤ 0.9 while fixing the Grashof number at 104. Results show the formation of recirculation zone in the vicinity of the magnetic source under the influence of Kelvin force. It grows as the magnetic number increases. The friction factor increases by increasing the magnetic number and diminishes with the increase in Darcy number. The flow accelerates as the magnetic field intensifies. The heat transfer rate increases by increasing the volume fraction of the nanoparticles and the magnetic number. The effect of magnetic field on the hydrodynamic and thermal behaviours of the ferrofluid flow considerably intensifies by increasing Reynolds number and Darcy number. The combined effect of ferromagnetic nanoparticles and magnetic field on the enhancement rate of heat transfer becomes more pronounced at high values of Reynolds number, permeability and/or porosity parameter. Keywords. Mixed convection; porous medium; ferrofluid; magnetic field. PACS Nos 44.15.+a; 44.25.+f; 44.27.+g; 47.65.Cb 1. Introduction modification of the flow field and the temperature distribution. It is created by swirling the zones in the Several techniques are there to increase heat transfer vicinity of the magnetic sources, modifying thus the in engineering applications using cooling and heating characteristics of the thermal boundary layer. This fact systems such as electronic and microelectronic devices, largely affects the heat transfer rate in the ferrofluid flow. heat exchangers, engines and automobiles, solar energy, In recent years, the problem of ferrofluid flow in the refrigerator-freezers, nuclear reactors and transformers. presence of magnetic field, called ferrohydrodynamic The most recent technique is the one where thermal (FHD), is largely studied in various configurations by conductivity of the carrier fluid is increased by adding many researchers. Mokhtari et al [1] showed that the nanosized metallic or metallic oxide particles. The heat transfer rate can reach 30% by applying a mag- obtained suspension, called nanofluid, has shown its netic field in the ferrofluid flow inside the tube with effectiveness in terms of heat transfer enhancement in twisted tapes. Hassan et al [2] numerically investi- many engineering configurations. When the suspended gated FHD in stretchable rotating disk. They showed nanoparticles are magnetisable, a particular nanofluid that the maximum heat transfer rate is obtained with called ferrofluid is obtained. Apart from its improved prolate iron nanoparticles and by applying oscillat- thermophysical properties, the heat transfer and the ing magnetic field. Ashouri and Shafii [3] studied ferrofluid flow behaviour can be modified by apply- the magnetoconvection ferrofluid flow in a permanent ing external non-uniform magnetic field. In fact, under magnet-inserted cavity. They proved that heat rate will the effect of magnetic field, the magnetic moments be maximum for an optimum size of the permanent of the particles follow the field lines, leading to the magnet. Kamıs and Atalık [4] studied the influence 0123456789().: V,-vol 156 Page 2 of 12 Pramana – J. Phys. (2020) 94:156 of thermomagnetic effect on the stability of Taylor– enhancement, especially at high frequency. Izadi et al Couette ferrofluid flow under an azimuthal magnetic [20] analysed the combined FHD–MHD natural con- field. They observed the stabilising effect of the strong vection of a hybrid carbon nanotube–Fe3O4 nanofluid magnetic field which can be amplified by increasing flow in an inversed T-shaped porous enclosure. Results the volume fraction and the size of the ferroparticles. show that increasing the Hartmann number restrains the The effect of FHD in the heat transfer enhancement convective motion and energy transport, and reduces the of a fin-and-tube compact heat exchanger was investi- heat transfer rate. However, the increment of the mag- gated by Bezaatpour and Rostamzadeh [5]. They found netic field strength intensifies the circulation and thermal that the local and average heat transfer coefficients transmission. Fadaei et al [21] investigated the forced- increase around all tubes by increasing the magnetic convection heat transfer problem in a pipe partially filled field strength. Gibanov et al [6] studied the MHD with porous medium under the influence of a magnetic and FHD effects on the mixed convection heat trans- field. They showed that the convective heat transfer rate fer ferrofluid flow in a lid-driven cavity containing increases up to 30% in the presence of magnetic field a heat-conducting solid backward facing step. They induced by a solenoid traversed by a current of inten- found that the heat transfer rate increases with the sity 10 A. Bezaatpour and Goharkhah [22] investigated increment of magnetic number and volume fraction of the FHD effect on the Fe3O4/water ferrofluid flow in a nanoparticles, whereas it decreases by increasing Hart- porous fin heat sink. They indicated that the heat transfer mann number. Sheikholeslami et al [7] investigated the rate enhances by increasing the volume fraction of fer- impact of variable magnetic forces on the magnetis- roparticles, the magnetic field intensity and fin porosities able hybrid nanofluid heat transfer through a circular whereas it is weakened with the Reynolds number. Izadi cavity. They demonstrated that adding hybrid nanopar- et al [23] showed that for certain pertinent parameters, ticles of MWCNT–Fe3O4 enhances the heat transfer. the heat transfer can increase by applying two mag- This depends on the pertinent parameters such as mag- netic fields on the magnetisable hybrid nanofluid inside a netic strengths ratio parameter, magnetic number and porous enclosure. Ghalambaz et al [24] emphasised the Hartmann number. Selimefendigil et al [8] examined the combined effect of FHD and MHD on the heat and mass effect of variable magnetic field on the forced convection transfers of magnetic nanofluid flow inside a hexago- Fe3O4–water nanofluid in a bifurcating channel. They nal cavity. They found that there is an increase in rates revealed that the heat transfer enhancements were in the of heat and mass transfers by increasing the magnetic range of 12–15% and 9–12% in the absence and pres- number but a decrease with the increase in Hartmann ence of magnetic field, respectively. Many investiga- number. tions studying the FHD of clear medium in channels and The aforementioned literature shows that only the microchannels were published (see refs [9–18]). In these effects of magnetic field on the ferrofluid flow in a clear works, various methods were used and different empir- medium in a horizontal channel have been studied in ical and theoretical correlations modelling the magnetic some recent works. However, this problem is not stud- moment and the Kelvin force were employed. The com- ied yet in a porous medium. The present study deals with mon point between the results is the strong effect of the FHD effect on the hydrodynamic and thermal char- magnetic field on the heat transfer enhancement. acteristics of mixed convection Fe3O4/water ferrofluid Porous medium is a rigid solid matrix having commu- flow in a horizontal porous saturated channel. nicant voids (pores) and containing one or more fluid phases (gas or liquid) which can flow and exchange the energy and the matter between them and with the 2. Physical configuration solid phase. Porous media play important roles in many industrial domains and in various field of science such as Figure 1 presents the studied configuration with bound- petroleum engineering, chemical engineering and elec- ary conditions. It is a horizontal channel with an aspect trochemistry, hydrogeology, geothermal energy, thermal ratio of L/H = 10 where L and H are the length and engineering, civil engineering, medicine, biochemistry the height of the channel respectively. A fully developed and nuclear engineering. Thus, the FHD in porous parabolic velocity profile and low temperature (TC ) are medium is considerably important because it can influ- deployed at the inlet. No-slip conditions are prescribed ence the transport and exchange of energy. In this regard, at the channel walls. At the outlet, convective boundary Amani et al [19] conducted an experimental investi- conditions velocity and temperature are imposed. The gation on the influence of variable magnetic field on lower wall is maintained isothermal at high temperature / the hydrothermal behaviour of Fe3O4 water ferrofluid (TH ) whereas the upper wall is thermally insulated. The flow through the metal foam. They showed the strong channel is filled by glass balls as the porous medium. effect of variable magnetic field on the heat transfer The ferrofluid is the pure water as the carrier fluid where Pramana – J. Phys. (2020) 94:156 Page 3 of 12 156 Figure 1. Physical configuration. Table 1. Thermophysical properties of the base fluid, solid coordinates are given as follows [25,27]: nanoparticles and glass balls. ∂ ∂v u + = Physical properties Water Fe3O4 Glass balls ∂ ∂ 0(4) x y ρ(kg/m3) 997.1 5200 2700 1 ∂u 1 ∂u ∂u / ρ + u + v cp (J kg K) 4179 670 840 nf ε ∂t ε2 ∂x ∂y k (W/m K) 0.613 6 1.05 −5 −1 ∂ μ ∂2 ∂2v β × 10 (K ) 21 1.3 0.9 =− p + nf u + ∂x ε ∂x2 ∂y2 ferronanoparticles of Fe3O4 are suspended.