Natural Convection of Fe3O4-Ethylene Glycol Nanouid under the Impact of Electric Field in a Porous Enclosure
Sheikholeslami M.1, Shehzad S. A.2, *, Kumar R.3
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran
Department of Mathematics, COMSATS Institute of Information Technology, Sahiwal 57000, Pakistan
Department of Mathematics, Central University of Himachal Pardesh, Dharamshala, India

 

† Corresponding author. E-mail: sabirali@ciitsahiwal.edu.pk

Abstract
Abstract

Free convection of Fe3O4-Ethylene glycol nanofluid in existence of Coulomb forces is studied. Effect of thermal radiation is taken into account. Properties of nanofluid are varied with supplied voltage and shape of nanoparticles. The bottom wall is considered as positive electrode. Control Volume based Finite Element Method is used to obtain the results, which are the roles of Darcy number (Da), radiation parameter (Rd), Rayleigh number (Ra), nanofluid volume fraction (ϕ), and supplied voltage (Δφ). Results indicate that Nusselt number is an enhancing function of supplied voltage and Darcy number. Maximum values for temperature gradient are occurred for platelet shape nanoparticles.

Nomenclature

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Subscripts

1 Introduction

One interesting active method for heat transfer augmentation is Electrohydrodynamic. Rarani et al.[1] reported good correlation for viscosity of nanofluid. Nanofluid has various applications in presence of various external forces. Heat transfer and pressure drop characteristics in the microchannel heat sink (MCHS) have been investigated by Liu et al.[2] They showed that interlaced microchannel leads to better heat transfer performance. Also they proved that pressure drop of the T-Y type microchannel is low. Kumar et al.[3] demonstrated radiative heat transfer of non-Newtonian nanofluid over a Riga sheet. Three-dimensional nanofluid flows was demonstrated by Sheikholeslami and Ellahi.[4] They illustrated that velocity detracts with augment of Lorentz forces. Sheikholeslami and Sadoughi[5] demonstrated water based nanofluid flow in presence of melting surface. Sheikholeslami and Shehzad[6] presented the influence of radiative mode on ferrofluid motion. They were taken into account variable viscosity. Nanofluid concentration has been reported by Hayat et al.[7] in existence of radiative mode. Kumar et al.[8] investigated Joule heating effect on nanofluid flow a rotating system. Sheikholeslami[9] investigated nanofluid EHD flow in a porous media. Sheikholeslami et al.[10] utilized mesoscopic method for nanofluid forced convection. Promvonge et al.[11] utilized V-finned twisted tapes in a duct to improve the thermal behavior. Influence of viscous dissipation on heat transfer in a circular micro-channel has been investigated by Liu et al.[12] Sheikholeslami and Seyednezhad[13] simulated nanofluid flow and natural convection in a porous media under the influence of electric field. Impact of variable Kelvin forces on ferrofluid motion was reported by Sheikholeslami Kandelousi.[14] Heat flux boundary condition has been utilized by Sheikholeslami and Shehzad[15] to investigate the ferrofluid flow in porous media. Sheikholeslami[16] investigated CuO-water nanofluid flow in a porous enclosure under the impact of Lorentz forces. In recent decade, various researcher published papers about heat transfer.[1722]

This article intends to model the influence of thermal radiation on nanofluid behavior in existence of Coulomb forces via CVFEM. Roles of Darcy number, Rayleigh number, supplied voltage, radiation parameter and Fe3O4 volume fraction are presented in outputs.

2 Problem Definition

Figure 1 depicts the porous enclosure and its boundary conditions. Ethylene glycol - Fe3O4 nanofluid is utilized. All walls are stationary. Influence of Darcy and Rayleigh number on contour of q is demonstrated in Fig. 2. Effect of Ra on q is less sensible than Da. As Darcy number augments the distortion of isoelectric density lines become more.

Fig. 1 (a) Geometry and the boundary conditions with, (b) Sample mesh, (c) A sample triangular element and its corresponding control volume.
Fig. 2 Electric density distribution injected by the bottom electrode when Δφ = 6 kV, ϕ = 0.005, Rd = 0.8.
3 Governing Formula and Modeling
3.1 Governing Formula

The definition of electric field is[23]

The governing formulae are[20]

(ρCp)nf, βnf, (μnf) and ρnf can be obtained as:[23]

Properties of Fe3O4 and ethylene glycol are illustrated in Table 1. EFD viscosity is presented by Ref. [1]. Table 2 illustrates the coefficient values of this formula.

Table 1

Thermo physical properties of Ethylene glycol and nanoparticles.

.
Table 2

The physical values of Eq. (13).[1]

.

knf can be expressed as:

Different values of shape factors for various shapes of nanoparticles are illustrated in Table 3.

Table 3

The values of shape factor of different shapes of nanoparticles.

.

So, the final PDE in existence of thermal radiation and electric field in porous media are:[20]

where

Vorticity and stream function should be employed in order to diminish pressure gradient:

Nuloc and Navg along the bottom wall are calculated as:

3.2 CVFEM

CVFEM uses both benefits of two common CFD methods. This method uses triangular element (see Fig. 1(b)). Upwind approach is utilized for advection term. Gauss-Seidel method is applied to find the solution of the algebraic system. Further notes exist in Ref. [24].

4 Mesh Study and Code Validation

Various mesh sizes have been tested to find the mesh independent result. Table 4 demonstrated an example. This table indicated that the size 81 × 241 of can be selected. The FORTRAN code has been validated by comparing the outputs with those of reported in Ref. [23] (see Fig. 3). Good agreement can be found.

Fig. 3 Comparison of temperature profile at middle line between the present results and numerical results by Khanafer et al.[23] Gr = 104, ϕ = 0.1 and Pr = 6.8 (Cu-water).
Table 4

Comparison of Nuave along hot wall for different grid resolution at Rd = 0.8, Ra = 500, Da = 102, Δφ = 6, ϕ = 0.05, and Pr = 6.8.

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5 Results and Discussion

Influence of Coulomb forces on nanofluid natural convection heat transfer is reported considering thermal radiation. Nanofluid viscosity is a function of electric field. The porous enclosure is filled with Fe3O4 Ethylene glycol. Roles of Darcy number (Da = 10−2 to 102), Radiation parameter (Rd = 0 to 0.8), supplied voltage (Δφ = 0 to 6 kV), volume fraction of Fe3O4 (0% to 5%), Rayleigh number (Ra = 50 to 500) are depicted.

In order to find the influence of nanoparticles’ shape of heat transfer rate, a comparison has been reported in Table 5. As Platelet shape Fe3O4 nanoparticle selected, maximum value of Nusselt number can be obtained. In continued result, we used this shape of nanoparticles. Influences of Δφ, Da, and Ra on nanofluid treatments are depicted in Figs. 4, 5, 6, and 7. When conduction is dominant, there exist two eddies, which are rotated in opposite direction. In existence of Coulomb forces, thermal plume appears and eddies are stretched. Isotherms become more disturb in presence of electric field. As buoyancy forces augments, another eddy appears. In high values of Rayleigh number, increasing permeability of porous media leads to convert all eddies to one clock wise eddy and thermal plume shift to left side.

Fig. 4 Effect of Darcy number on streamlines and isotherm when Ra = 50, Δϕ = 0 kV, ϕ = 0.05, Rd = 0.8.
Fig. 5 Effect of Darcy number on streamlines and isotherm when Ra = 50, Δϕ = 6 kV, ϕ = 0.05, Rd = 0.8.
Fig. 6 Effect of Darcy number on streamlines and isotherm when Ra = 500, Δϕ = 0 kV, ϕ = 0.05, Rd = 0.8.
Fig. 7 Effect of Darcy number on streamlines and isotherm when Ra = 500, Δϕ = 6 kV, ϕ = 0.05, Rd = 0.8.
Table 5

Effect of shape of nanoparticles on Nusselt number when Rd = 0.8, Ra = 500, Δφ = 6, ϕ = 0.05.

.

Figures 8 and 9 show the impacts of effective parameters on heat transfer rate. The related correlation is:

where Ra* = 0.01Ra, Da* = 0.01Da, and Δφ is voltage supply in Kilovolt. Nusselt number augments with increase of Rayleigh number. Electric field helps the convective mode to improve because thermal boundary layer thickness decreases with augment of Δφ. So, Nuave augments with augment of Δφ. Temperature gradient near the bottom wall increases with augment of radiation parameter. Influence of Darcy number is as same as radiation parameter. Therefore, Nave is an increasing function of Rd, Da.

Fig. 8 Effects of Da, Δφ, Rd, and Ra on average Nusselt number.
Fig. 9 Effects of Da, Δφ, Rd, and Ra on average Nusselt number.
6 Conclusions

Electric field effect on nanofluid natural convection in a porous cavity is simulated by means of CVFEM. Outputs are reported for various values of Rd, Da, Δφ, ϕ, and Ra. Outputs demonstrate that the distortion of isotherms becomes more with augment of Darcy number, radiation parameter, and Coulomb forces. As radiation parameter increases, temperature gradient near the hot wall enhances. Nusselt number has direct relationship with Darcy number, radiation parameter and Coulomb forces.

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