Numerical simulation for impact of Coulomb force on nanofluid heat transfer in a porous enclosure in presence of thermal radiation

doi:10.1016/j.ijheatmasstransfer.2017.11.041

International Journal of Heat and Mass Transfer

Volume 118, March 2018, Pages 823-831

https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.041 Get rights and content

Highlights

•
Fe₃O₄-Ethylene glycol nanofluid EHD flow is investigated.
•
Thermal radiation effect on nanofluid behavior is considered.
•
New numerical approach (CVFEM) is utilized.
•
Nusselt number is an augmenting function of Coulomb force.
•
Platelet shape nanoparticle has highest Nusselt number.

Abstract

Influence of thermal radiation and external electric field on Fe₃O₄-Ethylene glycol nanofluid hydrothermal treatment is presented in this article. The lid driven cavity is porous media and the bottom wall is selected as positive electrode. Influence of supplied voltage on viscosity of nanofluid is taken into account. Control Volume based Finite Element Method is utilized to estimate the roles of radiation parameter $(Rd)$ , Darcy number $(Da)$ , Reynolds number $(Re)$ , nanofluid volume fraction $(ϕ)$ and supplied voltage $(Δ φ) .$ Results indicate that shape of nanoparticles can change the flow style and maximum rate of heat transfer is obtained by selecting platelet shape nanoparticles. The convective heat transfer improves with augment of permeability and Coulomb force.

Introduction

Electric field can be introduced as very effective active method for heat transfer improvement. Nanotechnology can be combined with this active method. Rarani et al. [1] reported good correlation for viscosity of nanofluid. Hayat et al. [2] investigated mixed convection of nanofluid in presence of thermal radiation. Sheikholeslami et al. [3] investigated the impact of external magnetic field on nanofluid convective heat transfer. Nanofluid natural convection in a three dimensional enclosure was demonstrated by Sheikholeslami and Ellahi [4]. They depicted that velocity detracts with augment of Lorentz forces. Sheikholeslami and Chamkha [5] presented the influence of electric field on natural convection of nanofluid in wavy cavity. Sheikholeslami and Shehzad [6] presented the influence of radiative mode on flow style of ferrofluid. They were taken into account MFD viscosity.

Sheikholeslami and Shehzad [7] presented the shape factor effect on nanofluid behavior in existence of external magnetic field. Yadav et al. [8] illustrated nanoparticle transportation due to external forces. Kuznetsov and Sheremet [9] reported the conjugate heat transfer in existence of constant heat flux. Conjugate heat transfer of nanofluid has been simulated by Selimefendigil and Oztop [10]. They considered various inclination angles. Sheikholeslami and Shehzad [6] considered variable viscosity in simulation of nanofluid flow in existence of Lorentz forces. Sheikholeslami and Sadoughi [11] investigated the influence of melting surface on nanofluid flow and heat transfer. Sheikholeslami [12] presented three dimensional simulation of MHD non-Darcy natural convection. Impact of variable Kelvin forces on ferrofluid motion was reported by Sheikholeslami Kandelousi [13]. Heat flux boundary condition has been utilized by Sheikholeslami and Shehzad [14] to investigate the ferrofluid flow in a porous media. Nanoparticle movement in a channel due to Lorentz forces was demonstrated by Akbar et al. [15]. Sheikholeslami et al. [16] reported the nanoparticle transportation under the influence of thermal radiation. In recent decade, various researcher published papers about heat transfer [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29].

The main goal of this paper is to model the influence of thermal radiation on nanofluid behavior in existence of Coulomb forces via CVFEM. Roles of Darcy number, Reynolds number, supplied voltage, radiation parameter and Fe₃O₄ volume fraction are presented in outputs.

Section snippets

Problem definition

Porous enclosure and its boundary conditions are depicted in Fig. 1. Ethylene glycol-Fe₃O₄ nanofluid is considered as working fluid. All walls are stationary except for positive electrode. Influences of Darcy and Reynolds number on contour of $q$ are depicted in Fig. 2. As Darcy number enhances the distortion of isoelectric density lines become more. Effect of $Re$ on $q$ is less sensible than $Da$ .

Governing formula

The definition of electric field is [5]: $\vec{E} = - \nabla φ$ $q = \nabla \cdot ε \vec{E}$ $\vec{J} = q \vec{V} - D \nabla q + σ \vec{E}$ $\nabla \cdot \vec{J} + \frac{\partial q}{\partial t} = 0$

The governing equations are [5]: $\{\begin{matrix} \nabla \cdot \vec{V} = 0, \\ ((\vec{V} \cdot \nabla) \vec{V} + \frac{\partial \vec{V}}{\partial \bar{t}}) = \frac{q \vec{E}}{ρ_{nf}} + \frac{μ_{nf}}{ρ_{nf}} \nabla^{2} \vec{V} - \frac{\nabla p}{ρ_{nf}} - \frac{μ_{nf}}{K ρ_{nf}} \vec{V}, \\ ((\vec{V} . \nabla) T + \frac{\partial T}{\partial \bar{t}}) = \frac{k_{nf}}{{(ρ C_{p})}_{nf}} \nabla^{2} T + \frac{\vec{J} . \vec{E}}{{(ρ C_{p})}_{nf}} - \frac{1}{{(ρ C_{p})}_{nf}} \frac{\partial q_{r}}{\partial y}, [q_{r} = - \frac{4 σ_{e}}{3 β_{R}} \frac{\partial T^{4}}{\partial y}, T^{4} ≅ 4 T_{c}^{3} T - 3 T_{c}^{4}] \\ \nabla φ = - \vec{\bar{E}}, \\ \frac{\partial \bar{q}}{\partial t} = - \nabla . \vec{J}, \\ \bar{q} = \nabla . ε \vec{\bar{E}} \end{matrix},$ ${(ρ C_{p})}_{nf}, μ_{nf}$ and $ρ_{nf}$ can be obtained as [30]: ${(ρ C_{p})}_{nf} = {(ρ C_{p})}_{f} (1 - ϕ) + {(ρ C_{p})}_{s} ϕ, μ = A_{1} + A_{2} (Δ φ) + A_{3} {(Δ φ)}^{2} + A_{4} {(Δ φ)}^{3}, ρ_{nf} = ρ_{f} (1 - ϕ) + ρ_{s} ϕ$

Properties of Fe₃O₄ and ethylene glycol are demonstrated in Table 1 [1]. EFD viscosity is presented by [1]

Mesh study and code validation

Table 4 depicts a sample for mesh independency analysis. It proves that the grid size of $81 \times 241$ can be selected. The FORTRAN code was validated by comparing the outputs with those of reported in [30], [32] (see Fig. 3). Good agreement can be found.

Results and discussion

Influence of thermal radiation on nanofluid EHD forced convection is simulated. Viscosity of nanofluid is a function of Coulomb force. The porous enclosure is filled with Fe₃O₄ – Ethylene glycol and has one lid wall. Roles of Darcy number ( $Da = 10^{2} - 10^{5}$ ), Radiation parameter ( $Rd = 0 - 0.8$ ), supplied voltage ( $Δ φ = 0 - 10 kV$ ), volume fraction of Fe₃O₄ ( $ϕ = 0 - 5 %$ ), Reynolds number ( $Re = 3000 - 6000$ ) are investigated.

Influence of shape factor on Nusselt number is reported in Table 5. In this table, various shapes of

Conclusions

Nanofluid treatment in existence of electric field in a porous lid driven cavity is simulated via CVFEM considering radiative heat transfer. Outputs are reported for different values of $Da, Rd, ϕ, Δ φ$ and $Re$ . Outputs demonstrate that Nusselt number has direct relationship with radiation parameter. The convective mode enhances with increase of Darcy number, radiation parameter and Coulomb forces.

Conflict of interest

Our paper is original.

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Numerical simulation for impact of Coulomb force on nanofluid heat transfer in a porous enclosure in presence of thermal radiation

Highlights

Abstract

Introduction

Section snippets

Problem definition

Governing formula

Mesh study and code validation

Results and discussion

Conclusions

Conflict of interest

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

J. Mol. Liq.

Int. J. Heat Mass Transf.

Physica B

Int. J. Heat Mass Transf.

J. Magn. Magn. Mater.

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Int. J. Heat Mass Transf.

Int. J. Hydrogen Energy