Mesoscopic method for MHD nanofluid flow inside a porous cavity considering various shapes of nanoparticles

doi:10.1016/j.ijheatmasstransfer.2017.05.054

International Journal of Heat and Mass Transfer

Volume 113, October 2017, Pages 106-114

https://doi.org/10.1016/j.ijheatmasstransfer.2017.05.054 Get rights and content

Highlights

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Magnetohydrodynamic nanofluid convective flow in a porous cavity is investigated.
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Shape effect of nanoparticles is taken into account.
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Lattice Boltzmann method is selected for numerical procedure.
•
Nu_ave enhances with increase of $ϕ$ , Ra and Da.

Abstract

Lattice Boltzmann method has been utilized to investigate magnetic field impact on nanofluid natural convection inside a porous enclosure with four square heat sources. Brownian motion impact on nanofluid properties is considered. Impacts of shapes of nanoparticle, Rayleigh number $(Ra)$ , Darcy number $(Da)$ , nanofluid volume fraction $(ϕ)$ , Hartmann number $(Ha)$ on heat transfer treatment are demonstrated. Outputs indicate that convective heat transfer decreases with increase of $Ha$ but it augments with increase of $Da, Ra$ .

Introduction

One of the great kinetic based theory approaches is LBM. In this mesoscopic method, pressure can be obtained by using equation of state. Mustafa et al. [1] investigated rotating flow with non-uniform conductivity. They utilized non-Fourier heat flux theory. Sultana and Hyder [2] reported the natural convection in a sinusoidal porous cavity. Sheikholeslami et al. [3] illustrated nanofluid forced convection in existence of non-uniform Lorentz forces. Nanofluid convection in 3D enclosure has been reported by Sheikholeslami and Ellahi [4]. Sheikholeslami [5] applied LBM for simulation of nanofluid flow in a permeable media in existence of magnetic field. Sheikholeslami and Shehzad [6] reported the impact of thermal radiation on ferrofluid motion. They were taken into account variable viscosity. Nithyadevi et al. [7] presented the impact of tilted angle on nanofluid mixed convection in a permeable media.

Sheikholeslami and Bhatti [8] illustrated the impact of shape factor on ferrofluid forced convection. Sheikholeslami and Zeeshan [9] simulated nanofluid movement in a permeable medium with constant heat flux. Conjugate heat transfer of nanofluid was reported by Selimefendigil and Oztop [10]. They considered various inclination angles. Uddin et al. [11] investigated the blowing impact on nanofluid flow. Sheikholeslami [12] demonstrated the three dimensional nanofluid forced convection in a cubic cavity. Hayat et al. [13] examined the MHD nanofluid flow over a plate. 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 a porous media. Nanoparticle movement in a channel in existence of Lorentz forces was demonstrated by Akbar et al. [16]. Sheikholeslami and Bhatti [17] utilized active methods for augmentation in heat transfer. Sheremet et al. [18] demonstrated transient nanofluid flow in a permeable cavity. In recent years, different researchers reported about nanofluid heat transfer [19], [6], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42].

In this paper, influence of Hartmann number on MHD convective flow in a permeable medium is modeled. Mesoscopic method is employed as numerical approach. KKL model is selected to estimate $μ_{nf}$ . Influences of shape of nanoparticle, nanofluid volume fraction, Darcy number, Hartmann and Rayleigh numbers on hydrothermal behavior are demonstrated.

Section snippets

Problem formulation

Porous cavity is filled with CuO-H₂O nanofluid and horizontal magnetic field has been applied. Geometry and detail of current paper is depicted (see Fig. 1).

LBM

f and g are two distribution functions which are used for velocity and temperature, respectively. Cartesian coordinate is used. Fig. 1(b) shows the D₂Q₉ model. f and g can be obtained by solving lattice Boltzmann equation. According to BGK approximation, the governing equations are [4]: $c_{i} Δ {tF}_{k} + [- f_{i} (x, t) + f_{i}^{eq} (x, t)] τ_{v}^{- 1} Δ t = f_{i} (x + c_{i} Δ t, t + Δ t) - f_{i} (x, t$

Mesh independency and validation

Various meshes have been examined. According to Table 4, a grid size of $140 \times 140$ can be chosen to complete this article. For verification purpose, the obtained outputs are compared with previous published papers [45], [46] in Fig. 2 and Table 5. According to these results, LBM code provides good correctness.

Results and discussion

Water based nanofluid convective flow in a permeable cavity with four square obstacles is simulated in existence of magnetic field. Two obstacles are hot and others are cold. LBM has been employed to simulate this problem. KKL model is utilized to estimate $μ_{nf}$ . Numerical simulation is completed by presenting the influence of active parameters namely: shape of nanoparticles; nanofluid volume fraction ( $ϕ = 0$ – $0.04$ ), Hartmann number ( $Ha = 0$ – $60$ ), Darcy number ( $Da = 0.001$ – $100$ ), Rayleigh number ( $Ra = 10^{4}$ – $10^{6}$

Conclusions

Nanofluid natural convective heat transfer inside a permeable cavity with four square obstacles is modeled using LBM. KKL model is considered for nanofluid. Influences of Rayleigh number, shape of nanoparticles, CuO-H₂O volume fraction, Hartmann and Darcy numbers on heat transfer treatment are reported. Results demonstrate that Darcy number can enhance the temperature gradient. Temperature gradient increases with enhance of Ra but it detracts with rise of magnetic field.

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Mesoscopic method for MHD nanofluid flow inside a porous cavity considering various shapes of nanoparticles

Highlights

Abstract

Introduction

Section snippets

Problem formulation

LBM

Mesh independency and validation

Results and discussion

Conclusions

Int. J. Heat Mass Transfer

Int. Commun. Heat Mass Transfer

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