Uniform magnetic force impact on water based nanofluid thermal behavior in a porous enclosure with ellipse shaped obstacle.

In the present research, aluminum oxide- water (Al2O3-H2O) nanofluid free convection due to magnetic forces through a permeable cubic domain with ellipse shaped obstacle has been reported. Lattice Boltzmann approach is involved to depict the impacts of magnetic, buoyancy forces and permeability on nanoparticles migration. To predict properties of Al2O3- water nanofluid, Brownian motion impact has been involved. Outcomes revels that considering higher magnetic forces results in greater conduction mechanism. Permeability can enhance the temperature gradient.

Introduction

By suggesting nanoparticles from nanoscience as useful working fluid, thermal performance enhances. Nano sized metallic particles are dispersed into common fluid to generate such fluid. Nanofluids must be utilized to augment the conduction and can be more stable with better mixing[1,2]. Nano science can suggest appropriate working fluid to reach thermal efficiency enhancement[3-6]. The furthermost current publications on nanofluids with new applications can be demonstrated in[7-12]. Kumar et al.[13] involved the Brownian motion impact on characteristics of nanoparticles in bioconvective flow. Irfan et al.[14] displayed the roles of chemical terms on transient energy equation. Ahmed et al.[15] illustrated the carbon nanotubes flow between Riga sheets in existence of viscous dissipation. Kumar et al.[16] employed the non-Fourier heat flux model for investigation of magnetic force effect on Carreau fluid convective transient flow. Ali et al.[17] demonstrated hidden events during magnetohydrodynamic (MHD) migration in a permeable media. Soomro et al.[18] employed Finite difference method (FDM) for dual solution of nanoparticle migration over a cylinder. They used water as pure fluid. Reddy et al.[19] depicted the impact of magnetic terms on fluid flow along a sheet considering heat sink. Raizah et al.[20] illustrated the power law nanofluid natural convection inside a titled permeable duct. The furthermost recent articles about Nano sized particles transportation by involving various methods were reported by Shah et al.[9,21,22]. Choosing active working fluid becomes popular subject in recent decade[23-51].

The main aim of current research is to simulate and examine nanoparticles migration within a cubic porous cavity under the influence of constant magnetic force. Hydrothermal behaviors for various permeability, Lorentz and buoyancy forces are mainly focused and shown through graph.

Geometry Explanation

Figure 1 displays the permeable cubic cavity which is full of alumina. Cold, adiabatic and hot surfaces are depicted in this graph. One direction magnetic force has been involved. (θ = 0.5 π = θ).

Figure 1

Current porous cubic cavity.

Simulation by Mesoscopic Method

Mesoscopic method

To find the temperature and velocity, distribution functions were used namely (g and f). Boltzmann equations help to find functions g and f. According to assumptions exist in[38], we have:

Here τ, Δt, τ and c are, relaxation time for T, time step, relaxation time for u and lattice velocity.

D3Q19 model is good method for such problem (as shown in Fig. 2):

Figure 2

Diagram of D3Q19 model.

& are:

Body forces can calculate as:

To calculate scholars we have:

Working fluid

Density, (ρβ), (ρC), σ, μ and k are ([39]):

Tables 1 and 2[39] can be used to find needed parameters. Nu and Nu over the hot surface are:

Table 1

Properties of Water, Al2O3.

	σ(Ω · m)−1	k(W/m.k)	Cp(j/kgk)	ρ(kg/m3)
Pure water	0.05	0.613	4179	997.1
Al2O3	10−12	25	765	3970

Table 2

Related coefficient for alumina.

Coefficient values	Al2O3−Water
a6	−298.19819084
a7	−34.532716906
a8	−3.9225289283
a9	−0.2354329626
a10	−0.999063481
a1	52.813488759
a2	6.115637295
a3	0.6955745084
a4	4.174555527E-02

The fluid kinetic energy is:

Mesh Independency and Validation

No alter should be seen in outputs by changing mesh sizes. So, various sizes must be employed. As an example, we presented Table 3. Figure 3 illustrates the agreement of Lattice Boltzmann Method (LBM)[40,41]. Also, previous paper[42] indicates that this code is verified for MHD flow.

Table 3

Nu over the hot surface with various grid sixes when Da = 100, ϕ = 0.04, Ra = 105, and Ha = 60.

Mesh size	51 × 51 × 51	61 × 61 × 61	71 × 71 × 71	81 × 81 × 81	91 × 91 × 91
Nuave	0.13622	0.14805	0.15061	0.15073	0.15097

Figure 3

Verification of current LBM code for (a) free convention[40]; (b) nanofluid flow[41].

Results and Discussion

Water-Aluminum oxide mixture hydrothermal behavior in a permeable three dimensional domain was modeled with mesoscopic method. Numerical outputs are depicted the variations of magnetic force (Ha = 0 to 60), buoyancy term ( and 105) and Darcy number (Da = 0.001 to 100).

Nanofluid behavior with change of and Da are displayed in Figs 4–7. In cases with low and Da, convection mode is not strong enough to change flow style and isotherms has shape of geometry. Convection enhancements with increase of permeability and isotherms convert to complex shape. Thermal plume appears as a result of strong convection mode. Employing magnetic forces makes conduction to be more sensible and thermal plumes vanish. Due to reduction effect of Ha on velocity, E detracts with rise of Ha. By augment of buoyancy force, main vortex stretch in z direction and convection mode rises.

Figure 4

Impacts of magnetic forces on (a) isotherm, (b) x velocity, (c) z velocity, (d) isokinetic energy at Y = y/L = 0.5 when ϕ = 0.04, Da = 0.001, Ra = 103.

Figure 7

Impacts of magnetic forces on (a) isotherm, (b) x velocity, (c) z velocity, (d) isokinetic energy at Y = y/L = 0.5 when Ra = 105, Da = 100, ϕ = 0.04.

Impacts of magnetic forces on (a) isotherm, (b) x velocity, (c) z velocity, (d) isokinetic energy at Y = y/L = 0.5 when Ra = 103, Da = 100, ϕ = 0.04.

Impacts of magnetic forces on (a) isotherm, (b) x velocity, (c) z velocity, (d) isokinetic energy at Y = y/L = 0.5 when Ra = 105, Da = 0.001, ϕ = 0.04.

Changes in Nu due to altering variables are illustrated in Fig. 8. Equation (17) is extracted for Nu:

Figure 8

Various values of Nu for different Ra, Da, Ha.

Due to augment in temperature gradient with rise of permeability and buoyancy terms, Nu is enhancing function of . Furthermore, conduction mode boosts with augment of Hartmann number. Thus, Nu detracts with rise of magnetic force.

Conclusions

In the current article, uniform magnetic force impacts on momentum equations were considered in a 3D porous enclosure. Mesoscopic approach was applied to analyze alumina nanofluid in these conditions. Brownian motion impact can changes the properties of working fluid. LBM was involved to report the impacts of Ha, Ra, Da on nanofluid behavior. Outcomes display that interaction of nanoparticles augments with augment of Da,Ra. Isotherms become less complex with applying magnetic force.