Numerical approach for MHD Al2O3-water nanofluid transportation inside a permeable medium using innovative computer method

https://doi.org/10.1016/j.cma.2018.09.042Get rights and content

Highlights

  • New computer approach was employed namely Control Volume Finite Element Method.

  • Nanofluid MHD flow inside a porous cavity was investigated using Darcy law.

  • Shape factor and Brownian motion effect were included in nanofluid modeling.

  • Nusselt number enhances with augmentation of radiation parameter.

Abstract

Innovative numerical approach was employed to demonstrate nanofluid MHD flow through a porous enclosure. To model porous medium, Darcy law has been employed. Radiation impact was included in energy equation. The new method (CVFEM) has been employed due to complex shape of porous cavity. Aluminium oxide with different shapes was dispersed in to water. Viscosity of nanofluid changes with Brownian motion impacts. Roles of radiation, buoyancy and Hartmann number on treatment of alumina were displayed. Results prove that convection detracts with augment of magnetic forces. Radiation can reduce the temperature gradient.

Introduction

Porous media has various uses in different sciences. Nanofluid is new working fluid can be employed to enhance thermal properties. Modeling of nanofluid in a porous medium has various ways. One of the effective ways is Darcy model which is used in this paper. Abbas et al. [1] demonstrated micropolar nanofluid migration over a cylinder. They considered slip conditions and studied stagnation point flow. Khan [2] displayed the transportation of nanoparticles in existence of MHD slip flow. He utilized MoS2 nanoparticles. Haq et al. [3] reported the convective flow under Lorentz forces in a porous wavy cavity. Sheikh et al. [4] demonstrated the second-grade fluid migration through a permeable medium using time-fractional derivative. They included magnetic force effect on their model. Hayat et al. [5] simulated slip effect on MHD nanofluid transportation on a disk. They supposed rotating system and added the related terms. Sheikholeslami [6] demonstrated alumina forced convection in three dimensional porous media. He employed LBM to find the impact of magnetic forces. Ali et al. [7] modeled blood flow in a pipe with fractional model. They added the influence of magnetic field. Ijaz and Nadeem [8] studied the nanoparticles’ migration in tube for drug delivery purpose.

Kefayati [9] demonstrated nanoparticles’ mixed convection through a double side driven cavity. He utilized combination of FDM and LBM. Khan et al. [10] demonstrated the spray of nanofluid over a cylinder. They considered stretching wall for cylinder and added magnetic field impact. Haq et al. [11] simulated the SWCNTs nanoparticles migration in a C shape cavity. Sheikholeslami [12] illustrated Darcy law application for estimating nanofluid behavior through a porous cavity under Lorentz force. They found that magnetic force can reduce the velocity. Hashim et al. [13] investigated nanofluid transient heat transfer due to Lorentz forces. They used variable thermal conductivity. Ali et al. [14] utilized the new model for magnetohydrodynamic natural convection flow. They employed Caputo–Fabrizio derivatives. Various ways was employed to augment thermal characteristics of common fluid [[15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]].

In current attempt, magnetic force influences on nanofluid MHD convective flow through a permeable medium was demonstrated via Darcy law. Innovative method (CVFEM) has been employed for simulation. Graphs display impacts of Ra, Rd and Ha on behavior of nanofluid.

Section snippets

Problem description

Current porous enclosure and related boundary conditions were displayed in Fig. 1. The porous cavity is full of H2O based nanofluid. To obtain the shape of outer cold surface Eq. (1) can be used. r=rin+AcosNζζ0Uniform heat flux was employed for inner wall. Constant Lorentz force was added to control the flow.

Formulation

Heat transfer and nanofluid flow inside a complex shape porous medium is examined in current article. Lorentz force and thermal radiation impacts are included in our model. Darcy model is selected for porous media. To predict nanofluid characteristics, homogeneous model with considering shape factor effect has been employed. To model such problem, following equations can be considered: ux+vy=0 μnfKuσnfB02sinγvcosγusinγ2=Px μnfKvTTcgρnfβnf=Py+σnfB02cosγsinγuvcosγ ρCpnf1qry+u

Grid analysis and validation

Each simulation outputs must be independent of mesh size. Different grids should be tested for each state as illustrated in Table 4. To being sure about accuracy of present code comparisons with previous publication are demonstrated in Fig. 2 and Table 5 [[28], [29], [30]]. According to these observations, we can be sure about correctness of code.

Results and discussion

Radiative nanoparticles migration through a permeable medium has been demonstrated considering Darcy law. Nanoparticle’s shape and Brownian forces’ impacts on nanofluid behavior are considered. Results are presented to show the impact of Alumina volume fraction (ϕ=0 to 0.04), radiation parameter (Rd=0 to 0.8), buoyancy forces (Ra=100,200 and 600) and Hartmann number (Ha=0 to 20).

Differences of Nusselt number due to shape of Al2O3 were depicted in Table 6. Highest Nu is reported for Platelet

Conclusions

Impact of constant magnetic force on alumina transportation inside a permeable enclosure is reported using Darcy law. Various shapes of nanoparticle and Brownian forces on nanofluid properties are involved. Innovative method was completed using CVFEM. Roles of Hartmann and Rayleigh numbers and radiation parameter are depicted. Outputs depict that Nu decreases with improvement of Ha while it enhances with rise of Ra and Rd.

Acknowledgment

The author must acknowledge the funding support of Babol Noshirvani University of Technology, Iran through Grant program No. BNUT/390051/97.

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