Numerical analysis of MHD flow and nanoparticle migration within a permeable space containing Non-equilibrium model

https://doi.org/10.1016/j.physa.2019.122459Get rights and content

Highlights

  • Migration of nanofluid heat transfer within porous media is investigated.

  • CVFEM is applied to simulate radiation effect.

  • As shape factor augments, convective mode enhances.

  • Nuave enhances with augment of Rd and Ra.

Abstract

This article deals with the numerical simulation to examine the significant effects of MHD flow and nanoparticle migration inside a permeable space including two temperature model. For more physical situation, thermal radiation influence is considered. Viable transformation is assumed to alter the governing set of PDEs into dimensionless form. CVFEM was adopted to model this article. Impacts of radiation parameter, Rayleigh number (103 < Ra < 104), nanofluid–solid interface factor (10 < Nhs <1000), Hartmann number (0 < Ha < 20) and nanoparticles’ shape (3 < m < 5.7) on nanofluid behavior were demonstrated. Outcomes depict that stronger convection can be obtained with augmenting in shape factor. Average Nusselt number increases as enhancing the buoyancy and radiation effect whereas decreases as enhancing nanofluid–solid interface factor and Hartmann number. Comparison of the numerical outputs achieved by means of CVFEM with published data was also deliberated. It is evident that the applied approach is very accurate to investigate solution of the discussed problem.

Introduction

Old-style carrier fluids, like oil are naturally poor in view of thermal behavior. So, there is fundamental need to develop such type of fluid which enhances the heat transfer rate and their thermal conductivities are significantly higher than the current available fluid. In spite of extensive past innovative work concentrating on modern heat exchange prerequisites, significant enhancements in heat exchange capacities have been kept down due to a crucial limit in the thermal conductivity of old-style carrier fluids. Nanoparticles having advanced thermal conductivity provide the better thermal characteristics of base fluid as mixing the particles which are nonmetallic or metallic like, Ag, Cu, Au, TiO2 CuO, SiO2, Al2O3. In 1995 [1], it is first time reported that suspension of nanoparticles with water, kerosene, engine oil and various others fluids can augment the thermal properties. Later, this novel concept verified theoretically and experimentally by many authors [2], [3], [4], [5]. To improve the specific heat of carrier fluid, Han et al. [6] have dispersed nanoparticles into PCMs. These are the pioneer who address thermal conductivity and this work allow industrial cooling applications. To measure the viability of nanomaterial in the field of special applications by refining the enactment of any water-cooled unit, Kim et al. [7], [8] accomplished a comprehensive study. In [9], it is proved that the reduction is possible in the area of the radiator up to 10% by using nanofluids having high thermal conductivity in radiators. This study helps to save the fuel up to 5% in aerodynamic drag. Xue [10] presented a detail investigation of the interface impact among the pure fluid and solid particles. In his study, author concluded that their obtained formulas have nice accuracy. Recently, Usman et al. [11] scrutinized the influences of H2O based Cu-nanoparticles on fluid flow among two parallel squeezing permeable disks. They deducted that Nu for water based nanofluid is smaller than ethylene glycol based. In other work, Hamid et al. [12] explore the shape effect of MoS2 on nanomaterial rotating flow and heat transfer over exponential plate.

Nowadays, heat transfer analysis is an encouraging topic because of its fundamental significance in engineering and technology including the frequent use in biomass, food processing, energy systems, fuel cells, solar, high capacity cooling processes, wind, photovoltaic, photosynthesis, PCMs avionics and vehicles, food, textile and other plants etc [13], [14], [15], [16]. Fluid flow, heat transfer and thermal control analysis enclosed a different shapes of cavity with different obstacles was found an emerging area of research. In that cases, fluids discovered best source to investigate the heat transport in cavities. Basak et al. [17] examined the free convection within a cavity occupied with permeable medium. They explored that Nu at bottom wall is as much as the center of the cavity. Haq and Aman [18] studied the migration of copper oxide nanoparticles inside a trapezoidal domain. They proved that as increasing Rayleigh number, stronger convective flow is obtained. Comprehensive investigation of the impact of Kelvin forces on hybrid nanomaterial behavior inside an annuls was discussed by Sheikholeslami et al. [19]. Obtained outputs displayed that the Nu has direct proportional to Hartman. Mahmoudi et al. [20] considered the significant effects of Lorentz force on free convection heat transfer enclosed a tank. In their study, they demonstrated that the Nu rises as enhancing Ra but it declines as enhancing the Hartmann number. Similarly, the applications of heat transfer enclosed an enclosure can be mentioned elsewhere [21], [22], [23], [24], [25], [26]. Apart from the heat transfer analysis within a permeable cavity with equilibrium model, the MHD effects have been theoretically discovered by many researchers. Due to its huge applications in meters, pumps, bearings, generators, this field becomes very hot nowadays. An advanced scheme has been applied to examine the impact of magnetic force on flow through a permeable zone by Sheikholeslami [27]. Hamid et al. [28] scrutinized a transient electrically conducting flow of a non-Newtonian fluid. The mathematical modeling was performed using Williamson model in existence of source/sink and natural convection impacts. Several efforts have been done to develop new numerical simulation [29], [30], [31], [32], [33], [34], [35], [36].

The above inclusive literature survey inspired us to investigate the significance influence of magnetohydrodynamic on nanoparticle migration inside a porous space including two temperature models in the appearance of thermal radiation. Therefore, the attained results will help out to readers and make contribution to understand the fluid flow style. Control volume finite element method was proposed to solve the achieved mathematical model. CVFEM is very powerful and can be applied to both problems related to solid mechanics and fluid flow. The CVFEM syndicates the flexibility of the traditional finite element method to discretize the problem having complex domain. Simulations are performed to analyze the impact of Hartmann number, radiation parameter, buoyancy forces, nanofluid–solid interface factor and nanoparticles’ shape. Comparison also deliberated to show the credibility of proposed scheme.

Section snippets

Problem explanation

Two-dimensional MHD flow and nanoparticle migration inside a permeable cavity is considered with two temperature model (as depicted in Fig. 1). CVFEM is engaged with triangular element. Assume the flow within the cavity is steady, laminar and incompressible. Magnetic field with strength |B0| is considered making an angle γ. Furthermore, small magnetic Reynolds number is considered that verify the neglecting induced magnetic field. All fluid properties except density are considered as constant.

Equations

In current model, non-equilibrium model has been included for porous space. According to the above mentioned limitations the PDEs take the below form [37]: ux+vy=0, Px+μnfKu=sinγσnfB02vcosγusinγ, Py+μnfKv=TTcgρnfβnf+cosγσnfB02usinγvcosγ, 1εuTnfx+vTnfy+1ρCpnfqry=knfρCpnf2Tnfx2+2Tnfy2+hnfsερCpnfTnf+Ts,qr=4σe3βRTnf4y,Tnf44Tc3Tnf3Tc4 ksρCps2Tsx2+2Tsy2+hnfs1ερCpsTnfTs=0,Components of velocity in the direction of x and y-axis are u and v. ρCpnf,ρβnf, ρnf and σnf

Results and discussion

The result was dedicated to detailed investigation of analyzing the impact of shape factor, Hartmann number, radiation parameter, nanofluid–solidinterface factor and buoyancy forces on streamlines, nanofluid isotherms and solid isotherms. The porous domain was filled with CuO–H2O. Two temperature model was utilized. Fig. 3, Fig. 4, Fig. 5, Fig. 6, Fig. 7 are plotted along with comprehensive discussion. Graphical relation between the dimensionless parameters and their influence on average

Conclusions

This paper contained the detailed investigation of the MHD effect on nanoparticle migration inside a porous space including two temperature model. Dimensionless form is obtained via suitable transformation. CVFEM is proposed to simulate the impact of physical parameters. It is detected that behavior of solid isotherms does not have significant changes by enhancing the magnetic field effect in the cavity. Average Nusselt number increase as enhancing the buoyancy and radiation effect whereas

Acknowledgment

Dr. Abdul Khader Jilani would like to thank Deanship of Scientific Research at Majmaah University, Saudi Arabia for supporting this work under the Project Number No. 1440-84.

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