Numerical simulation of double diffusive mixed convective nanofluid flow and entropy generation in a square porous enclosure

https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.082Get rights and content

Highlights

  • An increase is observed in entropy due to heat transfer with a growth in Ri,φ,Da and .

  • A decrease is noticed in entropy due to heat transfer with a rise in q,Kr and Le.

  • The average Nusselt number increases with a rise in Ri,φ,Da and .

  • The average Nusselt number decreases with a rise in q,Kr and Le.

  • The average Sherwood number grows with an increase in Ri,Da,q,Kr and Le.

Abstract

In the present work, the numerical analysis of a double diffusive mixed convective alumina-water nanofluid flow in a square porous lid driven cavity is investigated to determine the influence of different physical parameters on the heat transfer and entropy generation. The upper wall of the enclosure is moving to the right while all the other walls are at rest. The flow is generated due to the motion of the top wall and the buoyancy forces that are produced due to the difference in temperature. A monolithic Galerkin finite element approach together with geometric multigrid technique has been adopted to solve governing equations for various governing parameters. Analysis has been shown in the form of streamlines, isotherms and isoconcentration, tables and plots. The influence of various physical parameters on the flow, in specific ranges such as the Richardson number (0.01Ri5), Darcy number (0.00001Da0.01), porosity parameter (0.20.8), Lewis number (0.1Le7), buoyancy ratio parameter (-2Br2), heat generation/absorption parameter (-0.4q0.4), chemical reaction parameter (0Kr0.04) as well as the nanoparticles volume fraction (0ϕ0.04) are investigated and findings are very closely comparable to the previous analysis for the special cases in the literature.

Introduction

The combined temperature and concentration gradients phenomenon in a porous medium is termed as double-diffusive convection. Double diffusion study has gained an extensive attention for many years based on its geophysical as well as the industrial applications. Some applications of double diffusive convection such as biology, geosciences, astrophysics, chemical reaction are mentioned in [1], [2], and its significance is also observed by Mansour et al. [3], Joly et al. [4], Platten [5], Patha et al. [6] and Bahloul et al. [7]. The analysis of the double diffusive convection has been reported numerically in an enclosure by Hyun and Lee [8] and Lee and Hyun [9]. Numerical results of their study were compared favorably with previous results obtained through experiments. The study of double diffusion in a vertical enclosure was reported by Mamou et al. [10].

In literature, double diffusion with various aspects has been studied in the porous media. Shermet et al. [11] have considered the nanofluid filled porous cavity to study the double diffusive mixed convection. Lin [12] performed transient convective heat transfer in a porous medium. Nithiarasu et al. [13] studied the double diffusion with free convection in a fluid-saturated porous cavity. Mahapatra et al. [14] studied the effects of buoyancy ratio on double-diffusive natural convection in a lid-driven cavity. Xu et al. [15] investigated the double diffusive natural convection and oscillation characteristics in an enclosure filled with porous medium. Goyeau et al. [16] presented the free convection in porous media along with double diffusive phenomenon. The thermosolutal convection in an enclosure inserted with two porous layers was investigated by Bennacer et al. [17]. They found the rate of heat and mass transfer as a weak function of Darcy number. Furthermore, Mamou et al. [18] conducted the double diffusive convection numerically in a porous enclosure, where at the vertical sides of the enclosure heat and mass fluxes are imposed. In recent past, Basak et al. [19] analyzed the impact of thermal boundary conditions on free convection problem inside a cavity filled with porous medium. Forchheimer utilized a model by introducing a non-linear inertial term [20]. This model successfully solves the problems with higher porosity values, as well.

The convective flows in the lid driven cavity carries significant use in various industrial applications including crystal growth, solar collectors, food processing, oven drying and electronic cards cooling, etc. [21]. Nithyadevi et al. [22] considered the effects of inclination angle and non-uniform heating on mixed convection of a nanofluid filled porous enclosure with active mid-horizontal moving. Rashad et al. [23] examined mixed convection of localized heat source/sink in a nanofluid-filled lid-driven square cavity with partial slip. Biswal et al. [24] discussed the analysis of heatline based visualization for thermal management during mixed convection of hot/cold fluids within entrapped triangular cavities. Muthtamilselvan et al. [25] studied the mixed convection numerically to analyze the impact of magnetic field on the flow in a lid driven cavity. Öztop et al. [26] examined the heat transfer numerically by conjugate mixed convection in a lid driven cavity considered with thick bottom wall. Sharif [27] considered the mixed convection inside a shallow tilted cavity with hot and cooled moving lids on its top and bottom respectively. Effect of nanofluid on the mixed convection flow inside a lid driven cavity partially heated from bottom is observed by Mansour et al. [28]. The study of mixed convection in a cubic double lid driven enclosure is investigated by Ouertatani et al. [29]. Enhancement of the heat transfer by the mixed convection in a lid driven wavy surface cavity using Taguchi approach was considered by Mamourian et al. [30].

Entropy generation suppresses the thermodynamic efficiency of a system. It indicates the location of a system in which more energy dissipation occurs. Bejan [31] has investigated the fundamental principles to mitigate the entropy generation. Since entropy is one reason out of many for the wastage of energy in heat transfer process, therefore sometimes it becomes necessary to measure entropy generation in a very accurate way. More study on entropy generation can be consulted from [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42]. Mahmoudi et al. [43] analyzed the nanofluid flow in a cavity along with heat generation/absorption and entropy effects and it was observed that heat generation/absorption parameter has no effect on entropy for -10q5. It was also shown that addition of nanoparticles has reduced the entropy generation. Moreover, nanoparticles have significant effect for large values of Hartmann number. Selimefendigil and Öztop [44] have investigated the impact of heat generation and magnetic field in an enclosure filled with nanofluid. It was noticed that the heat transfer reduces due to the existence of different obstacles. Influence of MHD on heat transfer and entropy generation in an enclosure saturated with nanofluid was discussed by Mehrez et al. [45]. It was observed that the average Nusselt number and entropy generation enhance due to an increase in nanoparticles volume fraction.

In this work, we shall perform the numerical simulation to investigate the double-diffusive mixed convection and entropy generation in alumina-water nanofluid filled lid-driven square porous cavity considering the effects of internal heat generation/absorption and chemical reaction. According to a careful literature survey, such type of study with this configuration and effects has not been considered and investigated yet.

Section snippets

The problem configuration

The problem consists of a porous cavity saturated with nanofluid (see Fig. 1). The top wall of the cavity is moving to the right with velocity U0 while all the remaining walls are at rest. The left vertical wall is maintained at hot temperature Th and higher mass concentration ch whereas the right vertical wall is kept at cold temperature Tc and low mass concentration cc. Furthermore, the top and the bottom walls are assumed to be adiabatic. The fluid motion is generated in the cavity because

The discretization scheme

The finite element method (FEM) based on the Galerkin version is utilized to solve the governing equations. After establishing the weak formulation of the governing equations, the velocity, temperature, concentration and pressure components are discretized with standard Q2 and P1disc elements, respectively (see [59] for details). We consider sequences of grids which are generated by uniform refinement from a coarsest mesh with only one cell. Starting from the coarsest grid defined as grid level

Results and discussion

A double diffusive mixed convective square porous lid driven cavity saturated with alumina-water nanofluid has been considered. It is numerically examined the effect of different physical parameters on the entropy generation and the heat transfer. The standard values of different parameters are such as Re=100, ϕ=0.04, Ri=1, Pr=6.2, Da=0.01, =1, Le=1, Br=1, q=0 and Kr=0 unless these are mentioned, otherwise.

The variation of the Nuavg,Shavg,θavg,SHT,avg,SFF,avg and SDC,avg with respect to q and

Conclusions

In this work, the influence of the internal heat generation/absorption and chemical reaction on the double diffusive mixed convective nanofluid saturated square porous cavity are numerically investigated. The governing equations resulting from physical model are discretized by the Galerkin weighted residual finite element procedure. Some remarkable points of this work may be concluded as follows:

  • The average Nusselt number increases with an amplification in Ri,ϕ,Da and whereas it decreases

Conflict of interest

The authors declared that there is no conflict of interest.

Acknowledgments

Calculations have been carried out on the LiDOng cluster at TU Dortmund. The support by the LiDOng team at the ITMC at TU Dortmund is gratefully acknowledged. We would like to thank the LiDOng cluster team for their help and support. We also used FeatFlow (http://www.featflow.de) solver package and would like to acknowledge the support by the FeatFlow team.

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