Numerical simulation of double diffusive mixed convective nanofluid flow and entropy generation in a square porous enclosure
Graphical abstract
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 . 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 while all the remaining walls are at rest. The left vertical wall is maintained at hot temperature and higher mass concentration whereas the right vertical wall is kept at cold temperature and low mass concentration . 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 and 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 , , , , , , , , and unless these are mentioned, otherwise.
The variation of the and 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 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.
References (66)
- et al.
Numerical study of double-diffusive natural convection in a square cavity
Int. J. Heat Mass Transfer
(1992) Heat transfer in geothermal system
Adv. Heat Transfer
(1979)- et al.
Double-diffusive convection in a rectangle with opposing horizontal and concentration gradients
Int. J. Heat Mass Transfer
(1990) - et al.
Double-diffusive natural convection in a fluid saturated porous cavity with a freely convecting wall
Int. Commun. Heat Mass Transfer
(1997) - et al.
Effects of buoyancy ratio on double-diffusive natural convection in a lid-driven cavity
Int. J. Heat Mass Transfer
(2013) - et al.
Lattice Boltzmann simulation of the double diffusive natural convection and oscillation characteristics in an enclosure filled with porous medium
Int. J. Heat Mass Transfer
(2017) - et al.
Numerical study of double-diffusive natural convection in a porous cavity using the Darcy-Brinkman formulation
Int. J. Heat Mass Transfer
(1996) - et al.
Multiple solutions for double-diffusive convection in a vertical porous enclosure
Int. J. Heat Mass Transfer
(1995) - et al.
Natural convection in a square cavity filled with a porous medium: effects of various thermal boundary conditions
Int. J. Heat Mass Transfer
(2006) - et al.
MHD mixed convection in alumina-water nanofluid filled square porous cavity using KKL model: effects of non-linear thermal radiation and inclined magnetic field
J. Mol. Liq.
(2017)
Numerical simulation of three-dimensional double diffusive convection in a lid-driven cavity
Int. J. Therm. Sci.
Effects of inclination angle and non-uniform heating on mixed convection of a nanofluid filled porous enclosure with active mid-horizontal moving
Int. J. Heat Mass Transfer
Conjugate-mixed convection heat transfer in a lid driven enclosure with thick bottom wall
Int. Commun. Heat Mass Transfer
Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom
Appl. Therm. Eng.
Numerical simulation of mixed convection flows in a square lid-driven cavity partially heated from below using nanofluid
Int. Commun. Heat Mass Transfer
Mixed convection in a double lid-driven cubic cavity
Int. J. Therm. Sci.
Optimization of mixed convection heat transfer with entropy generation in a wavy surface square lid-driven cavity by means of Taguchi approach
Transp. Porous Media
Second law analysis in heat transfer
Energy
Role of entropy generation on thermal management due to thermal convection in porous trapezoidal enclosures with isothermal and non-isothermal heating of wall
Int. J. Heat Mass Transfer
Simulation of heat transfer and entropy generation of MHD natural convection of non-Newtonian nanofluid in an enclosure
Int. J. Heat Mass Transfer
Numerical study on mixed convection and entropy generation of Cu-water nanofluid in a differentially heated skewed enclosure
Int. J. Heat Mass Transfer
Analysis of the entropy generation in a nanofluid-filled cavity in the presence of magnetic field and uniform heat generation/absorption
J. Mol. Liq.
Numerical simulation of MHD mixed convection in alumina-water nanofluid filled square porous cavity using KKL model: effects of non–linear thermal radiation and inclined magnetic field
J. Mol. Liquid
Numerical investigation of MHD effects on -water nanofluid flow and heat transfer in a semi-annulus enclosure using LBM
Energy
Numerical study of MHD mixed convection in a nanofluid filled lid driven square enclosure with a rotating cylinder
Int. J. Heat Mass Transfer
Effects of inclination angle on mixed convective nanofluid flow in a double lid-driven cavity with discrete heat sources
Int. J. Heat Mass Transfer
Mixed convection in alumina-water nanofluid filled lid–driven square cavity with an isothermally heated square blockage inside with magnetic field effect: introduction
Int. J. Heat Mass Transfer
Viscous dissipation effects in microtubes and microchannels
Int. J. Heat Mass Transfer
Efficient Newton multigrid solution techniques for higher order space time Galerkin discretizations of incompressible flow
Appl. Numer. Math.
Mixed convection in a lid driven square cavity filled by a nanofluid: Buongiorno’s mathematical model
Appl. Math. Comput.
Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom
Appl. Therm. Eng.
Mixed convection in a driven cavity with a stable vertical temperature gradient
Int. J. Heat Mass Transfer
MHD mixed convection and entropy generation of water-alumina nanofluid flow in a double lid driven cavity with discrete heating
J. Magn. Magn. Mater.
Cited by (56)
Optimizing thermosolutal and hydrothermal performance of radiative hybrid ferrofluid and entropy generation in a wavy porous enclosure
2024, Journal of Magnetism and Magnetic MaterialsUnveiling the Dynamics of Entropy Generation in Enclosures: A Systematic Review
2024, International Journal of ThermofluidsEntropy generation and exergy loss of R123-MWCNTs nanorefrigerant in flow condensation
2024, International Journal of RefrigerationNumerical simulation of the natural double-diffusive convection in an elliptical cylinder -Impact of the buoyancy force-
2023, International Communications in Heat and Mass TransferNumerical investigation of double-diffusive mixed convection in a split lid-driven curvilinear cavity
2022, International Communications in Heat and Mass TransferCitation Excerpt :They concluded that increasing Re and Da increases heat transfer while decreasing the effects of porosity and Richardson. These results have been improved by Hussain et al. [22], who studied mixed convection in a square lid-driven cavity filled with porous media. Hatami et al. [23] studied mixed convection in a lid-driven cavity, T-shaped, filled with nanofluid and porous media.