Double diffusion natural convection in a square cavity filled with nanofluid
Introduction
Nanofluid is a mixture of base fluid (e.g. water) and nanometer-sized particles. The suspending nanoparticles, typically made of metals, oxides, carbides, or carbon nanotubes, can significantly enhance the thermal conductivity of base fluid [1]. Consequently, as a promising new generation of coolant, nanofluid has a great potential adopted in many important applications such as microelectronics, domestic refrigerator and aircrafts. One can refer to Refs. [2], [3], [4], [5] for the latest progress in this field.
Compared with the available numerous studies on the characteristics of heat transfer of nanofluid induced by thermal buoyancy [4], the exploration taking effects of compositional buoyancy into account is quite limited, although compositional buoyancy exists and plays an important role in many industrial applications utilizing nanofluid, such as solar energy industry [6]. Esfahani and Bordbar [7] perhaps are some of the pioneers on this topic. In Ref. [7], they investigated laminar double-diffusive natural convection heat transfer enhancement in a square enclosure filled with various nanofluids by numerical simulation. The influences of the nanoparticle volume fraction, Rayleigh and Lewis number on the Nusselt and Sherwood number were discussed. Later, Parvin et al. [8] numerically analyzed the flow and natural convection patterns of water–Al2O3 nanofluid in a partially heated enclosure. In their study, the nanoparticle volume fraction varies from 0 to with the Rayleigh number up to . Through their work, it is very clear that the distributions of isotherms and iso-concentrations depend closely on the position of active walls of the cavity. Recently, laminar double diffusive convection in a solar collector using water–CuO nanofluid was modelled in Ref. [9]. The cross section of the solar collector is triangular. The authors revealed the incident angle of the solar collector influenced the performance of heat and mass transfer of nanofluid significantly. The above publications all focus on the behavior of double diffusive convection of nanofluid confined by a closed container. The double diffusive convection in a nanofluid layer was firstly reported by Nield and Kuznetsov [10], [11]. They discussed the onset and thickness of such layer through analytical study. In succession, the same authors extended their discussion to a porous medium saturated by nanofluid [12]. More recently, Beg and Tripathi [13] conducted a theoretical study on double diffusive convection in nanofluid through a deformable channel. Through the work, the authors tried to deepen our understanding on the usability of nanofluid in physiological areas. About buoyant flow of nanofluid in a cavity, some interesting work also has been published. For example, in Ref. [14] the influence of inclination angles of cavity on fluid flow has been reported and Ho et al. [15] investigated the Ludwig–Soret effect in nanofluid enclosed by a cavity.
Through the above literature survey it is clear that at least three fundamental questions on double diffusive convection of nanofluid are not answered yet: firstly, the characteristics of double diffusive convection of nanofluid beyond laminar regimes; secondly, the influence of the ratio of buoyancy forces on heat and mass transfer; and thirdly, the correlation among the Nusselt/Sherwood number, Rayleigh number and nanoparticle volume fraction under double diffusive natural convection. The goal of this paper is to answer these three critical questions with the aid of a comprehensive numerical experiment. What should be pointed out is that a two-dimensional investigated domain is adopted in the present work while turbulence is an inherently three-dimensional phenomenon, so further work is required in the future to validate the reliability of the present research for real applications.
Section snippets
Investigated domain and boundary conditions
In this work, double diffusive natural convection in a square cavity [7], [16] is adopted as it is a good research prototype to reply the above questions. The investigated domain and boundary conditions are illustrated by Fig. 1. The dimensionless length of each side of the square cavity is unity. The dimensionless temperature and concentration on the hot wall and cold wall read and , respectively. The top and bottom walls of the investigated domain are adiabatic.
Governing equations
For nanofluid simulation, generally there are two ways: single phase and two-phase modelling [17]. In the former approach it is assumed that the suspending nanoparticles are in thermal equilibrium with the base fluid and there is no velocity slip between the solid particles and base fluid. Therefore the solid–liquid mixture can be treated as a kind of Newtonian fluid. However, in the latter, the discrete phase and continuum phase are described in a Lagrangian and a Eulerian scheme,
Numerical method
The lattice Boltzmann (LB) LES model, developed in our previous work [16], for turbulent double diffusive natural convection simulation is adopted in this study.
The evolution equation for the flow field readswhere is the distribution function associated with the fluid particle moving with the discrete velocity . is the fluid particle speed. and are the lattice grid spacing and the time step, respectively. The term is a forcing
Numerical validation
The reliability of the present LB-LES approach for turbulent double diffusive natural convection simulation has been demonstrated in Ref. [16], where the Rayleigh number varies from to . Therefore, in this section we only validate its applicability for nanofluid. For this purpose, natural convection of water–SiO2 nanofluid in a square enclosure proposed in Ref. [19] is adopted. Fig. 2 illustrates the variation of the averaged Nusselt number (Nu) with the nanoparticle volume fraction ()
Results and discussions
In the present study, we simulate double-diffusive convection of water–SiO2 nanofluid in a square cavity with and . In Ref. [19] the physical properties of water–SiO2 nanofluid, which obtained through experimental measure, were provided only for , so this work also focuses on the same range. When the grid resolution is employed while for . Our previous study [16] has shown that such grid resolutions are fine enough to capture the
Conclusion
Double diffusive natural convection of nanofluid is commonly found in renewable energy industry. However, the related studies on its fundamental characteristics are quite sparse, especially beyond the laminar regimes. As emphasized in the latest review paper [3], the insight into the performance of nanofluid in turbulent regimes arises a challenge not only in academic research but also in energy engineering. To deepen our understanding in this important area, the present work tries to reveal
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 51176061), the Foundation of State Key Laboratory of Coal Combustion and the British Newton Alumni Fellowship Scheme.
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