Research On Enhanced Heat Transfer Of Nanofluids Using Lattice Boltzmann Method

With the development of science and technology and the increasing problem of energy,the heat transfer load and heat transfer intensity of the traditional heat exchange system are increasing.The structural limitation of the heat exchange equipment and the increasingly harsh environment are becoming more and more important.In such a case,a higher demand for the heat transfer enhancement is required.Nanofluid is in this context came into being.The term nanofluid describing diluted suspensions of metal or metal oxide nanoparticles in the base fluid.Compared with the traditional pure liquid(such as water,alcohol,etc.),the outstanding advantages of nanofluid is reflected in the enhanced heat transfer rate,a large thermal conductivity and a more stable suspension.The above advantages show that the nanofluid is an efficient heat exchanger with higher thermal conductivity and better heat transfer performance.Therefore,it is of great scientific and practical significance to study the microscopic mechanism of nanofluid fluid flow and energy transfer.With the rapid development of computer computing technology,numerical simulation as a basic research means,is expected to study the flow of nanofluid and energy transfer play an important role.The traditional computational methods(like finite difference method,finite element method)always have some shortcomings such as complex boundary processing and low efficiency of parallelism,while for the lattice Boltzmann method(LBM),which is come from the theory of gas dynamics,it is of great advantage to study the mechanism of heat transfer enhancement of nanofluids due to its microscopic and mesoscopic characteristics.Nowadays,although many domestic and foreign scholars have employed LBM to carry out a series of work in the enhancement of heat transfer of nanofluid,there are still some key basic problems yet to be solved:on the one hand,nanofluid flow and heat transfer are a kind of multi-field coupling problem involving flow field,temperature field and con-centration field,and it requires a high stability of the numerical method.However,it is found that the most widely used model for nanofluid is the single relaxation time(SRT)or Bhatangar-Gross-Krook(BGK)model,and its stability needs to be improved.On the other hand,the microscopic mechanism of nanofluid enhanced heat transfer is not clear,including non-Newtonian nanofluids,double-diffusion nanofluids,three-dimensional nanofluids and two-phase nanofluid.Therefore,in this paper,we first construct a LB model,whose nu-merical stability and accuracy are better than traditional BGK model.We then carry out a detailed study to investigate the nanofluid enhanced heat transfer mechanism with the pro-posed model.The main work of this paper includes the following aspects:(1)To improve the stability of LBM,we proposed a regularized lattice Boltzmann mod-el for the nonlinear convection-diffusion equation and incompressible Navier-Stokes equa-tions.The main idea of the present model is to introduce a set of precollision distribution functions that are defined only in terms of macroscopic moments such that the numerical stability and accuracy are improved.Specially,the proposed model is used to investigate natural convection in a square enclosure,and the numerical results show that the maximum thermal Rayleigh number that can be achieved is 1010,which is superior over the traditional LBGK model.The proposed model provides a theoretical basis for the subsequent study of nanofluid fluid flow and heat transfer problems.(2)We then investigated the double-diffusive convection of power-law nanofluids in rectangular enclosures with the regularized lattice Boltzmann method.The influence of Rayleigh number,power-law index,buoyancy rate,nanoparticle volume fraction,Lewis number and aspect ratio on the heat and mass transfer are analyzed emphatically.The re-sults show that the heat and mass transfer rates are increased with the increase of Rayleigh number.In addition,the increase of the power-law slows down the flow of the nanofluids in the cavity,which leads to the decrease of the mass transfer rate.At the same time,we also found that the heat transfer rate decreases with the increase of Lewis until it stabilizes at a certain value,and the mass transfer rate increases with the Lewis number.In addition,it is found that mass transfer rate decreases in nanoparticle volume fraction.Finally,the mass transfer rate of the nanofluid tends to increase with the increase of the aspect ratio of the cavity until it reaches a certain maximum value.When this value is exceeded,the mass transfer rate will decline as the aspect ratio increases.(3)The magnetic field effects on natural convection of power-law nanofluids in rectan-gular enclosure are investigated numbercally with the regularized lattice Boltzmann mod-el,and the effects of Rayleigh number,power-law index,Hartamann number,nanoparticle volume fraction and aspect ratio on the heat transfer rate are analyzed emphatically.The re-sults reveal that the flow oscillations can be suppressed effectively by imposing an external magnetic field,and the augmentation of Hartmann number and power-law index generally decreases the heat transfer rate.Additionally,it is observed that the average Nusselt number is increased with the increase of Rayleigh number and nanoparticle volume fraction.More-over,the present results also indicate that there is a critical value for aspect ratio at which the impact on heat transfer is the most pronounced.(4)Aiming at the natural convection of nanofluid in three-dimensional cavity,the influ-ence of two kinds of boundary conditions(ie,constant temperature boundary and constant flux boundary)on the nanofluid flow and heat transfer is investigated and compared.The results show that the temperature field distributions of the two boundary conditions are very different under the same conditions,and the numerical results show that the heat transfer rate obtained from the constant temperature boundary is larger than that of the constan-t flux boundary.In addition,we find that for the same nanoparticle volume fraction,the heat transfer rate of constant heat flux boundary is lower than that of constant temperature boundary.(5)A detailed investigation is performed for the nanofluid Rayleigh-Benard convection in a three-dimensional cavity,and the effects of the nanoparticle diameter,the temperature difference between the cold and hot wall,the temperature of the cold wall,the type of the nanoparticle and the nanoparticle volume fraction on nanofluid flow and heat transfer rate are studied.The results show that the heat transfer rate of nanofluid increases with the decrease of nanofluid diameter,and the increase of the cold wall temperature and the nanoparticle volume fraction can lead to the enhancement of the heat transfer rate.Finally,we also find that the heat transfer intensity depends on the thermal conductivity of the cor-responding nanoparticles.In particular,under the same physical parameters,the higher the thermal conductivity is,the stronger the heat transfer is.(6)Based on the Buongiomo's work,we develop a lattice Boltzmann model for the two-phase nanofluids flow,in which the important effects of Brownian motion and ther-mophoresis are incorporated.The Chapman-Enskog analysis shows that the macroscopic equations can be recovered correctly.Moreover,although some gradient operators are in-cluded in the evolution equations,they can be computed efficiently using local computation-al schemes such that the present model still retains the intrinsic parallelism characteristic of the LBM.We then investigated the influences of the Brownian diffusion coefficient and the thermophoretic diffusion coefficient,and the results show that the heat transfer rate increases in Brownian motion coefficient and decreases in thermophoretic diffusion coefficient.In conclusion,in this paper,we develop some basic lattice Boltzmann model in the study of nanofluid heat transfer enhancement,and also deeply investigate the heat transfer mechanism of non-Newtonian nanofluids,double-diffusion nanofluids and two-phase nanofluids.The results of this study not only deepen the understanding of the mechanism of nanofluid heat transfer enhancement,but also make many useful attempts to promote the application of LBM in numerical heat transfer.