On Stability of Plane and Cylindrical Poiseuille Flows of Nanofluids

Stability of plane and cylindrical Poiseuille flows of nanofluids to comparatively small perturbations is studied. Ethylene glycol-based nanofluids with silicon dioxide particles are considered. The volume fraction of nanoparticles is varied from 0 to 10%, and the particle size is varied from 10 to 210 nm. Neutral stability curves are constructed, and the most unstable modes of disturbances are found. It is demonstrated that nanofluids are less stable than base fluids; the presence of particles leads to additional destabilization of the flow. The greater the volume fraction of nanoparticles and the smaller the particle size, the greater the degree of this additional destabilization. In this case, the critical Reynolds number significantly decreases, and the spectrum of unstable disturbances becomes different; in particular, even for the volume fraction of particles equal to 5%, the wave length of the most unstable disturbances of the nanofluid with particles approximately 20 nm in size decreases almost by a factor of 4.     

Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid: Brinkman Model

The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium, the Brinkman model is employed. Three cases of free–free, rigid–rigid, and rigid–free boundaries are considered. The analysis reveals that for a typical nanofluid (with large Lewis number), the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles, whereas the contribution of nanoparticles to the thermal energy equation is a second-order effect. It is found that the critical thermal Rayleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy, by the presence of the nanoparticles. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution.     

Effect of Thermal Modulation on the Onset of Convection in a Porous Medium Layer Saturated by a Nanofluid

The effect of time-periodic temperature modulation at the onset of convection in a Boussinesq porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. The perturbation method is applied for computing the critical Rayleigh and wave numbers for small amplitude temperature modulation. The shift in the critical Rayleigh number is calculated as a function of frequency of modulation, concentration Rayleigh number, porosity, Lewis number, and thermal capacity ratio. It has been shown that it is possible to advance or delay the onset of convection by time-periodic modulation of the wall temperature. The nanofluid is found to have more stabilizing effect when compared to regular fluid. Low frequency is destabilizing, while high frequency is always stabilizing for symmetric modulation. Asymmetric modulation and only lower wall temperature modulation is stabilizing for all frequencies when concentration Rayleigh number is greater than one.     

The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium

The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium, the Brinkman model is employed. Three cases of free–free, rigid–rigid, and rigid–free boundaries are considered. The analysis reveals that for a typical nanofluid (with large Lewis number), the prime effect of the nanofluids is via a buoyancy effect coupled with the conservation of nanoparticles, whereas the contribution of nanoparticles to the thermal energy equation is a second-order effect. It is found that the critical thermal Rayleigh number can be reduced or increased by a substantial amount, depending on whether the basic nanoparticle distribution is top-heavy or bottom-heavy, by the presence of the nanoparticles. Oscillatory instability is possible in the case of a bottom-heavy nanoparticle distribution.     

Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition

The unsteady laminar magnetohydrodynamics(MHD) boundary layer flow and heat transfer of nanofluids over an accelerating convectively heated stretching sheet are numerically studied in the presence of a transverse magnetic field with heat source/sink. The unsteady governing equations are solved by a shooting method with the Runge-KuttaFehlberg scheme. Three different types of water based nanofluids, containing copper, aluminium oxide, and titanium dioxide, are taken into consideration. The effects of the pertinent parameters on the fluid velocity, the temperature, the entropy generation number, the Bejan number, the shear stress, and the heat transfer rate at the sheet surface are graphically and quantitatively discussed in detail. A comparison of the entropy generation due to the heat transfer and the fluid friction is made with the help of the Bejan number. It is observed that the presence of the metallic nanoparticles creates more entropy in the nanofluid flow than in the regular fluid flow.     

Natural convection cooling of a localised heat source at the bottom of a nanofluid-filled enclosure

This article presents a numerical study of natural convection cooling of a heat source embedded on the bottom wall of an enclosure filled with nanofluids. The top and vertical walls of the enclosure are maintained at a relatively low temperature. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, location and geometry of the heat source, the type of nanofluid and solid volume fraction of nanoparticles on the cooling performance is studied. The results indicate that adding nanoparticles into pure water improves its cooling performance especially at low Rayleigh numbers. The type of nanoparticles and the length and location of the heat source proved to significantly affect the heat source maximum temperature.     

Non-homogeneous model for a side heated square cavity filled with a nanofluid

A side heated two dimensional square cavity filled with a nanofluid is here studied. The side heating condition is obtained by imposing two different uniform temperatures at the vertical boundary walls. The horizontal walls are assumed to be adiabatic and all boundaries are assumed to be impermeable to the base fluid and to the nanoparticles. In order to study the behavior of the nanofluid, a non-homogeneous model is taken into account. The thermophysical properties of the nanofluid are assumed to be functions of the average volume fraction of nanoparticles dispersed inside the cavity. The definitions of the nondimensional governing parameters (Rayleigh number, Prandtl number and Lewis number) are exactly the same as for the clear fluids. The distribution of the nanoparticles shows a particular sensitivity to the low Rayleigh numbers. The average Nusselt number at the vertical walls is sensitive to the average volume fraction of the nanoparticles dispersed inside the cavity and it is also sensitive to the definition of the thermophysical properties of the nanofluid. Highly viscous base fluids lead to a critical behavior of the model when the simulation is performed in pure conduction regime. The solution of the problem is obtained numerically by means of a Galerkin finite element method.     

Thermal Instability in a Porous Medium Layer Saturated with a Viscoelastic Nanofluid

The onset of convection in a horizontal layer of a porous medium saturated with a viscoelastic nanofluid was studied in this article. The modified Darcy model was applied to simulate the momentum equation in porous media. An Oldroyd-B type constitutive equation was used to describe the rheological behavior of viscoelastic nanofluids. The model used for the viscoelastic nanofluid incorporates the effects of Brownian motion and thermophoresis. The onset criterion for stationary and oscillatory convection was analytically derived. The effects of the concentration Rayleigh number, Prandtl number, Lewis number, capacity ratio, relaxation, and retardation parameters on the stability of the system were investigated. Oscillatory instability is possible in both bottom- and top-heavy nanoparticle distributions. Results indicated that there is competition among the processes of thermophoresis, Brownian diffusion, and viscoelasticity that causes the convection to set in through oscillatory rather than stationary modes. Regimes of stationary and oscillatory convection for various parameters were derived and are discussed in detail.     

Natural convection of SiO_2-water nanofluid in square cavity with thermal square column

A square with a thermal square column is a simple but nontrivial research prototype for nanofluid research. However, until now, the effects of the temperature of the square column on the heat and mass transfer of nanofluids have not been revealed comprehensively, especially on entropy generation. To deepen insight into this important field, the natural convection of the SiO_2-water nanofluid in a square cavity with a square thermal column is studied numerically in this study. The effects of the thermal column temperature(T = 0.0, 0.5, 1.0, 1.5), the Rayleigh number(ranging from 10~3 to 10~6),and the volume fraction of the nanoparticle(varying from 0.01 to 0.04) on the fluid flow,heat transfer, and entropy generation are investigated, respectively. It is found that, no matter at a low or high Rayleigh number, the volume fraction of the nanoparticle shows no considerable effects on the flow field and temperature field for all the temperatures of the thermal column. With an increase in the volume fraction, the mean Nusselt number increases slightly. At the same time, it is found that, with an increase in the temperature of the thermal column, the average Nusselt number gradually decreases at all values of the Rayleigh number. Meanwhile, it is found that, at a high Rayleigh number, the heat transfer mechanism is the main parameter affecting the increase in the total entropy generation rather than the volume fraction. In addition, no matter at a high or low Rayleigh number, when T = 0.5, the total entropy generation is the minimum.     

Estimating the Hydraulic Conductivity of Two-Dimensional Fracture Networks Using Network Geometric Properties

Based on a modified Darcy–Brinkman–Maxwell model, a linear stability analysis of a Maxwell fluid in a horizontal porous layer heated from below by a constant flux is carried out. The non-oscillatory instability and oscillatory instability with different hydrodynamic boundaries such as rigid and free surfaces at the bottom are studied. Compared with the rigid surface cases, onset of fluid motion due to non-oscillatory instability and oscillatory instability is found to occur both more easily for the system with a free bottom surface. The critical Rayleigh number for onset of fluid motion due to non-oscillatory instability is lower with a constant flux heating bottom than with an isothermal heating bottom, but the result due to oscillatory instability is in contrast. The effects of the Darcy number, the relaxation time, and the Prandtl number on the critical Rayleigh number are also discussed.     

Thermo-diffusion impact on immiscible flow characteristics of convectively heated vertical two-layered Baffle saturated porous channels in a suspension of nanoparticles: an analytical study

The heat and mass transfer of two immiscible fluids in an inclined channel with thermal diffusion, vicious, and Darcy dissipation is studied. The first region consists of a clear fluid, and the second one is filled with a nanofluid saturated with a porous medium. The behaviors of Cu-H₂O, In-H₂O, and Au-H₂O nanofluids are analyzed. The transport properties are assumed to be constant. The coupled non-linear equations of the flow model are transformed into the dimensionless form, and the solutions for the velocity, temperature, and concentration are obtained by the regular perturbation technique. Investigations are carried out on the flow characteristics for various values of the material parameters. The results show that the velocity and temperature of the fluids enhance with the thermal Grashof number, solutal Grashof number, and Brinkman number while decrease with the porosity parameter and solid volume fraction.     

Two numerical modelings of free convection heat transfer using nanofluids inside a square enclosure

This work describes the numerical simulation of natural convection heat transfer of Cu–water nanofluids in a square enclosure for Rayleigh numbers varying from 10³ up to 10⁵. Two different numerical approaches were used: the finite volume method and the finite element method. The nanofluids were assumed to be single-phase fluids with modified thermal properties obtained from experimental results and theoretical models. The results showed that the Nusselt number for nanofluids was basically the same as that obtained for the base fluid. Therefore, the enhancement observed in the heat transfer coefficient was significant due to the augmentation in the thermal conductivity.     

Non-linear Convective Transport in a Binary Nanofluid Saturated Porous Layer

In this article, we study double-diffusive convection in a horizontal porous medium saturated by a nanofluid, for the case when the base fluid of the nanofluid is itself a binary fluid such as salty water. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, while the Darcy model is used for the porous medium. The thermal energy equations include the diffusion and cross-diffusion terms. The linear stability is studied using normal mode technique and for non-linear analysis, a minimal representation of the truncated Fourier series analysis involving only two terms has been used. For linear theory analysis, critical Rayleigh number has been obtained, while non-linear analysis has been done in terms of the Nusselt numbers.     

多孔介质内黏弹性流体的热对流稳定性研究

基于修正的Darcy模型, 介绍了多孔介质内黏弹性流体热对流稳定性研究的现状和主要进展. 通过线性稳定性理论, 分析计算多孔介质几何形状(水平多孔介质层、多孔圆柱以及多孔方腔)、热边界条件(底部等温加热、底部等热流加热、底部对流换热以及顶部自由开口边界)、黏弹性流体的流动模型(Darcy-Jeffrey, Darcy-Brinkman-Oldroyd以及Darcy-Brinkman -Maxwell模型)、局部热非平衡效应以及旋转效应对黏弹性流体热对流失稳的临界Rayleigh数的影响. 利用弱非线性分析方法, 揭示失稳临界点附近热对流流动的分叉情况, 以及失稳临界点附近黏弹性流体换热Nusselt数的解析表达式. 采用数值模拟方法, 研究高Rayleigh数下黏弹性流体换热Nusselt数和流场的演化规律,分析各参数对黏弹性流体热对流失稳和对流换热速率的影响.主要结果:(1)流体的黏弹性能够促进振荡对流的发生;(2)旋转效应、流体与多孔介质间的传热能够抑制黏弹性流体的热对流失稳;(3)在临界Rayleigh数附近,静态对流分叉解是超临界稳定的, 而振荡对流分叉可能是超临界或者亚临界的,主要取决于流体的黏弹性参数、Prandtl数以及Darcy数;(4)随着Rayleigh数的增加,热对流的流场从单个涡胞逐渐演化为多个不规则单元涡胞, 最后发展为混沌状态.      

Boiling heat transfer characteristics of nanofluids jet impingement on a plate surface

The jet boiling heat transfer of a bar water–CuO particle suspensions (nanofluids) jet impingement on a large flat surface was experimentally investigated. The experimental results were compared with those from water. The quantificational effects of the nanoparticles concentration and the flow conditions on the nucleate boiling heat transfer and the critical heat flux (CHF) were investigated. The experimental data showed that the jet boiling heat transfer for the water–CuO nanofluid is significantly different from those for water. The nanofluids have poor nucleate boiling heat transfer compared with the base fluid due to that a very thin nanoparticle sorption layer was formed on the heated surface. The CHF for the nanofluid increased compared with that of water. The reasons were that the solid–liquid contact angle decreased due to a very thin sorption layer on the heated surface and the jet and agitating effect of the nanoparticles on the subfilm layer enhance supply of liquid to the surface.     

Experimental investigation of forced convective heat transfer coefficient in nanofluids of Al2O3/EG and CuO/EG in a double pipe and plate heat exchangers under turbulent flow

Nanofluid is the term applied to a suspension of solid, nanometer-sized particles in conventional fluids; the most prominent features of such fluids include enhanced heat characteristics, such as convective heat transfer coefficient, in comparison to the base fluid without considerable alterations in physical and chemical properties. In this study, nanofluids of aluminum oxide and copper oxide were prepared in ethylene glycol separately. The effect of forced convective heat transfer coefficient in turbulent flow was calculated using a double pipe and plate heat exchangers. Furthermore, we calculated the forced convective heat transfer coefficient of the nanofluids using theoretical correlations in order to compare the results with the experimental data. We also evaluated the effects of particle concentration and operating temperature on the forced convective heat transfer coefficient of the nanofluids. The findings indicate considerable enhancement in convective heat transfer coefficient of the nanofluids as compared to the base fluid, ranging from 2% to 50%. Moreover, the results indicate that with increasing nanoparticles concentration and nanofluid temperature, the convective heat transfer coefficient of nanofluid increases. Our experiments revealed that in lower temperatures, the theoretical and experimental findings coincide; however, in higher temperatures and with increased concentrations of the nanoparticles in ethylene glycol, the two set of results tend to have growing discrepancies.     

The Effect of Vertical Throughflow on Thermal Instability in a Porous Medium Layer Saturated by a Nanofluid

The effect of vertical throughflow on the onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is studied analytically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The dependences of the critical Rayleigh number for the non-oscillatory and oscillatory modes of instability on the thermophoresis and Brownian motion parameters for the cases with and without throughflow are investigated.     

Rayleigh-Bénard convection heat transfer in nanoparticle suspensions

Natural convection heat transfer of nanofluids in horizontal enclosures heated from below is investigated theoretically. The main idea upon which the present work is based is that nanofluids behave more like a single-phase fluid rather than like a conventional solid-liquid mixture, which implies that all the convective heat transfer correlations available for single-phase flows can be extended to nanoparticle suspensions, provided that the thermophysical properties appearing in them are the nanofluid effective properties calculated at the reference temperature. In this connection, two empirical equations, based on a wide variety of experimental data reported in the literature, are developed for the evaluation of the nanofluid effective thermal conductivity and dynamic viscosity, whereas the other effective properties are evaluated by the traditional mixing theory. The heat transfer enhancement that derives from the dispersion of nano-sized solid particles into the base liquid is calculated for different operating conditions, nanoparticle diameters, and combinations of solid and liquid phases. One of the fundamental results is the existence of an optimal particle loading for maximum heat transfer across the bottom-heated enclosure. In particular, for any assigned combination of suspended nanoparticles and base liquid, it is found that the optimal volume fraction increases as the nanofluid average temperature increases, and may either increase or decrease with increasing the nanoparticle size according as the flow is laminar or turbulent. Moreover, the optimal volume fraction has a peak at a definite value of the Rayleigh number of the base fluid, that depends on both the average temperature of the nanofluid and the diameter of the suspended nanoparticles.     

Nanofluids: Stability, phase diagram, rheology and applications

There is no doubt about the potential technological significance of nanofluids. The promising application areas have been identified as effective heat transfer fluids, contrast agents in magnetic resonance imaging, magnetohyperthermia treatment, precursors to high performance nanocomposites and ordered nanostructures. However, commercial applications are rare, in part due to the limited understanding of the nanofluid fundamentals such as colloid stability, phase diagrams and rheology. This paper intends to provide a brief overview of the scientific disciplines that are important to nanofluids, and the interconnection among different disciplines in order to gain a perspective on the future development of this intriguing area.     

Experimental study of critical heat flux enhancement during forced convective flow boiling of nanofluid on a short heated surface

Enhancements of nucleate boiling critical heat flux (CHF) using nanofluids in a pool boiling are well-known. Considering importance of flow boiling heat transfer in various practical applications, an experimental study on CHF enhancements of nanofluids under convective flow conditions was performed. A rectangular flow channel with 10-mm width and 5-mm height was used. A 10 mm-diameter disk-type copper surface, heated by conduction heat transfer, was placed at the bottom surface of the flow channel as a test heater. Aqueous nanofluids with alumina nanoparticles at the concentration of 0.01% by volume were investigated. The experimental results showed that the nanofluid flow boiling CHF was distinctly enhanced under the forced convective flow conditions compared to that in pure water. Subsequent to the boiling experiments, the heater surfaces were examined with scanning electron microscope and by measuring contact angle. The surface characterization results suggested that the flow boiling CHF enhancement in nanofluids is mostly caused by the nanoparticles deposition of the heater surface during vigorous boiling of nanofluids and the subsequent wettability enhancements.