Lattice Boltzmann simulation of alumina-water nanofluid in a square cavity

A lattice Boltzmann model is developed by coupling the density (D2Q9) and the temperature distribution functions with 9-speed to simulate the convection heat transfer utilizing Al₂O₃-water nanofluids in a square cavity. This model is validated by comparing numerical simulation and experimental results over a wide range of Rayleigh numbers. Numerical results show a satisfactory agreement between them. The effects of Rayleigh number and nanoparticle volume fraction on natural convection heat transfer of nanofluid are investigated in this study. Numerical results indicate that the flow and heat transfer characteristics of Al₂O₃-water nanofluid in the square cavity are more sensitive to viscosity than to thermal conductivity.     

Optimization of natural convection heat transfer of Newtonian nanofluids in a cylindrical enclosure

This study characterizes and optimizes natural convection heat transfer of two Newtonian Al2O3 and TiO2/water nanofluids in a cylindrical enclosure. Nusselt number (Nu) of nanofluids in relation to Rayleigh number (Ra) for different concentrations of nanofluids is investigated at different configurations and orientations of the enclosure. Results show that adding nanoparticles to water has a negligible or even adverse influence upon natural convec-tion heat transfer of water:only a slight increase in natural convection heat transfer of Al2O3/water is observed, while natural convection heat transfer for TiO2/water nanofluid is inferior to that for the base fluid. Results also reveal that at low Ra, the likelihood of enhancement in natural convection heat transfer is more than at high Ra:at low Ra, inclination angle, aspect ratio of the enclosure and nanoparticle concentration influence natural convec-tion heat transfer more pronouncedly than that in high Ra.     

Particle Shape and Aspect Ratio Effect of Al2O3–Water Nanofluid on Natural Convective Heat Transfer Enhancement in Differentially Heated Square Enclosures

The present numerical investigation, based on the finite volume method, deals with the characterization of flow and thermal fields inside differentially heated square enclosures filled with Al₂O₃–water nanofluid. The study focuses on the effect of shapes and aspect ratios of nanoparticles (NPs), depicted by Rayleigh number (Ra), solid volume fraction (?), and enclosure on both flow and heat transfer enhancement. Streamlines, isotherms contours, and velocity profiles as well as the average Nusselt number are considered. Results found show that the heat transfer rate increases with Rayleigh number as well as with nanofluid volume fraction. For the six different examined cases of NPs’ aspect ratios, nanofluid with oblate spheroids NPs (d_p = 0.13) was found to engender a significant enhancement in the overall heat transfer. In addition, heat transfer rate was more pronounced at great values of aspect ratios of NPs for prolate spheroids. Results also showed that heat transfer enhancement decreases as the Rayleigh number increases independently of the considered enclosure, shapes, and aspect ratios of NPs.     

Facile method to synthesize magnetic iron oxides/TiO2 hybrid nanoparticles and their photodegradation application of methylene blue

The primary objective of this study is to investigate the effect of slip mechanisms in nanofluids through scaling analysis. The role of nanoparticle slip mechanisms in both water- and ethylene glycol-based nanofluids is analyzed by considering shape, size, concentration, and temperature of the nanoparticles. From the scaling analysis, it is found that all of the slip mechanisms are dominant in particles of cylindrical shape as compared to that of spherical and sheet particles. The magnitudes of slip mechanisms are found to be higher for particles of size between 10 and 80 nm. The Brownian force is found to dominate in smaller particles below 10 nm and also at smaller volume fraction. However, the drag force is found to dominate in smaller particles below 10 nm and at higher volume fraction. The effect of thermophoresis and Magnus forces is found to increase with the particle size and concentration. In terms of time scales, the Brownian and gravity forces act considerably over a longer duration than the other forces. For copper-water-based nanofluid, the effective contribution of slip mechanisms leads to a heat transfer augmentation which is approximately 36% over that of the base fluid. The drag and gravity forces tend to reduce the Nusselt number of the nanofluid while the other forces tend to enhance it.     

Scaling analysis for the investigation of slip mechanisms in nanofluids

The primary objective of this study is to investigate the effect of slip mechanisms in nanofluids through scaling analysis. The role of nanoparticle slip mechanisms in both water- and ethylene glycol-based nanofluids is analyzed by considering shape, size, concentration, and temperature of the nanoparticles. From the scaling analysis, it is found that all of the slip mechanisms are dominant in particles of cylindrical shape as compared to that of spherical and sheet particles. The magnitudes of slip mechanisms are found to be higher for particles of size between 10 and 80 nm. The Brownian force is found to dominate in smaller particles below 10 nm and also at smaller volume fraction. However, the drag force is found to dominate in smaller particles below 10 nm and at higher volume fraction. The effect of thermophoresis and Magnus forces is found to increase with the particle size and concentration. In terms of time scales, the Brownian and gravity forces act considerably over a longer duration than the other forces. For copper-water-based nanofluid, the effective contribution of slip mechanisms leads to a heat transfer augmentation which is approximately 36% over that of the base fluid. The drag and gravity forces tend to reduce the Nusselt number of the nanofluid while the other forces tend to enhance it.     

Heterogeneous nanofluids: natural convection heat transfer enhancement

Convective heat transfer using different nanofluid types is investigated. The domain is differentially heated and nanofluids are treated as heterogeneous mixtures with weak solutal diffusivity and possible Soret separation. Owing to the pronounced Soret effect of these materials in combination with a considerable solutal expansion, the resulting solutal buoyancy forces could be significant and interact with the initial thermal convection. A modified formulation taking into account the thermal conductivity, viscosity versus nanofluids type and concentration and the spatial heterogeneous concentration induced by the Soret effect is presented. The obtained results, by solving numerically the full governing equations, are found to be in good agreement with the developed solution based on the scale analysis approach. The resulting convective flows are found to be dependent on the local particle concentration φ and the corresponding solutal to thermal buoyancy ratio N. The induced nanofluid heterogeneity showed a significant heat transfer modification. The heat transfer in natural convection increases with nanoparticle concentration but remains less than the enhancement previously underlined in forced convection case.     

MHD FREE CONVECTION FLOW OF A NANOFLUID PAST A VERTICAL PLATE IN THE PRESENCE OF HEAT GENERATION OR ABSORPTION EFFECTS

This work is focused on the numerical solution of steady natural convection boundary-layer flow of a nanofluid consisting of a pure fluid with nanoparticles along a permeable vertical plate in the presence of magnetic field, heat generation or absorption, and suction or injection effects. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing boundary-layer equations of the problem are formulated and transformed into a non-similar form. The obtained equations are then solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method. Comparisons with previously published work are performed and are found to be in excellent agreement. Representative results for the longitudinal velocity, temperature, and nanoparticle volume fraction profiles as well as the local heat transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms.     

Natural convection heat transfer of nanofluids along a vertical plate embedded in porous medium

The unsteady natural convection heat transfer of nanofluid along a vertical plate embedded in porous medium is investigated. The Darcy-Forchheimer model is used to formulate the problem. Thermal conductivity and viscosity models based on a wide range of experimental data of nanofluids and incorporating the velocity-slip effect of the nanoparticle with respect to the base fluid, i.e., Brownian diffusion is used. The effective thermal conductivity of nanofluid in porous media is calculated using copper powder as porous media. The nonlinear governing equations are solved using an unconditionally stable implicit finite difference scheme. In this study, six different types of nanofluids have been compared with respect to the heat transfer enhancement, and the effects of particle concentration, particle size, temperature of the plate, and porosity of the medium on the heat transfer enhancement and skin friction coefficient have been studied in detail. It is found that heat transfer rate increases with the increase in particle concentration up to an optimal level, but on the further increase in particle concentration, the heat transfer rate decreases. For a particular value of particle concentration, small-sized particles enhance the heat transfer rates. On the other hand, skin friction coefficients always increase with the increase in particle concentration and decrease in nanoparticle size.     

Conjugate heat transfer of laminar mixed convection of a nanofluid through an inclined tube with circumferentially non-uniform heating

Laminar mixed convection of a nanofluid consisting of water and Al₂O₃ in an inclined tube with heating at the top half surface of a copper tube has been studied numerically. The bottom half of the tube wall is assumed to be adiabatic (presenting a tube of a solar collector). Heat conduction mechanism through the tube wall is considered. Three-dimensional governing equations with using two-phase mixture model have been solved to investigate hydrodynamic and thermal behaviours of the nanofluid over wide range of nanoparticle volume fractions. For a given nanoparticle mean diameter the effects of nanoparticle volume fractions on the hydrodynamics and thermal parameters are presented and discussed at different Richardson numbers and different tube inclinations. Significant augmentation on the heat transfer coefficient as well as on the wall shear stress is seen.     

冷热圆管在封闭方腔内不同垂直位置的自然对流数值研究

利用有限体积法对冷热圆管在封闭方腔内不同垂直位置的自然对流现象进行了数值研究。讨论了瑞利数Ra和冷热圆管间距δ对方腔内自然对流流动与换热的影响, 其中瑞利数的变化范围为10³～10⁶, 圆管间距变化范围为0.3～0.6。为了揭示冷热圆管间的相互作用和圆管与方腔间的相互作用对自然对流换热与流动的影响规律, 比较分析了热圆管在上、冷圆管在下和热圆管在下、冷圆管在上两种情形下冷热圆管、方腔的自然对流换热能力的差异。研究表明:瑞利数的改变, 对方腔内温度场分布和涡流结构有显著影响;热圆管在下、冷圆管在上这种情形更有利于自然对流换热的进行;增加圆管间距δ, 热圆管和方腔的换热能力增强, 但冷圆管的换热能力却有所减弱。研究结果为核电站安全壳非能动余热排出系统的性能研究提供了理论依据。     

Mixed convection flows in a square lid‐driven cavity with heat source at the bottom utilising nanofluid

This paper presents a numerical investigation of laminar mixed convection cooling of heat source embedded on the bottom wall of an enclosure filled with nanofluids. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influences of governing parameters, namely, 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 present results are validated by favourable comparisons with previously published results. The results of the problem are presented in graphical and tabular forms and discussed. © 2011 Canadian Society for Chemical Engineering     

Natural Convection in Heat Generating Oval Porous Enclosures: A Non‐Darcian Model

This paper presents a series of numerical simulations dealing with the problem of natural convection flows and associated heat transfer in an enclosure filled with a fluid‐saturated porous medium. The analysis is based on the finite element technique and incorporates the Brinkman‐extended Darcy model for an oval enclosure. The numerical results obtained for a modified Rayleigh number, Ra, Darcy number, Da, offset, E, and eccentricity, e, are presented and discussed. The numerical predictions for a square enclosure compared well with published data. It is found that any increase in Da or Ra results in a higher fluid velocity that is responsible for shifting the core of the flow. Moreover, at higher ovality (E = 0.5), asymmetric flow is observed even at the lower range of Rayleigh number (Ra ? 20), which may be attributed to the effect of curved isothermal wall.     

含内热源的梯形腔自然对流换热数值模拟

引言 封闭腔体内的自然对流换热问题在实际工程中有着重要应用,因而受到越来越多的关注,工程实际中常用的腔体结构有方腔、圆形腔、三角形腔等.     

CO2 Absorption Using Nanofluids in a Wetted‐Wall Column with External Magnetic Field

A new method for enhancing the mass transfer coefficient in the gas absorption process is reported. CO₂ absorption experiments were carried out in a wetted‐wall column using different aqueous nanofluids as the solvent. The mass transfer characteristics were found to increase by applying Al₂O₃/water nanofluid. The mass transfer coefficient decreased with TiO₂/water nanofluid. In the case of Fe₃O₄/water nanofluid, the mass transfer rate was enhanced by increasing the nanoparticle volume fraction, but the mass transfer coefficient was lower than that obtained with water for all experimental conditions studied. Finally, applying a downward magnetic field resulted in higher mass flux and mass transfer coefficient in comparison with experiments without a magnetic field.     

Simulation of forced convection in a channel with nanofluid by the lattice Boltzmann method

This paper presents a numerical study of the thermal performance of fins mounted on the bottom wall of a horizontal channel and cooled with either pure water or an Al₂O₃-water nanofluid. The bottom wall of the channel is heated at a constant temperature and cooled by mixed convection of laminar flow at a relatively low temperature. The results of the numerical simulation indicate that the heat transfer rate of fins is significantly affected by the Reynolds number (Re) and the thermal conductivity of the fins. The influence of the solid volume fraction on the increase of heat transfer is more noticeable at higher values of the Re.     

Finite element analysis of natural convection in a triangular enclosure: Effects of various thermal boundary conditions

The phenomena of natural convection in a right-angled triangular enclosure is studied numerically. A penalty finite element analysis with bi-quadratic elements is used for solving the Navier-Stokes and energy balance equations. The detailed study is carried out in two cases depending on various thermal boundary conditions:

(a)

Vertical wall is uniformly or linearly heated while inclined wall is cold isothermal.

(b)

Inclined wall is uniformly or linearly heated while vertical wall is cold isothermal.

In all the cases horizontal bottom wall is adiabatic and the aspect ratio of the lengths of base and height is considered to be one. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters of Rayleigh number Ra(10³?Ra?10⁵) and Prandtl number Pr(0.07?Pr?1000) in all the cases mentioned above. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. It has been found that at low Rayleigh numbers (Ra?10⁴), the isotherms are almost parallel near the bottom portion of the triangular enclosure while at Ra=10⁵, the isotherms are more distorted. This is because the heat transfer is primarily due to conduction for lower values of Rayleigh number. As Rayleigh number increases, there is a change from conduction dominant region to convection dominant region, and the critical Rayleigh number corresponding to on-set of convection is obtained. It has been shown that the average Nusselt number for vertical wall is times that of the inclined wall as the bottom wall is adiabatic and that verifies the thermal equilibrium of the system for all case studies.     

NUMERICAL STUDY OF DEVELOPED LAMINAR MIXED CONVECTION OF Al2O3/WATER NANOFLUID IN AN ANNULUS

This work aims to study the combined free and forced convection of an Al₂O₃/water nanofluid flowing throughout an annulus. A set of three-dimensional elliptic governing equations were solved numerically using the finite volume technique. The effect of the volume fraction of the nanoparticles and the Richardson number on the thermal and hydrodynamic parameters was extensively investigated. The distribution of the axial velocity and temperature at different cross sections is shown. The axial variation of the frictional and heat transfer coefficients is presented. Results indicate that the Richardson number does not influence the frictional coefficient, while the heat transfer coefficient directly depends on the Ri number. The dimensional axial velocity continually increases with greater volume fraction of nanoparticles at the upper and lower sides of the annulus, while this behavior for dimensionless axial velocity is not continuous. The results indicate that any increase in the volume fraction results in secondary flow enhancement and, therefore, a delay in the occurrence of the maximum heat transfer coefficient.     

NATURAL CONVECTION OF A BINARY MIXTURE IN A VERTICAL CLOSED ANNULUS

This article reports an analytical and numerical study of natural convection of a binary mixture within a vertical closed annulus. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the short walls are insulated. The solutal buoyancy forces are assumed to be induced either by the imposition of constant fluxes of mass on the vertical walls (double-diffusive convection, a = 0) or by temperature gradients (Soret effect, a = 1). The governing parameters for the problem are the thermal Rayleigh number R_T, Prandtl number Pr, Lewis number Le, buoyancy ratio ?, aspect ratio A, constant a, and curvature parameter η. An analytical solution, based on the assumption of parallel flow over a large portion of enclosure, is derived. Numerical confirmation of the analytical results is also presented.     

Boundary layer flow of nanofluid over an exponentially stretching surface

The steady boundary layer flow of nanofluid over an exponential stretching surface is investigated analytically. The transport equations include the effects of Brownian motion parameter and thermophoresis parameter. The highly nonlinear coupled partial differential equations are simplified with the help of suitable similarity transformations. The reduced equations are then solved analytically with the help of homotopy analysis method (HAM). The convergence of HAM solutions are obtained by plotting h-curve. The expressions for velocity, temperature and nanoparticle volume fraction are computed for some values of the parameters namely, suction injection parameter α, Lewis number Le, the Brownian motion parameter Nb and thermophoresis parameter Nt.     

Modeling of Rayleigh convection in gas–liquid interfacial mass transfer using lattice Boltzmann method

Interfacial Rayleigh convection can be generated by concentration gradient near the interface in mass transfer processes. In the present study, a 2D time-dependent lattice Boltzmann method (LBM) with a double distribution model was established for simulating the liquid-phase Rayleigh convection in the mass transfer process of CO₂ absorption into various solvents. Two random parameters P and C_D denoting respectively the possibility and the magnitude of concentration perturbation at interface were introduced to model the interfacial disturbance, which is known as one of the necessary conditions of onset of Rayleigh convection. The values of the parameters were identified (0.05 ≤ P < 0.3 and 0 < C_D ≤ 10⁻⁹ kg m⁻³) by comparing simulated critical onset times of the Rayleigh convection with the experimental result from Blair and Quinn (1969) and theoretical predictions proposed by Kim et al. (2006) and 0245 and 0250. The maximum penetration depths, maximum transient Rayleigh numbers, and critical times for the onset of Rayleigh convection were obtained by the proposed model. The simulations captured the detailed information of the onset and the temporal–spatial evolution of Rayleigh convection, and gave the concentration contours of typical plume convection patterns which were well consistent with literatures. Enhancement of mass transfer by the Rayleigh convection was also demonstrated by comparing the simulated instantaneous mass flux across the interface with that predicted by penetration theory.