Stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition

The problem of a steady laminar two‐dimensional stagnation point flow towards a stretching/shrinking sheet in a micropolar fluid with a convective surface boundary condition is studied. The governing partial differential equations are transformed into ordinary differential equations using a similarity transformation, before being solved numerically using the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter and the convective parameter on the fluid flow and heat transfer characteristics are disscussed. It is found that the skin friction coefficient and the heat transfer rate at the surface decrease with increasing values of the material parameter. Moreover, dual solutions are found to exist for the shrinking case, while for the stretching case, the solution is unique. © 2011 Canadian Society for Chemical Engineering     

Enhancements of thermal conductivities with Cu,CuO, and carbon nanotube nanofluids and application of MWNT/water nanofluid on a water chiller system

In this study, enhancements of thermal conductivities of ethylene glycol, water, and synthetic engine oil in the presence of copper (Cu), copper oxide (CuO), and multi-walled carbon nanotube (MWNT) are investigated using both physical mixing method (two-step method) and chemical reduction method (one-step method). The chemical reduction method is, however, used only for nanofluid containing Cu nanoparticle in water. The thermal conductivities of the nanofluids are measured by a modified transient hot wire method. Experimental results show that nanofluids with low concentration of Cu, CuO, or carbon nanotube (CNT) have considerably higher thermal conductivity than identical base liquids. For CuO-ethylene glycol suspensions at 5 vol.%, MWNT-ethylene glycol at 1 vol.%, MWNT-water at 1.5 vol.%, and MWNT-synthetic engine oil at 2 vol.%, thermal conductivity is enhanced by 22.4, 12.4, 17, and 30%, respectively. For Cu-water at 0.1 vol.%, thermal conductivity is increased by 23.8%. The thermal conductivity improvement for CuO and CNT nanofluids is approximately linear with the volume fraction. On the other hand, a strong dependence of thermal conductivity on the measured time is observed for Cu-water nanofluid. The system performance of a 10-RT water chiller (air conditioner) subject to MWNT/water nanofluid is experimentally investigated. The system is tested at the standard water chiller rating condition in the range of the flow rate from 60 to 140 L/min. In spite of the static measurement of thermal conductivity of nanofluid shows only 1.3% increase at room temperature relative to the base fluid at volume fraction of 0.001 (0.1 vol.%), it is observed that a 4.2% increase of cooling capacity and a small decrease of power consumption about 0.8% occur for the nanofluid system at a flow rate of 100 L/min. This result clearly indicates that the enhancement of cooling capacity is not just related to thermal conductivity alone. Dynamic effect, such as nanoparticle dispersion may effectively augment the system performance. It is also found that the dynamic dispersion is comparatively effective at lower flow rate regime, e.g., transition or laminar flow and becomes less effective at higher flow rate regime. Test results show that the coefficient of performance of the water chiller is increased by 5.15% relative to that without nanofluid.     

Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet

In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter N_R, and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles.     

Combined effects of internal heat generation and higher order chemical reaction on the non‐darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium

In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two‐dimensional non‐Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear‐coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non‐dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction. © 2011 Canadian Society for Chemical Engineering     

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.     

Heat transfer and flow behaviour of aqueous suspensions of titanate nanotubes (nanofluids)

Titanate nanotubes of an aspect ratio of ~ 10 are synthesized, characterised and dispersed in water to form stable nanofluids containing 0.5, 1.0 and 2.5 wt.% of the nanotubes. Experiments are then carried out to investigate the effective thermal conductivity, rheological behaviour and forced convective heat transfer of the nanofluids. The results show a small thermal conductivity enhancement of ~ 3% at 25 °C and ~ 5% at 40 °C for the 2.5 wt.% nanofluid. The nanofluids are found to be non-Newtonian with obvious shear thinning behaviour with the shear viscosity decreasing with increasing shear rate at low shear rates. The shear viscosity approaches constant at a shear rate higher than ~ 100-1000 s^− 1 depending nanoparticle concentration. The high shear viscosity is found to be much higher than that predicted by the conventional viscosity models for dilute suspensions. Despite the small thermal conduction enhancement, an excellent enhancement is observed on the convective heat transfer coefficient, which is much higher than that of the thermal conductivity enhancement. In comparison with nanofluids containing spherical titania nanoparticles under similar conditions, the enhancement of both thermal conductivity and convective heat transfer coefficient of the titanate nanotube nanofluids is considerably higher indicating the important role of particle shape in the heat transfer enhancement. Possible mechanisms are also proposed for the observed enhancement of the convective heat transfer coefficient.     

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.     

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.     

羟基化多壁碳纳米管/R141b纳米流体核沸腾

向多壁碳纳米管引入羟基基团,改善了其在制冷剂R141b中的分散性和稳定性。同时研究了不同质量分数纳米流体热导率、表面颗粒沉积、接触角变化对核沸腾传热性能的影响。结果表明:羟基化碳纳米流体强化沸腾传热,强化率随质量分数的增加而增加,沸腾后期有所下降。在测试浓度范围内,质量分数为0.05%,热通量为87.4 kW·m^-2时,强化率达到最大168%。流体的热导率随着质量分数的增加而增大,质量分数为0.10%时其热导率是纯R141b的1.18倍。分析认为:纳米流体热导率的增加、表面沉积颗粒及纳米颗粒扰动是强化传热的主要影响因素,接触角变化的影响可忽略不计。结论由质量分数为0.03%纳米流体沸腾过程高速成像得到验证。     

Hydrodynamic and heat transfer properties of magnetic fluid in porous medium considering nanoparticle shapes and magnetic field-dependent viscosity

The purpose of this paper is to study the characteristics of the combined convection heat transfer and a micropolar nanofluid flow passing through an impermeable stretching sheet in a porous medium. The nanofluid flow field is affected by a magnetic field perpendicular to the sheet. The dynamic viscosity of the micropolar nanofluid changes under the influence of the magnetic field. The continuity, linear momentum, angular momentum, and energy equations are first simplified using the order of magnitude technique that, along with the applied boundary conditions and the definition of the appropriate parameters, are transferred to the similarity space using the similarity analysis. Then the resulting equations are solved using the Runge–Kutta method.The distinction of the macroscale and microscale flow fields and temperature fields resulting from different nanoparticle shapes was clarified. Increasing the Hartmann number, the vortex viscosity parameter, the magnetic parameter, the nanoparticle volume fraction, and the permeability parameter of the porous media increased the surface friction on the sheet. Increasing the vortex viscosity parameter, the magnetic parameter, and the volume fraction of the nanoparticles increases the Nusselt number.     

Mixed convective boundary layer flow over a vertical wedge embedded in a porous medium saturated with a nanofluid: Natural Convection Dominated Regime

A boundary layer analysis is presented for the mixed convection past a vertical wedge in a porous medium saturated with a nano fluid. The governing partial differential equations are transformed into a set of non-similar equations and solved numerically by an efficient, implicit, iterative, finite-difference method. A parametric study illustrating the influence of various physical parameters is performed. Numerical results for the velocity, temperature, and nanoparticles volume fraction profiles, as well as the friction factor, surface heat and mass transfer rates have been presented for parametric variations of the buoyancy ratio parameter Nr, Brownian motion parameter Nb, thermophoresis parameter Nt, and Lewis number Le. The dependency of the friction factor, surface heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number) on these parameters has been discussed.     

基于热舒适性纳米喷泉的流动与传热特性

目前关于纳米喷泉流动与传热特性及微区域热舒适度方面的研究较少,为了研究其流动与传热机理,本文基于气-液两相流模型和金刚石-乙二醇/水纳米流体高沸点、低冰点等优良特性,在有限柱体空间内建立了一种基于热舒适性的新型高效换热喷泉-“纳米喷泉”,对比研究了金刚石-乙二醇/水纳米流体、水射流工质分别对喷泉流动与传热的影响,同时讨论了纳米颗粒体积分数v和表征流体流动情况的雷诺数（Reynolds,Re）对喷泉流动与传热的影响,分析了局部温度分布、流线分布、平均温度和流体换热量在空间内的变化,并依据ASHRAE 55-1992标准和ISO7730标准对微区域的热舒适度进行了评价。结果表明：随着Re数和v增大,换热强度均得以不同程度地提升,热舒适程度也逐渐增加。Re=1.0×10⁵和Re=1.2×10⁵时,纳米颗粒体积分数从0增加至1%的换热强度提升较为明显,前后两种Re数可分别强化1.5%和2.8%;Re=1.4×10⁵时,体积分数从3%增至5%的换热强度可提升11.5%,强化效果最为明显。故较小Re数下,较低组分的纳米流体强化换热效果较好;而在较大Re数下,较高组分纳米流体的强化换热效果更好。     

Numerical simulation of natural convection in a square enclosure filled with nanofluid using the two-phase Lattice Boltzmann method

Considering interaction forces (gravity and buoyancy force, drag force, interaction potential force, and Brownian force) between nanoparticles and a base fluid, a two-phase Lattice Boltzmann model for natural convection of nanofluid is developed in this work. It is applied to investigate the natural convection in a square enclosure (the left wall is kept at a high constant temperature (T_H), and the top wall is kept at a low constant temperature (T_C)) filled with Al₂O₃/H₂O nanofluid. This model is validated by comparing numerical results with published results, and a satisfactory agreement is shown between them. The effects of different nanoparticle fractions and Rayleigh numbers on natural convection heat transfer of nanofluid are investigated. It is found that the average Nusselt number of the enclosure increases with increasing nanoparticle volume fraction and increases more rapidly at a high Rayleigh number. Also, the effects of forces on nanoparticle volume fraction distribution in the square enclosure are studied in this paper. It is found that the driving force of the temperature difference has the biggest effect on nanoparticle volume fraction distribution. In addition, the effects of interaction forces on flow and heat transfer are investigated. It is found that Brownian force, interaction potential force, and gravity-buoyancy force have positive effects on the enhancement of natural convective heat transfer, while drag force has a negative effect.     

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.     

Combined effects of internal heat generation and buoyancy force on boundary layer flow over a vertical plate with a convective surface boundary condition

This paper considers the effect of buoyancy force and internal heat generation on laminar thermal boundary layer over a vertical plate with a convective surface boundary condition. We assumed that left surface of the plate is in contact with a hot fluid while a stream of cold fluid flows steadily over the right surface with a heat source that decays exponentially. Using a similarity variable, the steady state governing non‐linear partial differential equations have been transformed into a set of coupled non‐linear ordinary differential equations, which are solved numerically by applying shooting iteration technique together with fourth order Runge–Kutta integration scheme. The effects of Prandtl number, local Biot number, the internal heat generation parameter and the local Grashof number on the velocity and temperature profiles are illustrated and interpreted in physical terms. A comparison with previously published results on special case of the problem shows excellent agreement. From our results, an overshoot of fluid velocity within the boundary layer is observed due to combined effect of buoyancy force and internal heat generation, in addition, internal heat generation causes thickening of thermal boundary layer. © 2011 Canadian Society for Chemical Engineering     

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.     

二氧化铈/水基纳米流体核沸腾传热特性

对CeO₂纳米流体进行了池沸腾传热特性研究,考察了CeO₂/水基纳米流体的热导率,静态接触角以及沸腾后表面沉积情况对沸腾传热的影响。结果表明,CeO₂纳米流体可提高沸腾传热系数,且纳米流体最佳质量分数为0.05%,其沸腾传热系数较去离子水提高36%。热导率以及接触角随纳米流体质量分数的增加而增加,在本实验范围内,热导率最大增加1%;而纳米流体接触角从50.5°增加到92.9°;表面沉积随纳米流体的质量分数增加越来越明显,去离子水在沉积表面的接触角发生较大变化(51.4°～134.4°)。纳米流体的热导率影响可忽略不计;而接触角和沸腾表面颗粒沉积对纳米流体的强化传热作用影响较大。     

MHD flow and heat transfer of a micropolar fluid over a nonlinear stretching surface with variable surface heat flux and heat generation

An analysis has been carried out to study magnetohydrodynamic boundary layer flow and heat transfer of an electrically conducting micropolar fluid over a nonlinear stretching surface with variable wall heat flux in the presence of heat generation/absorption and a non‐uniform transverse magnetic field. The governing system of partial differential equations is first transformed into a system of ordinary differential equations using similarity transformation. The transformed equations are solved numerically. Results for the dimensionless velocity, micro‐rotation, and temperature profiles are displayed graphically delineating the effects of various parameters characterising the flow. The results show that the velocity profile decreases as the magnetic parameter and the velocity exponent increase, while it increases as the material parameter increases. The results show also that the temperature profile increases as the magnetic parameter, the velocity exponent, and the heat generation parameter increase. Furthermore, the temperature profile decreases as the material parameter, the heat absorption parameter, and the Prandtl number increase.     

MHD flow of a micropolar fluid towards a vertical permeable plate with prescribed surface heat flux

The problem of a steady mixed convection stagnation point flow towards a permeable vertical plate with prescribed surface heat flux immersed in an incompressible micropolar fluid is studied numerically. The governing partial differential equations are first transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by a finite-difference scheme known as the Keller-box method and the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter, buoyancy parameter, suction/injection parameter and the Prandtl number on the fluid flow and heat transfer characteristics are discussed. It is found that dual solutions exist for both assisting and opposing flows. The skin friction coefficient and the local Nusselt number increase in the presence of suction and magnetic field. Moreover, suction as well as fluids with larger Prandtl number widens the range of the buoyancy parameter for which the solution exists.     

氧化铝有机纳米流体的流动传热基础特性

以氧化铝为纳米粒子、丙二醇和水为基础液体制备了氧化铝有机纳米流体,分别测量了它的沸点、热导率、比热容和黏度。以1％～5％（体积分数）的氧化铝纳米流体作为冷介质,测试了在车用机油冷却器中的传热系数和流动阻力。试验结果表明,纳米粒子能够显著强化基础液体在机油冷却器中的换热能力,粒子体积分数和流体温度是影响纳米流体热物性的重要因素。氧化铝纳米流体的沸点高于120℃,比热容随体积分数增加而降低,热导率、黏度和在机油冷却器中的传热系数均随粒子体积分数的增加而提高。在试验Ⅱ中,5％（体积分数）纳米流体的平均传热系数比基础液体提高了124.56％,而流动阻力增幅较小。