Integral treatment for forced convection heat and mass transfer of nanofluids over linear stretching sheet

An integral treatment is proposed for the analysis of the forced convection flow of a nanofluid over a stretching sheet.The obtained results agree well with the numerical results.The results of the presented solution provide an analytic solution,which can be conveniently used in engineering applications.Four types of nanoparticles,i.e.,alumina（Al₂O₃）,silicon dioxide（SiO₂）,silver（Ag）,and copper（Cu）,dispersed in the base fluid of water are examined.The analytical results show that an increase in the volume fraction of nanoparticles increases the thickness of the thermal boundary layer.The reduced Nusselt number is a decreasing function of the volume fraction of nanoparticles.     

Forced convection from an isolated heat source in a channel with porous medium

A numerical study is made of flow and heat transfer characteristics of forced convection in a channel that is partially filled with a porous medium. The flow geometry models convective cooling process in a printed circuit board system with a porous insert.The channel walls are assumed to be adiabatic. Comprehensive numerical solutions are acquired to the governing Navier-Stokes equations, using the Brinkman-Forchheimer-extended Darcy model for the regions of porous media. Details of flow and thermal fields are examined over ranges of the principal parameters; i.e., the Reynolds number Re, the Darcy number Da (≡K/H²), the thickness of the porous substrate S, and the ratio of thermal conductivities R_k (≡k_eff/k). Two types of the location of the porous block are considered. The maximum temperature at the heat source and the associated pressure drop are presented for varying Re, Da, S, and R_k. The results illustrate that as S increases or Da decreases, the fluid flow rate increases. Also, as R_k increases for fixed Da, heat transfer rates are augmented. Explicit influences of Re on the flow and heat transport characteristics are also scrutinized. Assessment is made of the utility of using a porous insert by cross comparing the gain in heat transport against the increase in pressure drop.     

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.     

水基MWCNTs/MoS2复合纳米流体的摩擦学性能研究

使用离子液体[EMIm]BF₄分散多壁碳纳米管(MWCNTs),再以[EMIm]BF₄-阿拉伯树胶(GA)为添加剂分散二硫化钼(MoS₂),二者的水溶液复配得到复合纳米流体. 采用拉曼光谱分析了MWCNTs的改性度,通过吸光度和粒度对复合纳米流体的分散与悬浮稳定性进行了表征. 对不同纳米颗粒配比的复合纳米流体润湿性能和摩擦学性能进行测试,结果表明:MWCNTs和MoS₂质量分数为0.6%、1.2%时复合纳米流体的铺展成膜能力最好,其接触角约为63.04°,相比于去离子水降低了23.55%. 摩擦磨损测试结果也表明此配比下的减摩抗磨性能最佳,平均摩擦系数为0.073,比去离子水降低了61.98%,同时体积磨损率降低了67.87%. 磨痕形貌观测表明,最优配比下磨痕浅,且表面光滑、无犁沟. X射线光电子能谱(XPS)表明MWCNTs和MoS₂共同参与摩擦并在基底成膜,由此协同实现了高效润滑.      

Effects of Brownian Motion and Thermophoresis on the Mixed Convection of Nanofluid in a Porous Channel Including Flow Reversal

This article is devoted to combined convection heat transfer of nanofluids through a vertical channel filled with a homogeneous and isotropic porous medium. The flow is assumed to be fully developed and the “Brinkman extended Darcy” model is used for the flow in the porous media and “clear compatible” viscous dissipation model is considered. Also the model utilized for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The governing momentum, energy, and nanopartices volume fraction equations are solved both analytically and numerically. The effects of the influential dimensionless parameters such as Brownian and thermophoresis parameters, mixed convection parameter (Gr/Re), Brinkman, Darcy and Lewis numbers on dimensionless velocity and temperature distributions and pressure drop are studied. Also, the results of the Nusselt number for the both left and right walls are presented and discussed.     

The Prandtl number effect near the onset of Bénard convection in a porous medium

This note focuses on Kladias and Prasad's claim that the critical Rayleigh number for the onset of Bénard convection in an infinite horizontal porous layer increases as the Prandtl number decreases, and argues that the critical Rayleigh number (Ra_c) depends only on the Darcy number (Da), as linear stability analysis indicates. The two-dimensional steady-convection problem is then solved numerically to document the convection heat transfer effect of the Rayleigh number, Darcy number, Prandtl number, and porosity. The note concludes with an empirical correlation for the overall Nusselt number, which shows the effect of Prandtl number at above-critical Rayleigh numbers. The correlation is consistent with the corresponding correlation known for Bénard convection in a pure fluid.     

Temperature and particle-size dependent viscosity data for water-based nanofluids – Hysteresis phenomenon

In the present paper, we have investigated experimentally the influence of both the temperature and the particle size on the dynamic viscosities of two particular water-based nanofluids, namely water–Al₂O₃ and water–CuO mixtures. The measurement of nanofluid dynamic viscosities was accomplished using a ‘piston-type’ calibrated viscometer based on the Couette flow inside a cylindrical measurement chamber. Data were collected for temperatures ranging from ambient to 75 °C, for water–Al₂O₃ mixtures with two different particle diameters, 36 nm and 47 nm, as well as for water–CuO nanofluid with 29 nm particle size. The results show that for particle volume fractions lower than 4%, viscosities corresponding to 36 nm and 47 nm particle-size alumina–water nanofluids are approximately identical. For higher particle fractions, viscosities of 47 nm particle-size are clearly higher than those of 36 nm size. Viscosities corresponding to water-oxide copper are the highest among the nanofluids tested. The temperature effect has been investigated thoroughly. A more complete viscosity data base is presented for the three nanofluids considered, with several experimental correlations proposed for low particle volume fractions. It has been found that the application of Einstein’s formula and those derived from the linear fluid theory seems not to be appropriate for nanofluids. The hysteresis phenomenon on viscosity measurement, which is believed to be the first observed for nanofluids, has raised serious concerns regarding the use of nanofluids for heat transfer enhancement purposes.     

Numerical simulation of MHD natural convection flow in a wavy cavity filled by a hybrid Cu-Al_2O_3-water nanofluid with discrete heating

We consider the combined effect of the magnetic field and heat transfer inside a square cavity containing a hybrid nanofluid(Cu-Al_2O_3-water). The upper and bottom walls of the cavity have a wavy shape. The temperature of the vertical walls is lower,the third part in the middle of the bottom wall is kept at a constant higher temperature,and the remaining parts of the bottom wall and the upper wall are thermally insulated.The magnetic field is applied under the angle γ, an opposite clockwise direction. For the numerical simulation, the finite element technique is employed. The ranges of the characteristics are as follows: the Rayleigh number(10~3≤Ra≤10~5), the Hartmann number(0≤Ha≤100), the nanoparticle hybrid concentration(?_(Al_2O_3),?_(Cu) = 0, 0.025, 0.05),the magnetic field orientation(0≤γ≤2π), and the Prandtl number P_r, the amplitude of wavy cavity A, and the number of waviness n are fixed at P_r = 7, A = 0.1, and n = 3, respectively. The comparison with a reported finding in the open literature is done,and the data are observed to be in very good agreement. The effects of the governing parameters on the energy transport and fluid flow parameters are studied. The results prove that the increment of the magnetic influence determines the decrease of the energy transference because the conduction motion dominates the fluid movement. When the Rayleigh number is raised, the Nusselt number is increased, too. For moderate Rayleigh numbers, the maximum ratio of the heat transfer takes place for the hybrid nanofluid and then the Cu-nanofluid, followed by the Al_2O_3-nanofluid. The nature of motion and energy transport parameters has been scrutinized.     

TiO<Subscript>2</Subscript>-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

The TiO₂-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem (BVP). The BVP is analytically solved with the homotopy analysis method (HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO₂ nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO₂ nanoparticles increases. This confirms the fact that the occurrence of the TiO₂ nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased. An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water, while the Nusselt number of the nanofluid is larger than that of pure water. However, both the parameters increase if the magnetic field intensity increases.     

Investigation of third-grade non-Newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method

In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the thirdgrade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method (Hybrid-MsDTM) and the Crank-Nicholson method (CNM) are used to solve the partial differential equation (PDE), and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, A_g, and reducing the lead angle of body acceleration, φ, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when A_g increases.     

Fully developed mixed convection in horizontal and inclined tubes with uniform heat flux using nanofluid

Fully developed laminar mixed convection of a nanofluid consists of water and Al₂O₃ in horizontal and inclined tubes has been studied numerically. Three-dimensional elliptic governing equations have been solved to investigate the flow behaviors over a wide range of the Grashof and Reynolds numbers. Comparisons with previously published experimental and numerical works on mixed convection in a horizontal and inclined tube are performed and good agreements between the results are observed. Effects of nanoparticles concentration and tube inclinations on the hydrodynamics and thermal parameters are presented and discussed. It is shown that the nanoparticles concentration does not have significant effects on the hydrodynamics parameters. Heat transfer coefficient increases by 15% at 4 Vol.% Al₂O₃. Skin friction coefficient continually increases with the tube inclination, but the heat transfer coefficient reaches a maximum at the inclination angle of 45°.     

The effect of the Reynolds number on the Reynolds stresses and vorticity in a turbulent far-wake

Using two orthogonal arrays of 16 X-wires, eight in the (x,y)-plane and eight in the (x,z)-plane, the effect of the Reynolds number in a turbulent plane far-wake has been investigated for two values of Re_θ (based on the free stream velocity and the momentum thickness), i.e. 1350 and 4600. It is observed that as the Reynolds number increases the magnitudes of the measured Reynolds stresses increase, as does the size of two-point vorticity correlation iso-contours. Discernible differences are also observed in probability density function, spectra and three-dimensional topologies. The Reynolds number dependence seems to vanish when Re_θ5000.     

血液-血管耦合特性与脉搏波传播特性的关系

脉搏波既不可简单地理解为可压缩血液流体中的压力纵波,也不可简单地理解为沿固体血管传播的涨缩位移横波,而是超乎普通想象的流-固耦合和纵波-横波耦合的复杂波。从分析耦合本构关系的新途径出发,本文中提出了一个流-固耦合/纵波-横波耦合的串联模型,可为解读“位数形势”中医脉诊提供更丰富的信息。结果表明,脉搏波耦合系统的等效体积压缩模量K_s以及相应的耦合系统脉搏波传播速度c_s主要依赖于两个无量纲参数:血液-血管模量比K_b(p)/E(p)和薄壁血管径厚比D(p)/h₀,它们因人而异、因人的不同脉搏位置而异。文中定量分析了它们对c_s的影响,显示人体的K_b/E值在103数量级,从而c_s值在100～101 m/s数量级,以适应人体生理生化反应。由临床有创测量,证实脉搏体积横波与脉搏压力纵波是相耦合地以相同速度传播;还显示脉搏波是在其波阵面上具有氧合生化反应的“生物波”。此外,还讨论了“脉压放大”现象与非线性本构关系和与血管分叉处加载增强反射之间的关系,并讨论了Lewis关于重搏波形成的假设。     

Effect of nanoparticles mean diameter on mixed convection heat transfer of a nanofluid in a horizontal tube

Fully developed mixed convection of a nanofluid (water/Al₂O₃) has been studied numerically. Two-phase mixture model has been used to investigate the effects of nanoparticles mean diameter on the flow parameters. The calculated results demonstrate that the convection heat transfer coefficient significantly increases with decreasing the nanoparticles means diameter. However it does not significantly change the hydrodynamics parameters. Nanoparticles distribution at the tube cross section shows that the non-uniformity of the particles distribution augments when using larger nanoparticles and/or considering relatively high value of the Grashof numbers.     

Effect of Local Thermal Non-equilibrium on the Onset of Convection in a Porous Medium Layer Saturated by a Nanofluid

The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is analytically studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium, the Darcy model is employed. The effect of local thermal non-equilibrium among the particle, fluid, and solid-matrix phases is investigated using a three-temperature model. The analysis reveals that in some circumstances the effect of LTNE can be significant, but for a typical dilute nanofluid (with large Lewis number and with small particle-to-fluid heat capacity ratio) the effect is small.     

Conjugate natural convection from an array of discrete heat sources: part 2 — a numerical parametric study

Coupled conduction and natural convection transport within a discretely heated cavity have been investigated numerically. One vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity. The opposite vertical wall and the horizontal walls are assumed to be isothermal and adiabatic, respectively. The governing steady-state partial differential equations for the fluid and solid region are solved simultaneously using a control volume formulation, coupled with an additive correction multigrid procedure that increases the convergence rate of the solution. The fluid Prandtl number and heater/fluid thermal conductivity ratio are fixed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77) and heaters manufactured from silicon. With increasing modified Rayleigh number (10⁴ < Ra_Lz^* < 109), the cavity flow becomes more boundary layer-like along the vertical walls, and multiple fluid cells develop in the central region. Thermal spreading in the substrate increases with decreasing modified Rayleigh number and with increasing values of the substrate/fluid thermal conductivity ratio (10⁻¹ <- R_s ≤ 10³). For large R_s, the discrete heat sources lose their thermal identity, and the streamlines and isotherms resemble those associated with a differentially heated cavity. Thermal spreading in the substrate also has a significant effect on circulation in the cavity and on maximum surface temperatures.     

Al2O3陶瓷动静态压缩下碎片形貌与破坏机理分析

为探究Al₂O₃陶瓷的宏观力学响应与破坏机理,分别利用材料试验机和分离式霍普金森压杆对其进行准静态和动态压缩实验,同时通过原位光学成像观测试样的破坏过程,并利用同步辐射CT和扫描电镜（SEM）对回收碎片的尺寸和形状以及微观破坏模式进行表征分析。宏观强度数据表明,Al₂O₃陶瓷的抗压强度符合Weibull分布,且与加载应变率呈现指数增长关系。原位光学成像和SEM回收分析共同揭示了动静态加载下裂纹成核与扩展模式存在明显差异。准静态加载时材料微观上更易发生沿晶断裂,宏观表现为劈裂裂纹较少,且倾向于沿加载方向传播并贯穿整个试样;而动态加载时穿晶断裂占主导地位,劈裂裂纹明显增加并发生相互作用,因此在传播过程中容易分叉而形成大量次生裂纹,提高了试样内裂纹密度。这与碎片的CT表征结果一致,即碎片平均球形度和伸长、扁平指数等均随应变率对数线性增加。破坏模式的改变最终导致高应变率下陶瓷材料应变率敏感性显著增强。     

TiO_2-water nanofluid in a porous channel under the effects of an inclined magnetic field and variable thermal conductivity

The TiO_2-water based nanofluid flow in a channel bounded by two porous plates under an oblique magnetic field and variable thermal conductivity is formulated as a boundary-value problem(BVP). The BVP is analytically solved with the homotopy analysis method(HAM). The result shows that the concentration of the nanoparticles is independent of the volume fraction of TiO_2 nanoparticles, the magnetic field intensity, and the angle. It is inversely proportional to the mass diffusivity. The fluid speed decreases whereas the temperature increases when the volume fraction of the TiO_2 nanoparticles increases. This confirms the fact that the occurrence of the TiO_2 nanoparticles results in the increase in the thermal transfer rate. The fluid speed decreases and the temperature increases for both the pure water and the nanofluid when the magnetic field intensity and angle increase. The maximum velocity does not exist at the middle of the symmetric channel, which is in contrast to the plane-Poiseuille flow, but it deviates a little bit towards the lower plate, which absorbs the fluid with a very low suction velocity. If this suction velocity is increased, the temperature in the vicinity of the lower plate will be increased.An explicit expression for the friction factor-Reynolds number is then developed. It is shown that the Hartmann number of the nanofluid is smaller than that of pure water,while the Nusselt number of the nanofluid is larger than that of pure water. However,both the parameters increase if the magnetic field intensity increases.     

Experimental studies on heat transfer and friction factor characteristics of CuO/water nanofluid under turbulent flow in a helically dimpled tube

An experimental investigation on the convective heat transfer and friction factor characteristics in the plain and helically dimpled tube under turbulent flow with constant heat flux is presented in this work using CuO/water nanofluid as working fluid. The effects of the dimples and nanofluid on the Nusselt number and the friction factor are determined in a circular tube with a fully developed turbulent flow for the Reynolds number in the range between 2500 and 6000. The height of the dimple/protrusion was 0.6 mm. The effect of the inclusion of nanoparticles on heat transfer enhancement, thermal conductivity, viscosity, and pressure loss in the turbulent flow region were investigated. The experiments were performed using helically dimpled tube with CuO/water nanofluid having 0.1%, 0.2% and 0.3% volume concentrations of nanoparticles as working fluid. The experimental results reveal that the use of nanofluids in a helically dimpled tube increases the heat transfer rate with negligible increase in friction factor compared to plain tube. The experimental results showed that the Nusselt number with dimpled tube and nanofluids under turbulent flow is about 19%, 27% and 39% (for 0.1%, 0.2% and 0.3% volume concentrations respectively) higher than the Nusselt number obtained with plain tube and water. The experimental results of isothermal pressure drop for turbulent flow showed that the dimpled tube friction factors were about 2-10% higher than the plain tube. The empirical correlations developed for Nusselt number and friction factor in terms of Reynolds number, pitch ratio and volume concentration fits with the experimental data within ±15%.     

Forced convection of gaseous slip-flow in porous micro-channels under Local Thermal Non-Equilibrium conditions

Steady laminar forced convection gaseous slip-flow through parallel-plates micro-channel filled with porous medium under Local Thermal Non-Equilibrium (LTNE) condition is studied numerically. We consider incompressible Newtonian gas flow, which is hydrodynamically fully developed while thermally is developing. The Darcy–Brinkman–Forchheimer model embedded in the Navier–Stokes equations is used to model the flow within the porous domain. The present study reports the effect of several operating parameters on velocity slip and temperature jump at the wall. Mainly, the current study demonstrates the effects of: Knudsen number (Kn), Darcy number (Da), Forchheimer number (Γ), Peclet number (Pe), Biot number (Bi), and effective thermal conductivity ratio (K _R) on velocity slip and temperature jump at the wall. Results are given in terms of skin friction (C _f Re ^*) and Nusselt number (Nu). It is found that the skin friction: (1) increases as Darcy number increases; (2) decreases as Forchheimer number or Knudsen number increases. Heat transfer is found to (1) decreases as the Knudsen number, Forchheimer number, or K _R increases; (2) increases as the Peclet number, Darcy number, or Biot number increases.