Stagnation-point flow past a shrinking sheet in a nanofluid

In this paper, the stagnation-point flow and heat transfer towards a shrinking sheet in a nanofluid is considered. The nonlinear system of coupled partial differential equations was transformed and reduced to a nonlinear system of coupled ordinary differential equations, which was solved numerically using the shooting method. Numerical results were obtained for the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the nanoparticle volume fraction φ, the shrinking parameter λand the Prandtl number Pr. Three different types of nanoparticles are considered, namely Cu, Al₂O₃ and TiO₂. It was found that nanoparticles of low thermal conductivity, TiO₂, have better enhancement on heat transfer compared to nanoparticles Al₂O₃ and Cu. For a particular nanoparticle, increasing the volume fraction φ results in an increase of the skin friction coefficient and the heat transfer rate at the surface. It is also found that solutions do not exist for larger shrinking rates and dual solutions exist when λ < −1.0.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump

The forced convection of nanofluid flow in a long microchannel is studied numerically according to the finite volume approach and by using a developed computer code. Microchannel domain is under the influence of a magnetic field with uniform strength. The hot inlet nanofluid is cooled by the heat exchange with the cold microchannel walls. Different types of nanoparticles such as Al₂O₃ and Ag are examined while the base fluid is considered as water. Reynolds number are chosen as Re=10 and Re=100. Slip velocity and temperature jump boundary conditions are simulated along the microchannel walls at different values of slip coefficient for different amounts of Hartmann number. The investigation of magnetic field effect on slip velocity and temperature jump of nanofluid is presented for the first time. The results are shown as streamlines and isotherms; moreover the profiles of slip velocity and temperature jump are drawn. It is observed that more slip coefficient corresponds to less Nusselt number and more slip velocity especially at larger Hartmann number. It is recommended to use Al₂O₃-water nanofluid instead of Ag-water to increase the heat transfer rate from the microchannel walls at low values of Re. However at larger amounts of Re, the nanofluid composed of nanoparticles with higher thermal conductivity works better.     

Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer by hydromagnetic three-dimensional free convection over a permeable stretching surface with radiation

The thermal-diffusion and diffusion-thermo effects on the heat and mass transfer characteristics of free convection past a continuously stretching permeable surface in the presence of magnetic field, blowing/suction and radiation are studied. The fluid viscosity is assumed to vary with temperature. The resulting, governing three-dimensional equations are transformed using a similarity transformation and then solved numerically by the shooting method. Comparison with previously published work is performed and full agreement is obtained. A parametric study showing the effects of variable viscosity parameter β, magnetic parameter M, Dufour number Df, Soret number Sr, radiation parameter R and blowing/suction parameter f₀ on the velocity, temperature, and concentration field of a hydrogen-air mixture as a non-chemical reacting fluid pair, as well as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number is carried out. These are illustrated graphically and in tabular form to depict special features of the solutions.     

Significance of activation energy and Wu's slip features in Cross nanofluid with motile microorganisms

The current article investigates the impact of the bioconvection in an unsteady flow of magnetized Cross nanofluid with gyrotactic microorganisms and activation energy over a linearly stretched configuration. The analysis has been performed by utilizing the realistic Wu's slip boundary and zero mass flux conditions. The effects of nonlinear thermal radiation and the activation energy are also addressed. The governing flow equations are deduced to a dimensionless form by considering suitable transformations which are numerically targeted via a shooting algorithm. The physical visualization of each physical parameter governing the flow problem has been displayed graphically for distribution of velocity, temperature, concentration and motile microorganisms. The numerical treatment for the variation of skin friction coefficient, local Nusselt number, local Sherwood number and motile density number is performed in tabular forms.     

MHD squeezed flow of water functionalized metallic nanoparticles over a sensor surface

Present study is devoted to analyze the magnetohydrodynamics (MHD) squeezed flow of nanofluid over a sensor surface. Modeling of the problem is based on the geometry and the interaction of three different kinds of metallic nanoparticles namely: copper (Cu), alumina (Al₂O₃) and titanium dioxide (TiO₂) with the homogeneous mixture of base fluid (water). The self-similar numerical solutions are presented for the reduced form of the system of coupled ordinary differential equations. The effects of nanoparticles volume friction, permeable velocity and squeezing parameter for the flow and heat transfer within the boundary layer are presented through graphs. Comparison among the solvent are constructed for both skin friction and Nusselt number. Flow behavior of the working nanofluid according to the present geometry has analyzed through Stream lines. Conclusion is drawn on the basis of entire investigation and it is found that in squeezing flow phenomena Cu–water gives the better heat transfer performance as compare with the rest of mixtures.     

Different nano-particles volume fraction and Hartmann number effects on flow and heat transfer of water-silver nanofluid under the variable heat flux

Nanofluid flow and heat transfer composed of water-silver nanoparticles is investigated numerically inside a microchannel. Finite volume approach (FVM) is applied and the effects of gravity are ignored. The whole length of Microchannel is considered in three sections as l₁=l₃=0.151 and l₂=0.71. The linear variable heat flux affects the microchannel wall in the length of l₂ while a magnetic field with strength of B₀ is considered over the whole domain of it. The influences of different values of Hartmann number (Ha=0, 10, 20), volume fraction of the nanoparticles (ɸ=0, 0.02, 0.04) and Reynolds number (Re=10, 50, 200) on the hydrodynamic and thermal properties of flow are reported. The investigation of slip velocity variations under the effects of a magnetic field are presented for the first time (to the best knowledge of author) while the non-dimensional slip coefficient are selected as B=0.01, 0.05, 0.1 at different states.     

Phénomènes de glissement à l'interface liquide–solide

The problem of liquid–solid slip is described here, in a simplified manner. Today, several experiments have shown that substantial slip appears when a non-wetting liquid flows along a surface which is smooth on an atomic scale. This phenomena is characterised by a length, called the slip length, or Navier length, generally denoted by L_s. A number of experiments indicate that this quantity may be as large as several hundreds of nanometers. Numerical simulations also show the existence of slip in non-wetting conditions, but the corresponding lengths found here are much smaller than those found experimentally. A theory, based on the existence of a gas film of nanometre thickness has been proposed, but has not yet been experimentally confirmed. Experiments on this are difficult, and sometimes controversial. To cite this article: P. Tabeling, C. R. Physique 5 (2004).     

Preparation and study of microstructures, optical properties and oscillator parameters of titanium (IV) oxide (TiO2) film

In this study, Titanium (IV) Oxide (TiO₂) film has been prepared and characterized by X-ray diffraction (XRD). The XRD pattern of TiO₂ film of anatase phase exhibit very sharp peaks at 25° and 47.85°. According to Scherrer??s formula the grain size of anatase (101) phase TiO₂ nananoparticle is 38.5 nm. The optical properties and constants of TiO₂ film of thickness (4 ??m) have been investigated at room temperature. The transmittance, reflectance and absorbance spectra are measured in the wavelength range (340?C900 nm). Optical constants of TiO₂ film are derived from the transmission spectra and the refractive index dispersion of the film. The oscillator energy, E ₀ dispersion energy, E _d , the static refractive index, n ₀, and other parameters have been determined by the single oscillator Wemple-DiDomenico method. This film can be used in the form of thin film in dye-sensitized solar cells.     

硼(氮、氟)掺杂对TiO2纳米颗粒光学性能的影响

利用X射线衍射谱、拉曼光谱和紫外-可见光吸收光谱研究了硼(氮、氟)掺杂对TiO₂纳米颗粒光学性能的影响.X射线衍射谱和拉曼光谱结果表明,掺硼(氮、氟)对TiO₂纳米颗粒的锐钛矿相晶体结构无明显影响,而其锐钛矿晶格出现畸变(c/a值增大),这被归因于掺杂原子对TiO₂纳米颗粒表面氧原子缺位沿晶格c轴方向的占据.另外,掺硼(氮、氟)TiO₂纳米颗粒吸收带红移与TiO相似文献