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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.  相似文献   

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 ωk, the dynamic structure function S(k, ω), the associated structure function Sm(k), and the one-particle spectral function A(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ωk by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ωk and some of the Sm(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function 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 S0(k) leads to the breakdown of the one-phonon Feynman relation at order k3. Both S(k, ω) and 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.  相似文献   

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.  相似文献   

吴雪炜  吴大建  刘晓峻 《物理学报》2010,59(7):4788-4793

We introduce the field algebra ΣD(M;n?ng) associated with the current algebra Dr(M;g) for the Lie algebra g over physical space M. The Heisenberg magnet model is generalized to this continuum. It is shown that the Hamiltonian can be given meaning as implementing a derivation of the field algebra in certain representations.We introduce new representations of the current algebra. For example, if G = SU(2), a representation in L2(R3)?3 is [σ(?)F]j = εjkl?kψl for (?k) = ? in Dr(M;g)(ψl = F. This has cyclic subrepresentations with prime parts.  相似文献   

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.  相似文献   

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.  相似文献   

The complete set of hydromagnetic equations is transformed into Poisson equations and equations of motion for flux densities and their associated variables. The toroidal components of the vector potential A and of the momentum density aπv are represented by the po loidal flux densities Ψ and Ψ, respectively, for which the equations of motion are derived. The poloidal components A and a are represen ed by the potentials atΦ, U and φ, u, for which we obtain Poisson equations in the poloidal plane. Thus one has to solve two Dirichlet and two von Neumann problems at every time step. The source terms of the four Poisson equations define the remaining four variables, namely, Λ = ▽ · A,Ω=(▽×A)ζ/R, λ=⊤·a, and ω=(▿×a)ζ/R, for which equations of motion are also derived. In the limit of small toroidicity ϵ we look fo r a selfconsistent scaling of the equations with v∼ε. But the curl of v×B in Faraday's law creates a toroidal plasma component of B which is one order of magnitude larger than in the case of a low β equilibrium; therefore, the motion becomes fully three-dimensional. Finally, an artificial pressure law is needed to balance the lowest order of the Lorentz force. The conclusion is then that the scaling laws previously used are not applicable for toroidal geometry, and that the effort to obtain numerical solutions is not dramatically higher than without using any scaling law.  相似文献   

The Sn-TiO2−X nanoparticles have been prepared via a rapid and simple stannous chemical reducing method. The as-prepared Sn-TiO2−X nanoparticles were investigated by means of surface photovoltage spectroscopy (SPS), XPS, and DRS technology as well as photocatalytic degradation of RhB were studied under illumination. The experiment results revealed that the reduction of the TiO2 particles raised their Fermi level, which can enhance the driven force of photoinduced electrons transferring from TiO2 to adsorbed O2 and SnO2 on the surface of TiO2. On the other hand, the amount of oxygen vacancies of the Sn-TiO2−X increased after the stannous chemical reduction. The oxygen vacancies can also effectively inhibit the recombination of photoinduced electrons and holes pairs. These factors are favorable to the photocatalytic reaction.  相似文献   

Antifungal activity of TiO2/ZnO nanostructures under visible light irradiation was investigated. A simple chemical method was used to synthesize ZnO nanowires. Zinc acetate dihydrate, Polyvinyl Pyrrolidone and deionized water were used as precursor, capping and solvent, respectively. TiO2 nanoparticles were deposited on ZnO nanowires using an atmospheric pressure chemical vapor deposition system. X-ray diffraction pattern of TiO2/ZnO nano-composite has represented the diffraction peaks relating to the crystal planes of the TiO2 (anatase and rutile) and ZnO. TiO2/ZnO nanostructure antifungal effect on Candida albicans biofilms was studied and compared with the activity of TiO2 nanoparticles and ZnO nanowires. The high efficiency photocatalytic activity of TiO2 nanoparticles leads to increased antifungal activity of ZnO nanowires. Scanning electron microscope was utilized to study the morphology of the as prepared nanostructures and the degradation of the yeast.  相似文献   

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