Magnetic impact on heat and mass transfer utilizing nonofluid in an annulus between a superellipse obstacle and a cavity with periodic side-wall temperature and concentration

The magnetic impacts upon the transport of heat and mass of an electrically conducting nanofluid within an annulus among an inner rhombus with convex and outer cavity with periodic temperature/concentration profiles on its left wall are assessed by the ISPH method. The right wall has ${T}_{c}$ and ${C}_{c},$ flat walls are adiabatic, and the temperature and concentration of the left wall are altered sinusoidally with time. The features of the heat and mass transfer and fluid flow through an annulus are assessed across a wide scale of Hartmann number $Ha,$ Soret number $Sr,$ oscillation amplitude $A,$ Dufour number $Du,$ nanoparticles parameter $\phi ,$ oscillation frequency $f,$ Rayleigh number $Ra,$ and radius of a superellipse $a$ at Lewis number $Le=20,$ magnetic field's angle $\gamma =45^\circ ,$ Prandtl number ${\Pr }=6.2,$ a superellipse coefficient $n=3/2,$ and buoyancy parameter $N=1.$ The results reveal that the velocity's maximum reduces by $70.93 \% $ as $Ha$ boosts from 0 to 50, and by $66.24 \% $ as coefficient $a$ boosts from $0.1$ to $0.4.$ Whilst the velocity's maximum augments by $83.04 \% $ as $Sr$ increases from 0.6 to 2 plus a decrease in $Du$ from 1 to 0.03. The oscillation amplitude $A,$ and frequency $f$ are significantly affecting the nanofluid speed, and heat and mass transfer inside an annulus. Increasing the parameters $A$ and $f$ is augmenting the values of mean Nusselt number $\overline{Nu}$ and mean Sherwood number $\overline{Sh}.$ Increasing the radius of a superellipse $a$ enhances the values of $\overline{Nu}$ and $\overline{Sh}.$     

AN EMPIRICAL CORRELATION FOR NATURAL CONVECTION FROM CONFINED ELLIPTIC TUBE

An experimental study was conducted to obtain a correlation for free convection heat transfer from isothermal elliptic tubes of minor to major axis ratios of ∈ = 0.53, 0.67, 0.8, and 1 confined between two adiabatic walls. Local and average Nusselt numbers were determined for several different tube axis ratios, Rayleigh numbers, and wall spacings by means of the Mach-Zehnder Interferometery (MZI) technique. For each tube axis ratio, the Rayleigh number varied from 1,000–2,750 and the wall spacing to tube minor axis ratio from 1.25–∞. For all the tube axis ratios, the periphery and length of the tubes were kept constant. Experimental data are presented with a correlation which gives the average Nusselt number as a function of the tube axis ratio, Rayleigh number, and wall spacing to tube minor axis ratio. As the tube axis ratio decreases the average heat transfer coefficient increases. Also, for a constant Rayleigh number and tube axis ratio there is an optimum wall spacing which maximizes the heat transferred from the tube.     

Core structure and Peierls stress of the 90° dislocation and the 60° dislocation in aluminum investigated by the fully discrete Peierls model

The core structure, Peierls stress and core energy, etc. are comprehensively investigated for the $90^\circ$ dislocation and the $60^\circ$ dislocation in metal aluminum using the fully discrete Peierls model, and in particular thermal effects are included for temperature range $0\leq T \leq 900$ K. For the $90^\circ$ dislocation, the core clearly dissociates into two partial dislocations with the separating distance $D\sim 12$ Å, and the Peierls stress is very small $\sigma_{\rm p}<1$ kPa. The nearly vanishing Peierls stress results from the large characteristic width and a small step length of the $90^\circ$ dislocation. The $60^\circ$ dislocation dissociates into $30^\circ$ and $90^\circ$ partial dislocations with the separating distance $D\sim 11$ Å. The Peierls stress of the $60^\circ$ dislocation grows up from $1$ MPa to $2$ MPa as the temperature increases from $0$ K to $900$ K. Temperature influence on the core structures is weak for both the $90^\circ$ dislocation and the $60^\circ$ dislocation. The core structures theoretically predicted at $T=0$ K are also confirmed by the first principle simulations.     

Étude numérique du modèle de Boussinesq de convection naturelle laminaire axisymétrique permanente dans un espace annulaire compris entre deux sphères

Authors study numerically the axisymetric steady natural convection in the annular space between two vertically eccentric spheres applying the Boussinesq approximation and an integro-interpolation finite volumes method. In the case of two isothermal concentric spheres their results agree with those of the literature. Also, they obtain correlations between the average Nusselt number and the Rayleigh number quasi identical to those publish by Chiu and Scanlan. When the internal sphere is heated by the application of a constant heat flux and eccentric as compared to the supposed external sphere isothermal, they propose correlations between the average Nusselt number and the Rayleigh number that depend on the eccentricity and on the Prandtl number. According to initialising conditions of calculation, the external sphere being isothermal, authors show that there exists a critical Rayleigh number beyond which the flow can be found unicellular or bicellular. This critical Rayleigh number depends on others parameters of the system as the eccentricity and the aspect ratio when the internal sphere is isothermal as well as subjected to a uniform constant heat flux density.     

Thermo-Solutal Natural Convection in an Anisotropic Porous Enclosure Due to Non-Uniform Temperature and Concentration at Bottom Wall

This article summaries a numerical study of thermo-solutal natural convection in a square cavity filled with anisotropic porous medium. The side walls of the cavity are maintained at constant temperatures and concentrations, whereas bottom wall is a function of non-uniform (sinusoidal) temperature and concentration. The non-Darcy Brinkmann model is considered. The governing equations are solved numerically by spectral element method using the vorticity-stream-function approach. The controlling parameters for present study are Darcy number $(Da)$, heat source intensity i.e., thermal Rayleigh number $(Ra)$, permeability ratio $(K^∗)$, orientation angle $(ϕ)$. The main attention is given to understand the impact of anisotropy parameters on average rates of heat transfer (bottom, $Nu_b$, side $Nu_s$) and mass transfer (bottom, $Sh_b$, side, $Sh_s$) as well as on streamlines, isotherms and iso-concentration. Numerical results show that, for irrespective value of $K^∗$, the heat and mass transfer rates are negligible for $10^{-7}≤Da≤10^{−5}, Ra=2×10^5$ and $ϕ=45^◦$. However, a significant impact appears on Nusselt and Sherwood numbers when Da lies between $10^{−5}$ to $10^{−4}$. The maximum bottom heat and mass transfer rates ($Nu_b, Su_b$) is attained at $ϕ=45^◦$, when $K^∗= $0.5 and 2.0. Furthermore, both heat and mass transfer rates increase on increasing Rayleigh number ($Ra$) for all the values of $K^∗$. Overall, It is concluded from the above study that due to anisotropic permeability the flow dynamics becomes complex.     

Characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh-Bénard convection

We study the characteristics of temperature fluctuation in two-dimensional turbulent Rayleigh–Benard convection in′a square cavity by direct numerical simulations.The Rayleigh number range is 1×10⁸≤Ra≤1×10¹³,and the Prandtl number is selected as Pr=0.7 and Pr=4.3.It is found that the temperature fluctuation profiles with respect to Ra exhibit two different distribution patterns.In the thermal boundary layer,the normalized fluctuationθrms/θrms,max is independent of Ra and a power law relation is identified,i.e.,θrms/θrms,max～(z/δ)0.99±0.01,where z/δis a dimensionless distance to the boundary(δis the thickness of thermal boundary layer).Out of the boundary layer,when Ra≤5×10⁹,the profiles ofθrms/θrms,max descend,then ascend,and finally drop dramatically as z/δincreases.While for Ra≥1×10¹⁰,the profiles continuously decrease and finally overlap with each other.The two different characteristics of temperature fluctuations are closely related to the formation of stable large-scale circulations and corner rolls.Besides,there is a critical value of Ra indicating the transition,beyond which the fluctuation hθrmsiV has a power law dependence on Ra,given by hθrmsiV～Ra?0.14±0.01.     

Effect of internal heat source on magneto-stationary convection of couple stress fluid under magnetic field modulation

The present article provides an analytical solution of nonlinear heat transfer of an electrically conducting Couple stress liquid under a magnetic field modulation with an internal heat source. A weakly nonlinear theory is used to obtain the rate of heat transfer concerning the Nusselt number. A cubic Landau equation is derived in terms of amplitude of convection and solved by using Mathematica 8 software. The effect of various system parameters are obtained on nonlinear heat transfer which is discussed in detail by graphically. The Prandtl number, internal Rayleigh number, Couple stress parameter and magnetic Prandtl number destabilize the system while Chandrasekhar number has stabilizing effect. Hence, Couple stress parameter and internal Rayleigh number increase the rate of heat transfer.     

Bound on vertical heat transport at large Prandtl number

We prove a new upper bound on the vertical heat transport in Rayleigh-Bénard convection of the form under the assumption that the ratio of Prandtl number over Rayleigh number satisfies where the non-dimensional constant c₀ depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) bound (modulo logarithmic correction) on vertical heat transport for the infinite Prandtl number model for convection due to Constantin and Doering [P. Constantin, C.R. Doering, Infinite Prandtl number convection, J. Stat. Phys. 94 (1) (1999) 159-172] and Doering, Otto and Reznikoff [C.R. Doering, F. Otto, M.G. Reznikoff, Bounds on vertical heat transport for infinite Prandtl number Rayleigh-Bénard convection, J. Fluid Mech. 560 (2006) 229-241]. It also improves a uniform (in Prandtl number) bound for the Nusselt number [P. Constantin, C.R. Doering, Heat transfer in convective turbulence, Nonlinearity 9 (1996) 1049-1060] in the case of large Prandtl number.     

A numerical study of laminar natural convective heat transfer inside a closed cavity with different aspect ratio

Two-dimensional steady-state laminar natural convection was studied numerically for differentially heated air-filled closed cavity with adiabatic top and bottom walls. The temperature of the left heated wall and cooled right wall was assumed to be constant. The governing equations were iteratively solved using the control volume approach. In this paper, the effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively.Variations of the maximum stream function and the average heat transfer coefficient were also shown. The average Nusselt number and was correlated to the Rayleigh number based on curve fitting for each aspect ratio. The investigation covered the range 10⁴ ≤ RA ≤ 10⁷ and is done at Prandtl number equal to 0.693. The result shows the average Nusselt number is the increasing function of Rayleigh number. As the aspect ratio increases, Nusselt number decreases along the hot wall of the cavity. As Rayleigh number increases, Nusselt number increases. Result indicates that at constant aspect ratio, with increase in Rayleigh number the heat transfer rate increases.     

Triple differential cross-sections of Ne (2s<Superscript>2</Superscript>) in coplanar to perpendicular plane geometry

The distorted wave Born approximation (DWBA) with the spin averaged static exchange potential has been used to calculate the triple differential cross-sections (TDCSs) for Ne (2s ²) ionization by electron impact in coplanar to perpendicular plane symmetric geometry at 110.5 eV incident electron energy. The present theoretical results at gun angles (coplanar symmetric geometry) and (perpendicular plane geometry) are in satisfactory agreement with the available experimental data. A deep interference minimum appears in the TDCS in the coplanar symmetric geometry and a strong peak at scattering angle caused by the single collision mechanism has been observed in the perpendicular plane geometry. The TDCSs at the gun angles , and are predicted.Received: 16 July 2002, Published online: 22 July 2003PACS: 34.80.Gs Molecular excitation and ionization by electron impact - 34.80.Dp Atomic excitation and ionization by electron impact     

Long relaxation times and tilt sensitivity in Rayleigh Bénard turbulence

We study the influence of a small tilt angle ( rd) on the Nusselt number in a 1/2 aspect ratio Rayleigh-Bénard cell, at high Rayleigh number (5 x 10¹¹ < Ra < 4 x 10¹²). The small decrease observed is interpreted as revealing a two rolls structure of the flow. Transitions between different global flows are also observed, on very long times, comparable to the diffusion time on the whole cell. The consequence is that the Nusselt number observed in most high Ra experiments should significantly depend on initial conditions.Received: 19 May 2004, Published online: 12 August 2004PACS: 92.60.Ek Convection, turbulence, and diffusion - 47.27.Te Convection and heat transfer - 44.25. + f Natural convection     

自然对流换热的高精度非结构网格有限体积法

用非结构网格有限体积法求解自然对流换热时,传统的对流项离散格式难以兼顾数值精度与计算效率,我们发展了一种耦合高精度格式的延迟修正方法,用于对流项的离散.高Re数下方腔驱动流数值计算验证了该方法具有较高的计算精度和较好的稳定性.Boussinesq流体的自然对流换热数值模拟,表明该方法能有效克服高Ra数时数值计算发散,可准确捕捉自然对流换热问题中不同偏心率下的等温线和流线分布特征.     

An analysis of the time-dependent CP asymmetryin $B \to \pi \pi$ decays in the standard model

Measurements of the time-dependent CP-asymmetry in the decay and its charge conjugate by the BELLE and BABAR collaborations currently yield and , characterizing the direct and mixing-induced CP-asymmetries, respectively. We study the implication of these measurements on the CKM phenomenology taking into account the available information in the quark mixing sector. Our analysis leads to the results that the ratio |P _c /T _c | involving the QCD-penguin and tree amplitudes and the related strong phase difference in the decays are quite substantial. Using the isospin symmetry to constrain |P _c /T _c | and , where parameterizes the penguin-induced contribution, we present a fit of the current data including the measurements of and . Our best-fits yield , , , , and . At 68% C.L., the ranges are , , , and . Currently en vogue dynamical approaches to estimate the hadronic matrix elements in decays do not provide a good fit of the current data.Received: 5 April 2004, Published online: 14 July 2004A.Ya. Parkhomenko: On leave of absence from Department of Theoretical Physics, Yaroslavl State University, Sovietskaya 14, 150000 Yaroslavl, Russia.     

饱和含混多孔介质中环绕水平圆柱的自然对流

本文运用达西流模型，对饱和含湿多孔介质中环绕水平等温圆柱发生的自然对流进行了数值模拟和分析。流函数和温度分布采用傅里叶级数的形式，以联立求解二维流动的控制方程组，傅里叶级数项的系数由一维常微分方程的解得到。文中同时给出局部和平均努谢尔数随修正瑞利数的变化关系以及修正瑞利数处在０．１～１０范围内时二维流场和温度场分布。     

Collective Dand Structures in Doubly Odd 136La Nucleus

Using heavy-ion nuclear reaction and in-beam γ-ray spectroscopy technique,high spin states of ¹³⁶La have been studied. The nuclear reaction used is ¹³⁰Te(¹¹B,5n) with a beam energy 60MeV. The level scheme with three collective band structures has been updated with spin up to 20h. The collective backbending has been observed in $\uppi h_{11/2}\otimes \upnu h_{11/2}$ band. According to the TRS calculations,this backbending is due to the alignment of a pair of h_11/2 neutrons. The signature splitting and inversion for the $\uppi h_{11/2}\otimes \upnu h_{11/2}$ band were also discussed. Other two bands based on $12^-$ and $16^+$ levels were proposed as oblate deformation with $\gamma\approx -60^\circ$. They most probably originate from four- and six- quasiparticle configurations, that is,$\uppi h_{11/2}\otimes\upnu g_{7/2} h_{11/2}^2$ and $\uppi g_{7/2}\otimes\upnu g_{7/2}^2 d_{5/2}h_{11/2}^2$ respectively.     

The high-energy critical minimum in elastic electron scattering by argon

The position of high-energy critical minimum in elastic electron-argon scattering was investigated both experimentally and theoretically. Differential cross-sections (DCSs) were measured as a function of both incident electron energy (40-150 eV) and scattering angle ( ), in small steps around the critical minimum. The position of the high-energy critical minimum in elastic electron-argon scattering was experimentally found to be at eV and . To cover the energy and angular ranges of the present experiment, relevant relativistic ab initio calculations were carried out, based on the Dirac-Hartree-Fock method with the exchange calculated exactly. Target polarization is described by an ab initio potential taken from relativistic polarized orbital calculations. The calculated position of the high-energy critical minimum is eV, . It was shown that even slight difference of fixed scattering angle close to the critical point could affect significantly the energy dependent DCS. Discussion of behavior of DCS in the vicinity of the critical minimum was performed including convolution analysis in both energy and angle.Received: 31 October 2003, Published online: 20 April 2004PACS: 31.15.Ar Ab initio calculations - 34.80.Bm Elastic scattering of electrons by atoms and molecules     

Influence of the growth method upon the phase transition of RbCdCl $\mathsf{_{3}}$

Structural properties of two RbCdCl₃ samples grown either from the melt or from aqueous solution are studied via X-ray diffraction over a closed temperature cycle between 20 C and 300 C. During cooling step (300 C), the crystal grown from the melt undergoes a phase transition at 110 C that drives it from the cubic structure into a tetragonal structure that still persists at 20 C. It undergoes exactly the reverse phase transition at the same temperature during the heating ( C) step that immediately follows. The other crystal grows from aqueous solution at 20 C in an orthorhombic structure (i.e. not tetragonal as that of the crystal grown from the melt and cooled down to this temperature). During the heating ( C) step, it undergoes a direct orthorhombic-cubic phase transition at 240 C (without passing through the tetragonal phase) whereas, during subsequent cooling (300 C), it does not exhibit the corresponding reverse phase transition but rather exhibits exactly the same cubic-tetragonal phase transition at 110 C as the crystal grown from the melt. However, for both crystals, this tetragonal phase observed at room temperature is unstable and slowly converts into an orthorhombic phase over the course of time. Complementary Differential Scanning Calorimetry (D.S.C.) and Thermo Gravimetric Analysis (T.G.A.) measurements have been carried out over the range ( ) C in order to interpret diffraction experiments.Received: 19 May 2004, Published online: 30 September 2004PACS: 61.10.Nz X-ray diffraction - 64.70.Kb Solid-solid transitions - 65.40.Ba Heat capacity     

Compound diffractive telescope system: design, straylight analysis, and optical test

The compound diffractive telescope is a novel space optical system which combines the structure of compound eyes with diffractive optics and so it has a lighter weight, a wider field of view (FOV), a lower cost as well as looser fabrication tolerance. In this paper, the design of a compound diffractive telescope composed of one primary lens and twenty-one eyepieces is introduced. Then the influence of diffraction orders on the performance of the system is analysed. A modified phase function model of diffractive optics is proposed to analyse the modulation transfer function (MTF) curves for 0℃ FOV, which provides a more accurate prediction of the performance of the system. In addition, an optimized mechanism is also proposed to suppress stray light. The star image and resolution tests show that the system can achieve diffraction limit imaging within ± 2℃ of FOV and ±4~mm of eccentricity. Finally, a series of pictures of an object are taken from different channels, and the splicing of pictures from adjacent FOVs is demonstrated. In summary, the designed system has been proved to have great potential applications.     

General Solution for Unsteady Natural Convection Flow with Heat and Mass in the Presence of Wall Slip and Ramped Wall Temperature

This work is focused on the effect of heat and mass transfer with unsteady natural convection flow of viscous fluid along with ramped wall temperature under the assumption of the slip wall condition at the boundary. Analytical solutions are obtained by using Laplace transformation to the non-dimensional set of governing equations containing velocity, temperature and concentration. Moreover, the expression for skin-friction is derived by differentiating the analytical solutions of fluid velocity. Numerical tables for Skin-friction, Sherwood number and Nusselt-number are examined. For the physical aspects of the flow, we use various values of involved physical parameters such as Prandtl number (Pr), slip parameter ($\eta$), Schmidt number (Sc), buoyancy ratio parameter ($N$), Sherwood number (Sh), and time $(t)$. Additionally, the general solutions are plotted graphically and a comprehensive theoretical section of numerical discussions is included.     

Josephson vortices and intrinsic Josephson junctions in the layered iron-based superconductor Ca10(Pt3As8)((Fe0.9Pt0.1)2As2)5

Modulated electronic state due to the layered crystal structures brings about moderate anisotropy of superconductivity in the iron-based superconductors and thus Abrikosov vortices are expected in the mixed state. However, based on the angular and temperature dependent transport measurements in iron-based superconductor Ca$_{10}$(Pt$_3$As$_8$)((Fe$_{0.9}$Pt$_{0.1}$)$_2$As$_2$)$_5$ with $T_{\rm c} \simeq 12$ K, we find clear evidences of a crossover from Abrikosov vortices to Josephson vortices at a crossover temperature $T^{\star} \simeq 7 $ K, when the applied magnetic field is parallel to the superconducting FeAs layers, i.e., the angle between the magnetic field and the FeAs layers $\theta = 0^\circ$. This crossover to Josephson vortices is demonstrated by an abnormal decrease (increase) of the critical current (flux-flow resistance) below $T^{\star}$, in contrast to the increase (decrease) of the critical current (flux-flow resistance) above $T^{\star}$ expected for Abrikosov vortices. Furthermore, when $\theta$ is larger than $0.5^\circ$, the flux-flow resistance and critical current have no anomalous behaviors across $T^{\star}$. These anomalous behaviors can be understood in terms of the distinct transition from the well-pinned Abrikosov vortices to the weakly-pinned Josephson vortices upon cooling, when the coherent length perpendicular to the FeAs layers $\xi_\bot$ becomes shorter than half of the interlayer distance $d/2$. These experimental findings indicate the existence of intrinsic Josephson junctions below $T^{\star}$ and thus quasi-two-dimensional superconductivity in Ca$_{10}$(Pt$_3$As$_8$)((Fe$_{0.9}$Pt$_{0.1}$)$_2$As$_2$)$_5$, similar to those in the cuprate superconductors.