Complex singularity of a stokes wave

Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave propagating with the constant velocity. The increase in the scaled wave height H/λ from the linear limit H/λ = 0 to the critical value H _max/λ marks the transition from the limit of almost linear wave to a strongly nonlinear limiting Stokes wave. Here, H is the wave height and λ is the wavelength. We simulated fully nonlinear Euler equations, reformulated in terms of conformal variables, to find Stokes waves for different wave heights. Analyzing spectra of these solutions we found in conformal variables, at each Stokes wave height, the distance ν _c from the lowest singularity in the upper half-plane to the real line which corresponds to the fluid free surface. We also identified that this singularity is the square-root branch point. The limiting Stokes wave emerges as the singularity reaches the fluid surface. From the analysis of data for ν _c → 0 we suggest a new power law scaling ν _c ∝ (H _max ? H)^3/2 as well as new estimate H _max/λ ? 0.1410633.     

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.     

Temperature-dependent Brillouin scattering studies of surface acoustic modes in Nd0.5Sr0.5MnO3

Brillouin scattering experiments are carried out to study the surface acoustic waves in Nd_0.5Sr_0.5MnO₃ as a function of temperature in the range of 40-300 K covering the metal-insulator and charge-ordering phase transitions. The surface modes include surface Rayleigh wave, pseudo-surface acoustic wave (PSAW) and high velocity PSAW. The observed softening of the sound velocities for the surface modes below paramagnetic to ferromagnetic transition, T_c is related to the softening of the C₄₄ elastic constant. The subsequent hardening of the sound velocity below the charge ordering transition temperature T_co is attributed to the coupling of the acoustic phonon to the charge ordered state via long range ordering of the strong Jahn-Teller (JT) distortion.     

Critical surface wave velocity near phase transitions

The temperature dependent Rayleigh wave velocity is discussed for crystals with a surface layer of depth equal to the correlation length, ξ, with special reference to a critical region near phase transitions. For finite qξ the Rayleigh wave velocity reflects the specific critical properties of the surface layer. Under such conditions the temperature dependence of Rayleigh waves cannot be predicted on the temperature dependence of constants. A phenomenological analysis is made for qξ ≦? 1. Experimental results on SrTiO₃ show bulk-dominated critical Rayleigh wave velocities due to the short correlation length in this material.     

Model calculation of the surface tension of liquid Ga-Bi alloy

A convenient model, based on some assumptions, for calculating the composition and temperature dependence of the surface tension of binary liquid alloys is reported. The theoretical calculations of the surface tension of gallium-rich-bismuth alloys are presented. The calculated results are compared with the reported experimental data. A relatively good agreement with experimental behavior of the composition dependence of the surface tension was found, but a disagreement was observed with experimental temperature behavior of the surface tension of these alloys. The calculations were conducted in the temperature range from almost 320 K to about 800 K. The surface tension was calculated from eutectic composition (x_Bi = 0.0022) to x_Bi = 0.1, and worked out by linear equations. The model calculation and analysis indicate a first order surface phase transition in this system, which is in accord with experimental findings. For this system, γ decreases linearly with increasing temperature at fixed Bi mole fraction x_Bi, and thus, suggesting a positive surface excess entropy. It is also found that the surface tension isotherms show the linear dependence on the concentration, in the logarithm scale of x_Bi, in the very narrow concentration range.     

Mathematical Analysis for Peristaltic Flow of Two Phase Nanofluid in a Curved Channel

This paper describes the theoretical analysis for peristaltic motion of water base nanofluid containing distinct types of the nanoparticles like Cu, TiO₂, and Al₂O₃. Equations of nano fluid are modelled and simplified by constructing the suppositions of low Reynolds number as well as long wave length. The reduced equations are solved exactly. Solutions are represented through graphs. Outcomes for the velocity, temperature, pressure rise and stream lines are analyzed graphically. The work presented here is based on the fictitious values, however some other values can be tested experimentally.     

Performance characteristic of a Stirling refrigeration cycle in micro/nano scale

The aim of the paper is to present the performance characteristics of a Stirling refrigeration cycle in micro/nano scale, in which the working substance of cycle is an ideal Maxwellian gas. Due to the quantum boundary effect on the gas particles confined in the finite domain, the cycle no longer possesses the condition of perfect regeneration. The inherent regenerative losses, the refrigeration heat and coefficient of performance (COP) of the cycle are derived. It is found that, for the micro/nano scaled Stirling refrigeration cycle devices, the refrigeration heat and COP of cycle all depend on the surface area of the system (boundary of cycle) besides the temperature of the heat reservoirs, the volume of system and other parameters, while for the macro scaled refrigeration cycle devices, the refrigeration heat and COP of cycle are independent of the surface area of the system. Variations of the refrigeration heat ratio r_R and the COP ratio r_ε with the temperature ratio τ and volume ratio r_V for the different surface area ratio r_A are examined, which reveals the influence of the boundary of cycle on the performance of a micro/nano scaled Stirling refrigeration cycle. The results are useful for designing of a micro/nano scaled Stirling cycle device and may conduce to confirming experimentally the quantum boundary effect in the micro/nano scaled devices.     

MHD Maxwell flow modeled by fractional derivatives with chemical reaction and thermal radiation

Heat transfer in a time-dependent flow of incompressible viscoelastic Maxwell fluid induced by a stretching surface has been investigated under the effects of heat radiation and chemical reaction. The magnetic field is applied perpendicular to the direction of flow. Velocity, temperature, and concentration are functions of z and t for the modeled boundary-layer flow problem. To have a hereditary effect, the time-fractional Caputo derivative is incorporated. The pressure gradient is assumed to be zero. The governing equations are non-linear, coupled and Boussinesq approximation is assumed for the formulation of the momentum equation. To solve the derived model numerically, the spatial variables are discretized by employing the finite element method and the Caputo-time derivatives are approximated using finite difference approximations. It reveals that the fractional derivative strengthens the flow field. We also observe that the magnetic field and relaxation time suppress the velocity. The lower Reynolds number enhances the viscosity and thus motion weakens slowly. The velocity initially decreases with increasing unsteadiness parameter δ. Temperature is an increasing function of heat radiation parameter but a decreasing one for the volumetric heat absorption parameter. The increasing value of the chemical reaction parameter decreases concentration. The Prandtl and Schmidt numbers adversely affect the temperature and concentration profiles respectively. The fractional parameter changes completely the velocity profiles. The Maxwell fluids modeled by the fractional differential equations flow faster than the ordinary fluid at small values of the time t but become slower for large values of the time t.     

Heat and mass transfer of MHD convective boundary layer flow past a stretching porous wall embedded in a porous medium

The hydromagnetic convective boundary layer flow past a stretching porous wall embedded in a porous medium with heat and mass transfer in the presence of a heat source and under the influence of a uniform magnetic field is studied. Exact solutions of the basic equations of motion, heat and mass transfer are obtained after reducing them to nonlinear ordinary differential equations. The reduced equations of heat and mass transfer are solved using a confluent hypergeometric function. The effects of the flow parameters such as a suction parameter (N), magnetic parameter (M), permeability parameter (K _p ), wall temperature parameter (r), wall concentration parameter (n), and heat source/sink parameter (Q) on the dynamics are discussed. It is observed that the suction parameter appears in the boundary condition ensuring the variable suction at the surface. Transverse component of the velocity increases only when magnetic field strength exceeds certain value, but the thermal boundary layer thickness and concentration distribution increase for all values. Results presented in this paper are in good agreement with the work of the previous author and also in conformity with the established theory.     

Microscopic theory of longitudinal sound velocity in CDW and SDW ordered cuprate systems

We address here the self-consistent calculation of the spin density wave and the charge density wave gap parameters for high-T_c cuprates on the basis of the Hubbard model. In order to describe the experimental observations for the velocity of sound, we consider the phonon coupling to the conduction band in the harmonic approximation and then the expression for the temperature dependent velocity of sound is calculated from the real part of the phonon Green’s function. The effects of the electron–phonon coupling, the frequency of the sound wave, the hole doping concentration, the CDW coupling and the SDW coupling parameters on the sound velocity are investigated in the pure CDW phase as well as in the co-existence phase of the CDW and SDW states. The results are discussed to explain the experimental observations.     

INFLUENCE OF SEED CRYSTAL DIMENSION ON CRYSTAL GROWTH FROM SOLUTION UNDER MICROGRAVITY

The influence of the dimension of seed crystal on the characteristics of crystal growth from solution under microgravity is studied. The dimensionless average velocity of fluid V_av, the dimensionless maximum velocity of fluid V_max, the temperature distribution index S_θ, the concentration distribution index S_φ and the dimensionless average growth rate of crystal \overline{V}_cg are calculated by only taking into account the variation of the solution density caused by the temperature change, that caused by the concentration change being neglected. In certain regions of the parameter (Ra, Pr,Sc and μ) space, some scaling laws are generated: the scales of S_φ and \overline{V}_cg are given by power functions of μ with negative exponents. It is shown that the characteristics of crystal growth for small seed crystal are different from those for large seed crystal.     

Heat transfer analysis for stretching flow over a curved surface with magnetic field

The analysis of a viscous fluid flow and heat transfer is carried out under the influence of a constant applied magnetic field over a curved stretching sheet. Heat transfer analysis is carried out for two heating processes, namely, prescribed surface temperature (PST) and prescribed heat flux (PHF). The equations governing the flow are modeled in a curvilinear coordinate system (r, s, z). The nonlinear partial differential equations are then transformed to nonlinear ordinary differential equations by using similarity transformations. The obtained system of equations is solved numerically by a shooting method using Runge-Kutta algorithm. The interest lies in determining the influence of dimensionless radius of curvature on the velocity, temperature, skin friction, and rate of heat transfer at the wall prescribed by the Nusselt number. The effects of Hartmann number are also presented for the fluid properties of interest.     

A numerical simulation method for dissolution in porous and fractured media

We describe an algorithm for simulating reactive flows in porous media, in which the pore space is mapped explicitly. Chemical reactions at the solid–fluid boundaries lead to dissolution (or precipitation), which makes it necessary to track the movement of the solid–fluid interface during the course of the simulation. We have developed a robust algorithm for constructing a piecewise continuous (C₁) surface, which enables a rapid remapping of the surface to the grid lines. The key components of the physics are the Navier–Stokes equations for fluid flow in the pore space, the convection–diffusion equation to describe the transport of chemical species, and rate equations to model the chemical kinetics at the solid surfaces. A lattice-Boltzmann model was used to simulate fluid flow in the pore space, with linear interpolation at the solid boundaries. A finite-difference scheme for the concentration field was developed, taking derivatives along the direction of the local fluid velocity. When the flow is not aligned with the grid this leads to much more accurate convective fluxes and surface concentrations than a standard Cartesian template. A robust algorithm for the surface reaction rates has been implemented, avoiding instabilities when the surface is close to a grid point. We report numerical tests of different aspects of the algorithm and assess the overall convergence of the method.     

Study on blood flow containing nanoparticles through porous arteries in presence of magnetic field using analytical methods

In this paper, flow analysis for a third grade non-Newtonian blood in porous arteries in presence of magnetic field is simulated analytically and numerically. Blood is considered as the third grade non-Newtonian fluid containing nanoparticles. Collocation Method (CM) and Optimal Homotopy Asymptotic Method (OHAM) are used to solve the Partial Differential Equation (PDE) governing equation which a good agreement between them was observed in the results. The influences of the some physical parameters such as Brownian motion parameter, pressure gradient and thermophoresis parameter, etc. on temperature, velocity and nanoparticles concentration profiles are considered. For instance, increasing the thermophoresis parameter (N_t) caused an increase in temperature values in whole domain and an increase in nanoparticles concentration near the inner wall.     

Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation

In this paper, we investigated numerically an unsteady boundary layer flow of a nanofluid over a stretching sheet in the presence of thermal radiation with variable fluid properties. Using a set of suitable similarity transformations, the governing partial differential equations are reduced into a set of nonlinear ordinary differential equations. System of the nonlinear ordinary differential equations are then solved by the Keller-box method. The physical parameters taken into consideration for the present study are: Prandtl number Pr, Lewis number Le, Brownian motion parameter N _b, thermophoresis parameter N _t, radiation parameter N _r, unsteady parameter M. In addition to these parameters, two more new parameters namely variable thermophoretic diffusion coefficient parameter e and variable Brownian motion diffusion coefficient parameter β have been introduced in the present study. Effects of these parameters on temperature, volume fraction of the nanoparticles, surface heat and mass transfer rates are presented graphically and discussed briefly. To validate our method, we have compared the present results with some previously reported results in the literature. The results are found to be in a very good agreement.     

Electron-phonon coupling and longitudinal sound velocity of La0.5Ca0.5MnO3

In this paper, the microscopic theory of the relative change in velocity of sound with temperature of La_0.5Ca_0.5MnO₃ is reported. The phonon Green function is calculated using the Green function technique of Zubarev in the limit of zero wave vector and low temperature. The lattice model electronic Hamiltonian in the presence of the phonon interaction with hybridization between the conduction electrons and the l-electrons is used. The relative change in velocity of sound at various temperatures is studied for different model parameters, namely the position of the l-level, the effective phonon coupling strength and hybridization strength. The phonon anomalies observed experimentally at different temperatures are explained theoretically. An abrupt change in velocity at Neel temperature (T_N) is observed clearly. It is observed that different parameters influence the velocity of sound.     

Effect of temperature on rotational viscosity in magnetic nano fluids

Flow behavior of magnetic nano fluids with simultaneous effect of magnetic field and temperature is important for its application for cooling devices such as transformer, loud speakers, electronic cooling and for its efficiency in targeted drug delivery and hyperthermia treatment. Using a specially designed horizontal capillary viscometer, temperature-sensitive and non-temperature-sensitive magnetic nano fluids are studied. In both these case the temperature-dependent rotational viscosity decreases, but follows a quite different mechanism. For temperature-sensitive magnetic nano fluids, the reduction in rotational viscosity is due to the temperature dependence of magnetization. Curie temperature (^T _c ) and pyromagnetic coefficient are extracted from the study. A fluid with low T _c and high pyromagnetic coefficient is useful for thermo-sensitive cooling devices and magnetic hyperthermia. For non-temperature-sensitive magnetic nano fluids, reduction in rotational viscosity is due to removal of physisorbed secondary surfactant on the particle because of thermal and frictional effects. This can be a good analogy for removal of drug from the magnetic particles in the case of targeted drug delivery.      

Linear and nonlinear optical properties of MgO:LiTaO3

We derive new temperature dependent Sellmeier equations for the extra-ordinary and ordinary refractive indices of 0.5% MgO-doped stoichiometric LiTaO₃ crystal. The equations are based on quasi phase-matched frequency conversion measurements, as well as on interferometric measurements of the thermal expansion and thermal dispersion. These equations fit experimental data over wide spectral ranges: 0.35–6 μm for the extra-ordinary wave and 0.375–3.75 μm for the ordinary wave, from room temperature up to 200°C. The nonlinear optical measurements set lower-limit values for the d ₃₃, d ₂₂, and d ₂₄ elements of the second-order susceptibility tensor χ ⁽²⁾ of 12.9, 1.54, and 0.46 pm/V, respectively. The interferometric measurements enable one to determine the linear and quadratic expansion coefficients of 1.45762e?5 1/°C, and 2.68608e?8 (1/°C)², respectively. The Sellmeier equations are in good agreement with previously published data.     

Influence of metallic nanoparticles in water driven along a wavy circular cylinder

In the present study, simultaneous effects of metallic nanoparticles and magnetohydrodynamic due to stagnation point flow of nanofluid along a wave circular cylinder is presented. The effect of induced magnetic field is incorporated to deal the boundary and thermal boundary layer domain. Mathematical modelling for momentum and energy equation is constructed that is based upon three different kinds of nanoparticles namely: copper (Cu), Titanium di oxide (TiO₂), and alumina (Al₂O₃) within the working fluid water. Each mixture is analysed at the individual level and made comparison amongst all the mixture to examine the resistance and thermal conductivity of nanofluid within the boundary layer region. The solutions are exposed via boundary value problem using shooting method along with the Runge-Kutta-Fehlberg method. The characteristics of emerging parameters for the fluid flow and heat transfer are discussed through graphs and tables. The effects of ϕ (nanoparticle volume fraction) on heat transfer and shear stress at the wall are analysed in detail. It is finally concluded that by increasing the ratio of nanoparticles there is a significant increase in the temperature but slight decrease in the velocity profile.