Nonlinear Momentum Research Articles

Mixing of spin and orbital angular momenta via second-harmonic generation in plasmonic and dielectric chiral nanostructures

We present a theoretical study of the characteristics of the nonlinear spin-orbital angular momentum coupling induced by second-harmonic generation in plasmonic and dielectric nanostructures made of centrosymmetric materials. In particular, the connection between the phase singularities and polarization helicities in the longitudinal components of the fundamental and second-harmonic optical fields and the scatterer symmetry properties are discussed. By in-depth comparison between the interaction of structured optical beams with plasmonic and dielectric nanostructures, we have found that all-dielectric and plasmonic nanostructures that exhibit magnetic and electric resonances have comparable second-harmonic conversion efficiency. In addition, mechanisms for second-harmonic enhancement for single and chiral clusters of scatterers are unveiled and the relationships between the content of optical angular momentum of the incident optical beams and the enhancement of nonlinear light scattering is discussed. In particular, we formulate a general angular momenta conservation law for the nonlinear spin-orbital angular momentum interaction, which includes the quasi-angular-momentum of chiral structures with different-order rotational symmetry. As a key conclusion of our study relevant to nanophotonics, we argue that all-dielectric nanostructures provide a more suitable platform to investigate experimentally the nonlinear interaction between spin and orbital angular momenta, as compared to plasmonic ones, chiefly due to their narrower resonance peaks, lower intrinsic losses, and higher sustainable optical power.

Formation of solitary waves and oscillatory shocklets in a two-temperature electron κ–distributed plasma

Large-amplitude electron acoustic (EA) waves and shocklets are investigated in a two-temperature electron plasma. For this purpose, dynamical cold electrons are described by the fully nonlinear continuity and momentum equations, while superthermal (hot) inertialess electrons are described by the κ–distribution function with a neutralizing background of static positive ions. The fluid equations along with a quasineutrality equation are solved to obtain a set of two characteristic wave equations that admit analytical and numerical solutions. It is shown that variation due to hot electron superthermality and hot-to-cold electron density ratio strongly affects the profiles of nonlinear EA structures in terms of negative potential, cold electron velocity and density. In particular, at time τ=0, symmetric solitary pulses are formed, which develop into oscillatory shocklets with the course of time. Our results should be useful for understanding solitary excitations and associated nonstationary large-amplitude shocklets in laboratory κ–distributed plasmas, where superthermal (hot) energetic electrons exist.

Analytical and numerical solutions of squeezing unsteady Cu and TiO2-nanofluid flow in the presence of thermal radiation and heat generation/absorption

In this paper, an analytical study of squeezing unsteady nanofluid flow between two parallel plates is carried out. The effects of thermal radiation and heat generation/absorption along the temperature profile were observed. The homotopy perturbation method (HPM) was used to solve the two-dimensional nonlinear momentum and energy equations. The results found in this study are being compared with the result obtained using the RK4 technique with shooting scheme. The results obtained fascinatingly agree with the numerical solutions.

Nonlinear blade element-momentum analysis of Betz-Goldstein rotors

Blade element-momentum theory is a fundamental tool of wind turbine aerodynamics but several of its basic assumptions are not easily examined. By applying the theory to ideal Betz-Goldstein (BG) rotors, two important aspects of the theory are investigated. We prove for the first time that Glauert's inclusion of the tip loss factor in the angular and axial momentum equations is exact for BG rotors. Then we derive, also for the first time, the nonlinear contributions to the angular momentum balance when the rotor has a finite number of blades. The most important nonlinearity is the induced azimuthal velocity of the blades combined with that of the trailing vorticitiy. The derivation follows the recent formulation for the tip loss factor (F) by Wood et al. [1] in terms of the azimuthal variations in the induced velocities due to the trailing vortices. Nonlinearity is potentially important when F differs from unity. For a three-bladed BG rotor with the tip speed ratio (λ) varying from 0 to 15, we show that the nonlinear angular momentum peaks at 12% of the blade element torque when λ is in the range 0.8≤λ≤1.5. As λ increases above 1.5, the nonlinear terms reduce in importance. Nonlinearities also arise in the axial momentum equation but are more difficult to analyze. An approximate treatment of them suggests similar behaviour to the nonlinear angular momentum terms, but those in the axial momentum equation arise purely from the trailing vortices.

Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

This paper numerically investigates radiative magnetohydrodynamic mixed convection boundary layer flow of nanofluids over a nonlinear inclined stretching/shrinking sheet in the presence of heat source/sink and viscous dissipation. The Rosseland approximation is adopted for thermal radiation effects and the Maxwell-Garnetts and Brinkman models are used for the effective thermal conductivity and dynamic viscosity of the nanofluids respectively. The governing coupled nonlinear momentum and thermal boundary layer equations are rendered into a system of ordinary differential equations via local similarity transformations with appropriate boundary conditions. The non-dimensional, nonlinear, well-posed boundary value problem is then solved with the Keller box implicit finite difference scheme. The emerging thermo-physical dimensionless parameters governing the flow are the magnetic field parameter, volume fraction parameter, power-law stretching parameter, Richardson number, suction/injection parameter, Eckert number and heat source/sink parameter. A detailed study of the influence of these parameters on velocity and temperature distributions is conducted. Additionally the evolution of skin friction coefficient and Nusselt number values with selected parameters is presented. Verification of numerical solutions is achieved via benchmarking with some limiting cases documented in previously reported results, and generally very good correlation is demonstrated. This investigation is relevant to fabrication of magnetic nanomaterials and high temperature treatment of magnetic nano-polymers.

Eddy Influences on the Strength of the Hadley Circulation: Dynamic and Thermodynamic Perspectives

Abstract The strength of the equinoctial Hadley circulation (HC) is investigated in idealized simulations conducted on an equatorial beta plane in which the zonal width of the domain is varied to either permit or suppress large-scale eddies. The presence of such eddies is found to amplify the HC by a factor of 2–3 in simulations with slab-ocean boundary conditions or with a simple representation of ocean heat transport. Additional simulations in which the eddy forcing is prescribed externally indicate that this amplification is primarily associated with large-scale eddy momentum fluxes rather than large-scale eddy heat fluxes. These results contrast with results from simulations with fixed distributions of sea surface temperature (SST), in which the HC strength has been found to be relatively insensitive to large-scale eddy momentum fluxes. In both the interactive- and fixed-SST cases, the influence of nonlinear momentum advection by the mean flow complicates efforts to use the angular-momentum budget to constrain the HC strength. However, a strong relationship is found between the HC strength and a measure of the meridional gradient of boundary layer entropy, indicating a possible thermodynamic control on the HC strength. In simulations with interactive SSTs, meridional eddy momentum fluxes affect the boundary layer entropy by inducing a low-level frictional flow that reduces the ability of the HC to transport heat poleward. This allows for the maintenance of a large meridional entropy gradient in the presence of a strong HC. The results highlight the potential utility of a thermodynamic perspective for understanding the HC in flow regimes for which dynamical constraints may be difficult to apply.

Influence of non-linear thermal radiation on 2D unsteady flow of a Williamson fluid with heat source/sink

Abstract The present article reports a new mathematical formulation for a time dependent flow of a non-Newtonian Williamson fluid model by taking into account the impacts of infinite shear rate viscosity. By incorporating the constitutive relation of Williamson fluid model the basic conservation equations are obtained for two dimensional boundary layer flow. In addition, the heat transfer characteristics for flow filed over a stretching surface has been explored within the sight of thermal radiation and heat sink or source. The Rosseland approximation is being employed for non-linear thermal radiation impacts in the presence of convective heat transfer mode. The current work aims at revealing the solution of equations describing the flow of Williamson fluid by mean of employing the dimensionless approach. Therefore, the leading nonlinear momentum and energy equations are rendered into a set of simultaneously ordinary differential equations via non-dimensional variables with associated physical boundary conditions. Numerical treatment of these reduced conservation equations has been conducted by utilizing the Runge-Kutta Fehlberg integration scheme. We have examined the influence of various physical variables, like, the unsteadiness parameter, Weissenberg number, viscosity ratio parameter, Biot number, radiation parameter, temperature ratio parameter, Prandtl number and heat source/sink parameter on momentum and thermal boundary layers, which is illustrated by means of graphs and tables. The results suggest that the impact of larger viscosity ratio parameter lead to higher fluid velocity while the converse is true for the temperature field. It is noted that the greater unsteadiness parameter results in a significant enhancement in the friction factor. In addition, an increase in thermal radiation as well as temperature ratio parameters improves the heat transfer performance in fluid flow. The work of previous researchers is correlated with the findings of this paper in some special cases in the absence of Weissenberg number and viscosity ratio parameter for different values of unsteadiness parameter. A reasonably accurate predictions are achieved in this comparison.

CFD Simulations of Aeration for Cooling Paddy Rice in a Warehouse-Type Storage Facility

Aeration is an effective method for reducing deterioration of stored grain. A finite volume method was used to simulate temperature variations and distributions in stored paddy rice in a warehouse-type facility during cooling aeration. A CFD (computational fluid dynamics) software package (Fluent 14.0) was used to develop a model to solve coupled nonlinear heat, mass, and momentum transfer equations. An experiment was conducted in a large-scale (commercial) warehouse storage facility to measure temperature distributions in the stored paddy rice to validate the CFD model. The stored grain was aerated for 30 h, and temperature was measured at five depths within the grain bulk and at 24 locations for each depth. The simulated temperatures were in good agreement with the measured values, with relative differences less than 6.3%. The CFD model was shown to be effective in assessing the uniformity of temperature distribution in the grain bulk during aeration and the performance of the aeration system.

Study of the Flow Response of a Chiral Fluid Confined in a Channel in the Presence of the Transverse Magnetic Field

The chiral materials are composed of the chiral molecules or inclusions which have ability to rotate electromagnetic waves or polarized light to a desired angle depending on chirality or handedness of the molecule or inclusions and the length of the medium. Fluids like sugar solution, sugar cane juice, turpentine and most of the body fluids etc are chiral. In recent years considerable attention has been given on the study of effect of chirality of molecules or inclusions on the propagation of electromagnetic waves through chiral medium, fabrication of chiral bio-interface materials, synthesis of chiral drug and chiral polymers. In this regard, present paper is intended to study the flow response of chiral fluid flowing in a vertical channel bounded by rigid permeable boundaries in the presence of applied transverse magnetic field under the influence of viscous dissipation, and convection electric current. The simplified and generalised non-linear momentum and energy equations governing the flow of a chiral fluid confined in a channel are solved for velocity and temperature for various values of dimensionless parameter analytically using the regular perturbation method with buoyancy parameter ‘N’ as perturbation parameter and numerically using finite difference method with Successive Over Relaxation (SOR) technique. The results obtained are depicted graphically and found that the resistance to flow of chiral fluid decreases with increase in the transverse magnetic field and the flow reversal occurs with change in the chirality parameter γ from -1 to 1

Non-linear heat and mass transfer in a MHD Homann nanofluid flow through a porous medium with chemical reaction, heat generation and uniform inflow

The steady MHD axisymmetric flow of an incompressible viscous electrically conducting nanofluid impinging on a permeable plate is investigated with heat and mass transfer. An external uniform magnetic field as well as a uniform inflow, in the presence of either suction or injection, are applied normal to the plate. The effects of heat (generation/absorption) and chemical reaction have been accentuated. This study indicates the incorporated influence of both the thermophoresis phenomenon and the Brownian behavior. Numerical solutions for the governing non-linear momentum, energy and nanoparticle equations have been obtained. The rates of heat and mass transfer are presented and discussed.

The Impact of Gradient Wind Imbalance on Tropical Cyclone Intensification within Ooyama’s Three-Layer Model

Abstract This paper addresses the validity of the gradient wind balance approximation during the intensification phase of a tropical cyclone in Ooyama’s three-layer model. For this purpose, the sensitivity to various model modifications is examined, given by the inclusion of (i) unbalanced dynamics in the free atmosphere, (ii) unbalanced dynamics in the slab boundary layer, (iii) a height-parameterized boundary layer model, and (iv) a rigid lid. The most rapid intensification occurs when the model employs the unbalanced slab boundary layer, while the simulation with the balanced boundary layer reveals the slowest intensification. The simulation with the realistic height-parameterized boundary layer model exhibits an intensification rate that lies in between. Intensification is induced by a convective ring in all experiments, but a distinct contraction of the radius of maximum gradient wind only takes place with unbalanced boundary layer dynamics. In all experiments the rigid lid and the balance approximation for the free atmosphere have no crucial impact on intensification, and a linear stability analysis cannot explain the found sensitivity to intensification. Most likely the nonlinear momentum advection term plays an important role in the boundary layer. It is found on the basis of a diagnostic radial mass flux equation that the source term for latent heat provides the largest contribution to intensification and contraction. Furthermore, it turns out that the position of the convective ring inside or outside of the radius of maximum gradient wind (RMGW) is of vital importance for intensification and most likely explains the large impact of boundary layer imbalance.

Poloidal rotation driven by nonlinear momentum transport in strong electrostatic turbulence

Virtually, all existing theoretical works on turbulent poloidal momentum transport are based on quasilinear theory. Nonlinear poloidal momentum flux— is universally neglected. However, in the strong turbulence regime where relative fluctuation amplitude is no longer small, quasilinear theory is invalid. This is true at the all-important plasma edge. In this work, nonlinear poloidal momentum flux in strong electrostatic turbulence is calculated using the Hasegawa–Mima equation, and is compared with quasilinear poloidal Reynolds stress. A novel property is that symmetry breaking in fluctuation spectrum is not necessary for a nonlinear poloidal momentum flux. This is fundamentally different from the quasilinear Reynold stress. Furthermore, the comparison implies that the poloidal rotation drive from the radial gradient of nonlinear momentum flux is comparable to that from the quasilinear Reynolds force. Nonlinear poloidal momentum transport in strong electrostatic turbulence is thus not negligible for poloidal rotation drive, and so may be significant to transport barrier formation.

Unconventional pairings and radial line nodes in inversion symmetry broken superconductors

Noncentrosymmetric superconductors (NCSs) with broken inversion symmetry can have spin-dependent order parameters (OPs) with mixed parity which can also have nodes in the pair potential as well as the energy spectra. These nodes are distinct features that are not present in conventional superconductors. They appear as points or lines in the momentum space where the latter can have angular or radial geometries dictated by the dimensionality, the lattice structure and the pairing interaction.In this work we study the nodes in time reversal symmetry (TRS) preserving NCSs at the OP, the pair potential, and the energy spectrum levels. Nodes are examined by using spin independent pairing interactions respecting the rotational C∞v symmetry in the presence of spin-orbit coupling (SOC). The pairing symmetries and the nodal topology are affected by the relative strength of the pairing channels which is studied for the mixed singlet-triplet, pure singlet, and pure triplet. Complementary to the angular line nodes widely present in the literature, the C∞v symmetry here allows radial line nodes (RLNs) due to the nonlinear momentum dependence in the OPs. The topology of the RLNs in the mixed case shows a distinctly different characterization than the half-spin quantum vortex at the Dirac point. We apply this NCS physics to the inversion symmetry broken exciton condensates (ECs) in double quantum wells where the point and the RLNs can be found. On the other hand, for a pure triplet condensate, two fully gapped and topologically distinct regimes exist, separated by a QSHI-like zero energy superconducting state with even number of Majorana modes. We also remark on how the point and the RLNs can be manipulated, enabling an external control on the topology.

Combined effect of suction/injection on MHD free-convection flow in a vertical channel with thermal radiation

Abstract Transient hydromagnetic free-convection and thermal radiation flow of viscous, incompressible electrically conducting fluid in the presence of magnetic field in a vertical channel formed by two infinite porous plates is analyzed. The Rosseland diffusion approximation describes the radioactive heat flux in the energy equation. The non-linear time dependent energy and momentum equations under relevant initial and boundary conditions are solved numerically using implicit finite difference. To verify the accuracy of the numerical scheme, steady state version of the problem is solved by perturbation method. A series of numerical experiments show that time required to reach steady state velocity and temperature is directly proportional to the Prandtl number of the working fluid. In the course of numerical computation, an excellent agreement was found between transient and steady state solution at large value of time. The effect of various dimensionless parameters controlling the physical situation is extensively discussed with the aid of graphs.

Unsteady flow of a dusty Bingham fluid through a porous medium in a circular pipe

A time-varying flow through a porous medium of a dusty viscous incompressible Bingham fluid in a circular pipe is studied. A constant pressure gradient is applied in the axial direction, whereas the particle phase is assumed to behave as a viscous fluid. The effect of the medium porosity, the non-Newtonian fluid characteristics, and the particle phase viscosity on the transient behavior of the velocity, volumetric flow rates, and skin friction coefficients of both the fluid and particle phases is investigated. A numerical solution is obtained for the governing nonlinear momentum equations by using the method of finite differences.

Vector–vortex solitons in nonlinear photonic crystal fibers

In this article, I study a system of two incoherently coupled components in a nonlinear Kerr-type photonic crystal fiber presenting angular momentum in one or both components. I classify the different families of solutions and study their bifurcations in the power dispersion diagram. Finally, I analyze the stability of the different nonlinear modes by means of numerical simulations.

On heat transfer analysis of axisymmetric flow of viscous fluid over a nonlinear radially stretching sheet

This article deals with the exact solutions regarding heat transfer of viscous fluid over a non-linear radially stretching sheet. The effects of viscous dissipation on the heat transfer characteristics are considered in account in the presence of a transverse magnetic field for two types of boundary heating process namely prescribed power law surface temperature (PST) and prescribed heat flux (PHF). Similarity transformations are used to reduce the governing non-linear momentum and thermal boundary layer equations into a set of ordinary differential equations. The exact solutions of the reduced ordinary differential equations are developed in the form of confluent hypergeometric function and graphically sketched to see the influence of pertinent parameters on the temperature profiles. In addition the results for the wall temperature gradient (Nusselt number) are also presented in graphical form and discussed in detail. It is found that Prandtl number decelerates the temperature profiles in both PST and PHF cases. Thermal boundary layer thickness increases by increasing the Eckert number.

Simulation Of Natural Gas Combustion Process Using Pressure Based Solver

The aim of this research is to simulate the combustion process for methane using different heat transfer models combined with various fuel injection techniques to better understand the combustion process and heat transfer process inside IC engine which reflect on the engine efficiency. The simulation has been carried out using Lotus Engineering software. This model solves the nonlinear momentum and continuity equations to satisfy the conservation of mass and the conservation of momentum laws. In this analysis a single cylinder four stroke SI engine has been simulated. The fuel used in the simulation is methane. Two fuel systems have been investigated port injection and direct injection. The Wiebe heat release curve has been used. Two widely used for SI engines heat transfer models presented in the simulation, Annand and Woschni. The intension in this paper is to study the effect of various fuel systems and heat transfer models on engine efficiency for different engine speeds. Moreover, the evaluation of the heat transfer models for natural gas SI engine will be tested. Brake power, mean effective pressure, specific fuel consumption, brake thermal efficiency, and heat transfer rate were calculated and discussed to show the effect of varying heat transfer models and fuel systems on engine efficiency.

Slip flow and variable properties of viscoelastic fluid past a stretching surface embedded in a porous medium with heat generation

This study examines theoretically and computationally the non-Newtonian boundary layer flow and heat transfer for a viscoelastic fluid over a stretching continuous sheet embedded in a porous medium with variable fluid properties, slip velocity, and internal heat generation/absorption. The flow in boundary layer is considered to be generated solely by the stretching of the sheet adjacent to porous medium with boundary wall slip condition. Highly nonlinear momentum and thermal boundary layer equations governing the flow and heat transfer are reduced to set of nonlinear ordinary differential equations by appropriate transformation. The resulting ODEs are successfully solved numerically with the help of shooting method. Graphical results are shown for non-dimensional velocities and temperature. The effects of heat generation/absorption parameter, the porous parameter, the viscoelastic parameter, velocity slip parameter, variable thermal conductivity and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction coefficient and Nusselt number are presented. Comparison of numerical results is made with the earlier published results under limiting cases.

Similarity Solution for High Weissenberg Number Flow of Upper-Convected Maxwell Fluid on a Linearly Stretching Sheet

High Weissenberg boundary layer flow of viscoelastic fluids on a stretching surface has been studied. The flow is considered to be steady, low inertial, and two-dimensional. Upon proper scaling and by means of an exact similarity transformation, the nonlinear momentum and constitutive equations of each layer transform into the respective system of highly nonlinear and coupled ordinary differential equations. Numerical solutions to the resulting boundary value problem are obtained using an efficient shooting technique in conjunction with a variable stepping method for different values of pressure gradients. It is observed that, unlike the Newtonian flows, in order to maintain a potential flow, normal stresses must inevitably develop. The velocity field and stresses distributions over plate are presented for difference values of pressure gradient and Weissenberg numbers.