Schmidt Parameter Research Articles

Effects of Chemical Reaction and Jeffery Fluid on MHD Unsteady Heat and Mass Transfer Due to the Ramped Temperature

This research work was numerically prepared to investigate the impact of Jeffery fluid and chemical reaction on unsteady (MHD) heat mass transfer free-convective past an infinite vertical plate. The research used appropriate dimensional quantities in transforming the dimensional, coupled, non-linear boundary layer partial differential equations into non-dimensional form. Finite element method (FEM) was employed to find the Numerical solution of the dimensionless governing differential equations. The expressions of velocity, temperature, concentration, skin friction, Nusselt number as well as Sherwood number were obtained and discussed using line graph. From the result obtained, it was shown that velocity profile gets enlarged with the increase of porosity parameter K, ratio of mass transfer parameter N, Eckert number Ec and Jeffery fluid parameter β, while reverse is the case for the Magnetic parameter M, and Prandtl number Pr. Temperature profile magnifies with the increase porosity parameter K, ratio of mass transfer parameter N Eckert number Ec, while reverse is the case for Magnetic parameter M, and Prandtl number Pr. Concentration profile gets lowered by increasing the value Schmidt parameter Sc and chemical reaction parameter Kr . Jeffery fluid parameter β has enhancing effect on skin friction at both y = 0and y = 1, while reverse is the case for Chemical Reaction parameterKr . Rising the Jeffery fluid parameter β reduces the Nusselt number at y = 0 and reverse is the case for chemical reaction parameterKr and opposite behavior is seen at y = 1. Finally chemical reaction parameterKr does not have any significant effects on Sherwood number at y=0 and y=1. While Schmidt number reduces the Sherwood numberSc at y=0 and intensifies it at y=1

Convective boundary layer flow of MHD tangent hyperbolic nanofluid over stratified sheet with chemical reaction

<abstract> <p>We investigated the combined impact of convective boundary conditions, thermal conductivity, and magnetohydrodynamic on the flow of a tangent hyperbolic nanofluid across the stratified surface. Furthermore, the ramifications of Brownian motion, thermophoresis, and activation energy were considered. Heat generation, chemical reactions, mixed convection, thermal conductivity, and other elements were considered when analyzing heat transfer phenomena. The governing equations were converted via similarity transformations into non-dimensional ordinary differential equations in order to analyze the system. Using the shooting method, the problem's solution was determined. We showed the mathematical significance of the temperature, concentration profiles, and velocity of each fluid parameter. These profiles were thoroughly described and shown graphically. The findings demonstrated that as the Weissenberg number and magnetic number increased, the fluid velocity profile decreased. Higher heat generation and thermophoresis parameters resulted in an increase in the temperature profile. Higher Brownian motion and Schmidt parameter values resulted in a drop in the concentration profile. Tables were used to discuss the numerical values of skin friction ($ {C}_{fx} $), Nusselt number ($ {Nu}_{x} $), and Sherwood number ($ S{h}_{x} $). For the greater values of Weissenberg number and mixed convection parameters, skin friction numerical values fell while Nusselt numbers rose.</p> </abstract>

Entropy production in unsteady MHD double diffusive and chemically reactive nanofluid flow past a rotating permeable plate using overlapping grid spectral collocation technique

The entropy production phenomenon due to the applied external magnetic fields, thermal dissipation, chemical reaction and the impact of rotating pervious plate on heat transfer, nanofluid friction and mass transfer has been numerically explored. The nanofluid flow is presumed to be unsteady, smooth, hydro-dynamically and electrically conducting. The well known Navier–Stokes time-dependent equations in cartesian coordinates for velocity, temperature and concentration are modelled and scaled down to a system of ODEs by applying suitable similarity transformations with unsteady dimensionless parameters. A new numerical scheme known as the overlapping grids spectral collocation method (OGSCM) is applied in finding the approximate solutions to the highly nonlinear ODEs. The results obtained are then used for solving the entropy equation and the rate of irreversibility is represented graphically. Several engineering variables, such as the coefficient of heat transfer, Nusselt number and Sherwood number, are also thoroughly examined. The OGSCM proved to be accurate, computationally efficient, time efficient and converges fast. We discovered that increased applied magnetic field, chemical reaction parameter, rotation parameter, and Schmidt parameter insert more energy into the system which reduces the thermal boundary layer and hence reducing the rate of entropy generation. Furthermore, the entropy generation rate is increased by increasing the Grashof number, Brinkman number, permeability, Prandtl number, and thermal radiation parameter.

Cattaneo-Christov heat flux effect on Sakiadis magnetohydrodynamic boundary-layer transport phenomena in the Jeffrey fluid

This study aims to perform a numerical simulation of the boundary flow with the characteristic Sakiadis flow of the MHD Jeffrey fluid under the Cattaneo-Christov heat flux model over the horizontal plate. The similarity transformation for the local similarity solution was used to reduce the set of governing equations to non-linear ODE. The equations were solved by using ?dsolve? command with the numeric option for the boundary value problem in MAPLE. Simulations have been carried out for different values of the relaxation retardation times, the Deborah number, the magnetic field parameter, the heat flux relaxation time, the Prandtl number, and the Schmidt parameter. A comparative study of the numerical results from the previously published paper with the present result for the dimensionless velocity gradient over the horizontal plate shows excellent agreement. It has been found that the growth of the Deborah number leads to the dimensionless velocity gradient enhancement, while the increment of the relaxation retardation times parameter and the magnetic field parameter indicates the opposite trend. The heat transfer rate noticeably decreased with an increment in the Prandtl number and thermal relaxation time at the fluid regime. Also, fluid concentration decreases with larger values of the Schmidt parameter.

Novel Analysis of Two Kinds Hybrid Models in Ferro Martial Inserting Variable Lorentz Force Past a Heated Disk: An Implementation of Finite Element Method

In this article, the rheology of Ferro-fluid over an axisymmetric heated disc with a variable magnetic field by considering the dispersion of hybrid nanoparticles is considered. The flow is assumed to be produced by the stretching of a rotating heated disc. The contribution of variable thermophysical properties is taken to explore the momentum, mass and thermal transportation. The concept of boundary layer mechanism is engaged to reduce the complex problem into a simpler one in the form of coupled partial differential equations system. The complex coupled PDEs are converted into highly nonlinear coupled ordinary differential equations system (ODEs) and the resulting nonlinear flow problem is handled numerically. The solution is obtained via finite element procedure (FEP) and convergence is established by conducting the grid-independent survey. The solution of converted dimensionless problem containing fluid velocity, temperature and concentration field is plotted against numerous involved emerging parameters and their impact is noted. From the obtained solution, it is monitored that higher values of magnetic parameter retard the fluid flow and escalating values of Eckert number results in to enhance temperature profile. Ferro-fluid flow and heat energy for the case of the Yamada Ota hybrid model are higher than for the case of the Hamilton Crosser hybrid model. Developing a model is applicable to the printing process, electronic devices, temperature measurements, engineering process and food-making process. The amount of mass species is reduced vs. incline impacts of chemical reaction and Schmidt parameter.

Analytical investigations of the fractional free convection flow of Brinkman type fluid described by the Caputo fractional derivative

This paper considers a particular fluid model known as the fractional free convection flow of Brinkman-type fluid. We use the Caputo derivative to describe the constructive equations of this model. The main objective of the present investigations will be to propose the exact analytical solutions using the Laplace transformation and its inverse method. After the determination of the exact solutions, the Prandtl (Pr), the Grashof parameters (Gr) and (Gm), the Schmidt parameter (Sc), the Brinkman number for fluid, and the chemical reaction parameter will attract our attention, and their impacts on the modeling will be provided and explained in term of physical viewpoints. Due to the heredity and the memory, the Caputo derivative will impact the mass diffusivity of the considered fluid. Therefore, the velocity and the temperature distributions can increase or decrease depending on the value of the order of the fractional operator. The findings of the paper will be illustrated by graphical representations. Note that in the expression of the exact solutions some well-known functions will be used as the Gaussian error function, the convolution rule, the exponential functions, and many others.

Thermo-solutal dual stratified convective magnetized fluid flow from an exponentially stretching Riga plate sensor surface with thermophoresis

A theoretical study is presented for the coupled thermo-solutal free convection two-dimensional boundary layer flow of a of a magnetized fluid from an exponentially stretched magnetic sensor (Riga plate) surface. Heat generation/absorption, nonlinear thermal radiation and thermophoretic body force effects are included. Furthermore, thermal and solutal stratification are also featured in the boundary layer model. The derived nonlinear partial differential equation system with associated wall (sensor surface) and free stream boundary conditions is transformed to system of ordinary differential equations (ODE) via applicable similarity variables. A numerical solution is developed with the efficient Runge–Kutta–Fehlberg (RKF) technique with a shooting numerical method, in MATLAB software using the RKF-45 method. The graphical profiles were represented to examine the impacts of physically parameterics on the important physical stream features. Streamline and isotherm plots are also included for thermal buoyancy effect (Grashof number).Validation of solutions with earlier simpler models is included. A relatively well agreement is achived between model prediction and the benchmark value. Values for skin friction factor, Nusselt number and Sherwood numbers are also tabulated to quantify momentum, heat and mass (species) transfer characteristics at the sensor surface. The results indicate that the significant depletion in temperature accompanies accumulation in magnetization and thermal stratification parameters. Significant accumulation in mixed convection and Riga plate electrode width parameter enhance the concatenation profiles. Nusselt number grows substantially as thermal stratification and radiative parameter increases. Sherwood number grows substantially as solutal stratification, thermophoresis and Schmidt parameter increases. The present study generalizes previous models to include simultaneously exponential stretching, thermophoresis, thermal and solutal (mass) stratification and heat source/sink effects.

Surface construction for orthrotropic perfectly elastic-plastic Murnaghan material

The problem of constructing a yield surface is described. The magnitude of the stress velocity potential is explained graphically. The parameters of an elastic-plastic process are introduced: a modified R. Schmidt parameter and an analogue of the Lode parameter, the sign of which changes only when the singular point of the plasticity curve passes. The formal work area of the Murnaghan law is calculated, the real area will be much smaller. An effect similar to the Bauschinger effect for the deviator of the stress tensor is assumed to be fair. In the basic experiments of uniaxial and biaxial tension, compression and shear, a piecewise-linear generator with vertices at the corresponding singular points of the plasticity curves is determined. The magnitude of the effect is approximated by a quadratic dependence in the place parameter and piecewise-linear one in the hardening parameter. According to the magnitude of the effect, at the point of the active process there is a singular point of the curve, into which the basic generator moves. The yield surface is constructed by ductility curves drawn through the generator. Determination of the magnitude of the effect under repeated loading after unloading is considered.

Cosmic rays across the star-forming galaxy sequence – II. Stability limits and the onset of cosmic ray-driven outflows

ABSTRACT Cosmic rays (CRs) are a plausible mechanism for launching winds of cool material from the discs of star-forming galaxies. However, there is no consensus on what types of galaxies likely host CR-driven winds, or what role these winds might play in regulating galaxies’ star formation rates. Using a detailed treatment of the transport and losses of hadronic CRs developed in the previous paper in this series, here we develop a semi-analytical model that allows us to assess the viability of using CRs to launch cool winds from galactic discs. In particular, we determine the critical CR fluxes – and corresponding star formation rate surface densities – above which hydrostatic equilibrium within a given galaxy is precluded because CRs drive the gas off in a wind or otherwise render it unstable. Our model demonstrates that catastrophic, CR-driven wind loss is a possibility at galactic mean surface densities below ${\lesssim}10^2 \ \mathrm{ M}_{\odot }$ pc−2. In this regime – encompassing the Galaxy and local dwarfs – the locus of the CR-stability curve patrols the high side of the observed distribution of galaxies in the Kennicutt–Schmidt parameter space of star formation rate versus gas surface density. However, hadronic losses render CRs unable to drive global winds in galaxies with surface densities above the ∼102−103 M⊙ pc−2 transition region. Our results show that quiescent, low surface density galaxies like the Milky Way are poised on the cusp of instability, such that small changes to interstellar mass (ISM) parameters can lead to the launching of CR-driven outflows, and we suggest that, as a result, CR feedback sets an ultimate limit to the star formation efficiency of most modern galaxies.

Bioconvection casson nanofluid flow together with Darcy-Forchheimer due to a rotating disk with thermal radiation and arrhenius activation energy

In this research article, we examined the Darcy-Forchheimer 3D in bioconvection Casson nanofluid flow in light of a whirling disk with Arrhenius Activation Energy and thermal Radiation. The governing equations are converted to the similarity equations and solved afterward by utilizing the Homotopy Analysis Method on behalf of several controlling parameters. The findings from this study show, that the radial velocity and tangential component of velocity decreasing for increasing values of the Inertia coefficient and the Porosity parameter. Velocity profiles enlarge with the enlargement of Gr for nanofluids. Radial velocity diminishes with expanding Reynolds numbers {text{Re}}_{r} and magnetic field parameters. The tangential component of velocity gleft( xi right) increases with diminishing Reynolds numbers {text{Re}}_{r} and reduces with expanding magnetic field factors. For increasing values of Prandtl number temperature profile is increased. Heat rises with radiation parameter, thermophoresis and Brownian movement parameters. Also, nanoparticles concentration reduces on expanding Brownian motion parameter and Schmidt parameter.

Thermo-Solutal Convection of a Nanofluid Utilizing Fourier’s-Type Compass Conditions

Nanotechnology has infiltrated into duct design in parallel with many other fields of mechanical, medical and energy engineering. Motivated by the excellent potential of nanofluids, a subset of materials engineered at the nanoscale, in the present work, a new mathematical model is developed for natural convection in a vertical duct containing nanofluid. Numerical scrutiny for the double-diffusive free and forced convection within a duct encumbered with nanofluid is performed. Buongiorno’s model is deployed to define the nanofluid. Robin boundary conditions are used to define the surface boundary conditions. Thermal and concentration equations envisage the viscous, Brownian motion, thermosphores of the nanofluid, Soret and Dufour effects. Using the Boussi-nesq approximation the solutal buoyancy effect as a result of gradients in concentration are incorporated. The conservation equations which are nonlinear are numerically estimated using fourth order Runge-Kutta methodology and analytically ratifying regular perturbation scheme. The mass, heat, nanoparticle concentration and species concentration fields on eight dimensionless physical parameters such as thermal and mass Grashof numbers, Brownian motion parameter, thermal parameter, Prandtl number, Eckert number, Schmidt parameter, and Soret parameter are calculated. The impact of these parameters are outlined pictorially. The velocity and temperature fields are boosted with the thermal Grashof number. The Soret and the Schemidt parameters reduces the nanoparticle volume fraction but it heightens the momentum, temperature and concentration. At the cold wall thermal and concentration Grashof numbers reduces the Nusselt values but they increase the Nusselt values at the hot wall. The reversal consequence was attained at the hot plate. The perturbation and Runge-Kutta solutions are equal in the nonappearance of Prandtl number. The (E. Zanchini, Int. J. Heat Mass Transfer 41, 3949 (1998)). results are restored for the regular fluid. The heat transfer rate is high for nanofluid when matched with regular fluid.

MHD bioconvection Darcy‐Forchheimer flow of Casson nanofluid over a rotating disk with entropy optimization

AbstractIn this paper, we analyzed Darcy‐Forchheimer three‐dimensional bioconvection Casson nanofluid flow due to a rotating disk with entropy generation. The flow is considered with the outcome of thermal radiation and Arrhenius activation energy. For nondimensionality, we utilized the similarity transformations to deal with the problem equations. The homotopy analysis method is applied for the re‐creation of the modeled equations. The biothermal framework is investigated for all the implanted parameters whose impacts are observed through various graphs. There exist intriguing outcomes due to the impacts of various parameters on various distributions. Nanoparticles' concentration diminishes with expansion of the Schmidt parameter and Brownian motion constraint, whereas motile gyrotactic microorganisms' distribution diminishes with expansion of bioconvection Peclet and Lewis numbers. The entropy generation rate increases with the increase of the Brinkman number, Casson fluid parameters, and magnetic parameters. Enrichment in the Reynolds number () leads to a decrease in the entropy generation rate. Moreover, Bejan number reduces with escalating values of the magnetic parameter, Brinkman number, and Casson fluid parameters. Bejan number () is higher for larger Reynolds numbers and temperature difference parameter.

Effect of Thermal Radiation on an Unsteady Magnetohydrodynamic Double Diffusive Boundary Layer Flow past a Permeable Infinite Vertical Plate with Heat Source

In this paper, effect of radiation and heat source parameters on temperature, concentration and velocity profile of an electrically conducting fluid passing through an infinite permeable plate is investigated. The governing equation, which was based on the balanced mass, linear momentum, energy and species concentration, were non-dimensionalized to reduce the equations to system of ordinary differential equations. This was then solved by perturbation technique. Effects of radiation parameter, heat source parameter, and Schmidt parameter are analyzed. We observed that the velocity and concentration profiles increase with increase in radiation parameter and heat source parameter. The temperature profile increases with decrease in radiation parameter with increases boundary layer thickness.

Lorentz-invariant mass and entanglement of biphoton states

The concept of the Lorentz-invariant mass of a group of particles is shown to be applicable to biphoton states formed in the process of spontaneous parametric down conversion. The conditions are found when the Lorentz-invariant mass is related directly with (proportional to) the Schmidt parameter determining a high degree of entanglement of a biphoton state with respect to transverse wave vectors of emitted photons.

MHD Flow of Nanofluid with Homogeneous-Heterogeneous Reactions in a Porous Medium under the Influence of Second-Order Velocity Slip

The influence of second-order velocity slip on the MHD flow of nanofluid in a porous medium under the effects of homogeneous-heterogeneous reactions has been analyzed. The governing flow equation is exactly solved and compared with those in the literature for the skin friction coefficient in the absence of the second slip, where great differences have been observed. In addition, the effects of the permanent parameters on the skin friction coefficient, the velocity, and the concentration have been discussed in the presence of the second slip. As an important result, the behavior of the skin friction coefficient at various values of the porosity and volume fraction is changed from increasing (in the absence of the second slip) to decreasing (in the presence of the second slip), which confirms the importance of the second slip in modeling the boundary layer flow of nanofluids. In addition, five kinds of nanofluids have been investigated for the velocity profiles and it is found that the Ag-water nanofluid is the lowest. For only the heterogeneous reaction, the concentration equation has been exactly solved, while the numerical solution is applied in the general case. Accordingly, a reduction in the concentration occurs with the strengthening of the heterogenous reaction and also with the increase in the Schmidt parameter. Moreover, the Ag-water nanofluid is of lower concentration than the Cu-water nanofluid. This is also true for the general case, when both of the homogenous and heterogenous reactions take place.

High Intensity Generation of Entangled Photons in a Two‐Mode Electromagnetic Field

AbstractAt present, the sources of entangled photons have a low rate of photon generation. This limitation is a key component of quantum informatics for the realization of such functions as linear quantum computation and quantum teleportation. In this paper, we propose a method for high intensity generation of entangled photons in a two‐mode electromagnetic field. On the basis of exact solutions of the Schrödinger equation, when electrons interact in an atom with a strong two‐mode electromagnetic field, it is shown that there may be large quantum entanglement between photons. The quantum entanglement is analyzed on the basis of the Schmidt parameter. It is shown that the Schmidt parameter can reach very high values depending on the choice of characteristics of the two‐mode fields. We find the Wigner function for the considered case. Violation of Bell's inequalities for continuous variables is demonstrated.

Effect of Hall current and chemical reaction on MHD flow along a fluctuating porous flat plate with internal heat absorption/generation

Effect of Hall current on the unsteady free convection flow of a viscous incompressible and electrically conducting fluid past a fluctuating porous flat plate with internal heat absorption/generation in the presence of foreign gasses (such as H2, CO2, H2O, NH3) was investigated. The results are discussed with the effect of the parameters m, the Hall current, Mt, the hydromagnetic parameter, Gr the Grashoff number for heat transfer, Gc, the Grashoff number for mass transfer, S, the internal heat absorption/generation parameter, α, the transpiration parameter, Sc, the Schmidt parameter, and Kc the chemical reaction parameter for Prandtl number Pr = 0.71, which represents air. Further, the present study accounts for the 1st order chemical reaction affecting the flow characteristics. The governing equations are solved in closed form applying Hhn(x) function. The effects of pertinent parameters characterizing the flow field are discussed with the help of graphs and tables. The important observation of the present study is that heat generation/absorption modifies the flow of current simultaneously to a magnetic force and thermal bouncy force. Heat generation combined with blowing leads to a sharp fall of temperature.

Azimuthal entanglement and multimode schmidt decompositions for noncollinear biphotons

Noncollinear biphoton states are found to possess a very high degree of azimuthal entanglement with typical values of ~104 for Schmidt parameter K (the ratio of the pump wavelength to its waist). A scheme that provides conditions for Schmidt-type mode separation and multichannel Schmidt-type decomposition is proposed for the partial use of this enormous high-entanglement resource.

Azimuthal entanglement and multichannel Schmidt-type decomposition of noncollinear biphotons

Purely azimuthal entanglement is analyzed for noncollinear frequency-degenerate biphoton states. The degree of azimuthal entanglement is found to be very high, with the Schmidt parameter $K$ on the order of the ratio of the pump waist to its wavelength. A scheme is suggested for partial realization of this high entanglement resource in the form of a multichannel Schmidt-type decomposition.

Features of three-photon polarization states: Entanglement and polarization

In a general form, three-photon polarization states are superpositions of contributions from four three-photon polarization modes with four arbitrary complex coefficients. Entanglement of such states is defined as entanglement between their one-photon and two-photon parts. The degree of entanglement is found explicitly in terms of such entanglement quantifiers as the generalized concurrence, entropy of reduced states and the Schmidt parameter. Polarization Stokes vectors, as well as the Schmidt decompositions of three-photon states are found and discussed. Similarity and differences with respect to biphoton polarization states are discussed too.