Schmidt Number Sc Research Articles

The resonant drag instability of dust streaming in turbulent protoplanetary disc

ABSTRACT Damping of the previously discovered resonant drag instability (RDI) of dust streaming in the protoplanetary disc is studied using the local approach to dynamics of gas–dust perturbations in the limit of the small dust fraction. Turbulence in a disc is represented by the effective viscosity and diffusivity in equations of motion for gas and dust, respectively. In the standard case of the Schmidt number (ratio of the effective viscosity to diffusivity) Sc = 1, the reduced description of RDI in terms of the inertial wave (IW) and the streaming dust wave (SDW) falling in resonance with each other reveals that damping solution differs from the inviscid solution simply by adding the characteristic damping frequency to its growth rate. RDI is fully suppressed at the threshold viscosity, which is estimated analytically, first, for radial drift, next, for vertical settling of dust, and at last, in the case of settling combined with a radial drift of the dust. In the last case, RDI survives up to the highest threshold viscosity, with a greater excess for smaller solids. Once Sc ≠ 1, a new instability specific for dissipative perturbations on the dust settling background emerges. This instability of the quasi-resonant nature is referred to as settling viscous instability (SVI). The mode akin to SDW (IW) becomes growing in a region of long waves provided that Sc > 1 (Sc < 1). SVI leads to an additional increase in the threshold viscosity.

A Numerical Study of Dissipative Chemically Reactive Radiative MHD Flow Past a Vertical Cone with Nonuniform Mass Flux

A computational model is presented to explore the properties of heat source, chemically reacting radiative, viscous dissipative MHD flow of an incompressible viscous fluid past an upright cone under inhomogeneous mass flux. A numerical study has been carried out to explore the mass flux features with the help of Crank-Nicolson finite difference scheme. This investigation reveals the influence of distinct significant parameters and the obtained outputs for the transient momentum, temperature and concentration distribution near the boundary layer is discussed and portrayed graphically for the active parameters such as the Schmidt number Sc, thermal radiation <i>Rd</i>, viscous dissipation parameter ɛ, chemical reaction parameter λ, MHD parameter <i>M</i> and heat generation parameter Δ. The significant effect of parameters on shear stress, heat and mass transfer rates are also illustrated.

Radiation absorption on MHD free convective laminar flow over a moving vertical porous plate, viscous dissipation and chemical reaction with suction under the influence of transverses magnetic field

Abstract The aim of the present chapter is to investigate the problem of Study on MHD boundary layer flow over a moving vertical porous plate with heat generation and chemical reaction in the presence of thermal absorption. The governing equations of the flow are transformed into nonlinear ordinary differential equations and then solved by using Runge-Kutta-fourth order along with shooting method. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The influence of the various parameters like Magnetic parameter (M), thermal Grashof number (Gr), mass Grashof number (Gc), permeability parameter (K), Prandtl number (Pr), Dufour number (Df), Soret number (Sr), Schmidt number (Sc), Heat generation (B), Radiation Parameter (Ra) and Chemical reaction (Ch) on the flow are analyzed and discussed through graphs in detail. The values of the skin friction coefficient, Nusselt number and the Sherwood number for different physical parameters are also tabulated.

Heat and mass transfer in Maxwell fluid in view of local and non-local differential operators

Study of heat and mass transfer in Maxwell fluid is carried out near a vertical plate. It is proven in many already published articles that the heat and mass transfer does not really or always follow the classical mechanics process that is known as memoryless process. Therefore, the model using classical differentiation based on the rate of change cannot really replicate such dynamical process very accurately; thus, a different concept of differentiation is needed to capture such process. Very recently, new classes of differential operators were introduced and have been recognized to be efficient in capturing processes following the power law, the decay law and the crossover behaviors. For the study of heat and mass transfer, we applied the newly introduced differential operators to model such flow. The Laplace transform, inversion algorithm and convolution theorem were used to derive the exact and semi-analytical solutions for all cases. The obtained analytical solutions were plotted for different values of fractional order $$\alpha $$ , Maxwell fluid parameter $$\lambda $$ , thermal Grashof number Gr, mass Grashof number Gm, Prandtl number Pr and Schmidt number Sc on concentration and velocity fields. In comparison, velocity of Atangana–Baleanu fractional derivative is greater than that of Caputo and Caputo–Fabrizio for $$\alpha $$ , $$\lambda $$ , Gr and Gm. With the increase in Pr and Sc, there is a decrease in velocity. For fractional parameter, the effect of concentration field for ABC model is more than for C and CF. Moreover, from the present solutions already published results were found as limiting cases.

Perturbation analysis of thermophoresis, hall current and heat source on flow dissipative aligned convective flow about an inclined plate

This present examination researches the impacts of thermophoresis, heat source and Hall current on dissipative adjusted MHD joint convection stream about an inclined plate inserted in a permeable medium. Utilizing dimensionless variables, the system of partial differential equations is changed into dimensionless equations. By making use of perturbation technique, estimated solutions for velocity, temperature, concentration profiles, skin friction, rate of heat transfer and rate of mass transfer have been determined. The attained results are explained with an assistance of diagrams to examine the impact of distinct parameters such as Magnetic parameter (M), Aligned magnetic parameter (ξ), Schmidt number (Sc), Eckert number (Ec), inclined angle (α), Prandtl number (Pr), heat generation parameter (Q), and chemical reaction (Kr), assuming two cases viz. Case I: Gr < 0, Gm < 0 (flow on heated plate); Case II: when Gr > 0, Gm > 0(flow on cooled plate). Additionally, the impacts of the appropriate parameters on the skin-friction coefficient and rates of heat and mass transfer are numerically furnished in tabular form. Skin friction coefficients are firmly diminished as magnetic field rises. Sherwood and Nusselt numbers boost up as enhance in chemical reaction.

Aerosol deposition rates by mass diffusion in laminar boundary layers with an implemented blowing system. Approximate methods for flat plates

Solid or liquid particles within a carrier gas may be deposited on solid surfaces exposed to the gas stream and, in some practical applications, these aerosol deposits have deleterious effects. In order to mitigate these effects, particle repulsive fields may be applied near the surface to reduce the deposition rate. A current blowing through the exposed surface may play this repulsion role with such a forced stream pushing the aerosol particles away from the surface. The present paper develops a model to analyse and estimate the effect of blowing in reducing particle deposition for laminar flows with high Reynolds numbers over flat surfaces. A classical self-similarity analysis is used to solve the boundary layer equations for mass and momentum conservation. The solution of the particle transport problem provides the self-similarity mass fraction profile and the mass deposition rate in terms of two parameters: the Schmidt number Sc and the dimensionless blowing rate. Moreover, two approximate methods are implemented in two asymptotic limits: for large values of Sc and when the blowing parameter is sufficiently small.

Study of Magnetic Field Effects on the Oxygen Transfer in Liquid Lead Cavity Flow Using the Lattice Boltzmann Method

Abstract Natural convection and oxygen transfer characteristics in square cavity subjected to the magnetic field are studied numerically. Oxygen transfer in liquid metals has attracted much attention because it can decrease the corrosion rate of steel in contact with liquid metals. In advanced reactors, liquid lead has been utilized as an effective coolant. As indicated by many research reports that corrosion could be decreased by controlling the proper level of oxygen in the liquid lead. In this method, oxygen needs to mix in liquid lead homogenously and rapidly to produce a protective oxide layer. In this study, the impact of the magnetic force on oxygen transfer in a rectangular container is studied using the lattice Boltzmann method (LBM). Three different Schmidt numbers (Sc) and Hartmann numbers (Ha) have been simulated in this study. Some useful results are obtained such as an adverse effect was found that heat/mass transfer rates are decreased when Ha number is increased. In addition, the existence of an applied magnetic field has caused a significant increase in the required time to reach desired oxygen concentration and needs to be controlled in operation to have a faster distribution of the oxygen in the domain.

Analysis of one-dimensional models for exchange flows under strong stratification

One-dimensional models of exchange flows driven by horizontal density gradients are well known for performing poorly in situations with weak turbulent mixing. The main issue with these models is that the horizontal density gradient is usually imposed as a constant, leading to non-physically high stratification known as runaway stratification. Here, we propose two new parametrizations of the horizontal density gradient leading to one-dimensional models able to tackle strongly stratified exchange flows at high and low Schmidt number values. The models are extensively tested against results from laminar two-dimensional simulations and are shown to outperform the models using the classical constant parametrization for the horizontal density gradients. Four different flow regimes are found by exploring the parameter space defined by the gravitational Reynolds number Reg, the Schmidt number Sc, and the aspect ratio of the channel Γ. For small values of RegΓ, when diffusion dominates, all models perform well. However, as RegΓ increases, two clearly distinct regimes emerge depending on the Sc value, with an equally clear distinction of the performance of the one-dimensional models.

Analytical solution for differential nonlinear and coupled equations in micropolar nanofluid flow between rotating parallel plates

This paper presents solution to micropolar nanofluid between two parallel plates in a rotating system via a new and innovative semi-analytical method called Akbari-Ganji’s method (AGM). The nanofluid flow between two parallel plates is taken under the influence of Hall current. The flow of micropolar nanofluid is in steady state. We get a set of differential nonlinear and coupled equations from suitable similarity variables and the elementary governing equations. Moreover, the physical discussion of the embedded parameters in the equations that is, viscosity parameter Re, rotating parameter Kr, magnetic parameter M, Prandtl number Pr, thermophoretic parameter Nt, Brownian motion parameter Nb, and Schmidt number Sc, by showing figures and tables, they have been analyzed. Our results show that the employed method is very efficient and practical for obtaining solutions to this category of coupled equations and the solutions are in excellent agreement for nonlinear higher order differential equations in engineering.

Non-linear convection flow of micro polar nanofluid past an isothermal sphere

In this study, steady laminar two dimensional boundary layer flow of non-linear convection micropolar nanofluid over an isothermal sphere is examined. The mathematical developing for the flow problem has been made. By means of appropriate similarity transformation and dimensionless variable, the governing non-linear boundary value problems were reduced into combined high order non-linear ordinary differential equations. Then, solution for velocity, microrotation, temperature and concentration has been obtained numerically. The equations were calculated using method bvp4c from matlab software for various quantities of main parameters. The influences of diffident parameters on skin friction coefficient, wall duo stress coefficient the Nusselt number, Sherwood number as well as the velocities, temperature, and concentration are analyzed and discussed through the tables and plotted graphs. A comparison with previous paper obtainable in the literature has been performed and an excellent agreement is obtained. The finding results indicate the raise in either the values of thermal Grashof number Gr or Brownian motion parameter Nb or Schmidt number Sc allows to bringing down the kinematic viscosity of the fluid causes improve the temperature profile distribution within the boundary layer. On the other hand, it can be diminished by the growth in either the value of solutal Grashof number Gm or solutal non linear convection parameter s which agrees to enlarge fluid density.

Numerical Analysis of Mass Transfer in MHD Nanoparticle Based Crude Oil Flow on a Flat Plate under Various Slip Condition

This work analyzed of crude oil based nanofluid of Al2O3, Cu, SWCNTs (single walled carbon nanotubes) the mass transfer in two dimensional MHD of incompressible steady, viscous and electrically conducting in the presence of magnetic field over a flat plate under various slip conditions. The result was obtained using similarity transformation and the fourth-fifth order Runge Kutta Fehlberg technique with shooting method using Maple 18. The velocity profile and the nanoparticle concentration were plotted for both low and high velocity slip conditions. Various effects of parameters were tested on the rate of skin friction and mass transfer. The effect that involves the magnetic parameter M, buoyancy ratio G, Schmidt number Sc, velocity slip parameter and nanoparticle volume fraction were analyzed. It was found that magnetic field with Grashof number and Schmidt number parameters are dominant on momentum and concentration dimensionless parameters. Copper with velocity slip 0.1 was higher shear stress then other materials as well as, for SWCNT with velocity slip 1.0 was lower shear stress. Furthermore, copper with velocity slip 0.1 is higher of mass transfer than other materials as well as oxide aluminium is lower compared to other materials with velocity slip 1.0.

Homogenous–heterogenous reactions in Carreau fluid flow with heat generation/absorption: multiple solution

This research article investigates the two-dimensional stagnation boundary layer flow over a permeable stretching sheet with variable thickness and heat generation/absorption. The heat generation/absorption is taking place due to a homogenous/heterogenous reactions. Viscous dissipation and radiation effects are neglected here. We have utilized the appropriate dimensionless transformations to alter the basic conservation equations into a set of partially coupled ODEs. The related system of reduced ODEs together with physical boundary restrictions is numerically integrated via versatile and extensively validated, MATLAB bvp4c package with Labatto III A scheme. To obtain the numerical solution, problem is governed by active physical parameters, such as viscosity ratio parameter ($$\beta ^{{*}}$$), local Weissenberg number (We), heat generation/absorption parameter ($${\gamma }^{*})$$, homogeneous reaction parameter ( K), Schmidt number (Sc), heterogeneous reaction parameter (Ks), ratio of mass diffusion coefficient ($${\delta }$$), mass transfer parameter with suction ($${s>0}$$) and injection ($${s<0}$$). We exhibit and explain the impacts of these active parameters on dimensionless fluid velocity, fluid temperature, fluid concentration, skin friction, Nusselt number and Sherwood number by means of tables and graphs. From this study, it is observed that fluid concentration is depressed by higher heterogeneous reaction parameter (Ks). However, Prandtl number (Pr) and heat absorption/generation parameter $${(\gamma }^{*})$$ increase the fluid temperature.

Influence of Heat Generation and Radiation on MHD Flow of Natural Convection

This article explains an influence of heat generation on MHD natural flow convective a vertical permeable surface with radiation. By using perturbation technique the equations of governing are converted to a system of non-linear O.D.E’S and are explained mathematically. Numerous physical limitations like M, F, Pr and some other parameters are studied through diagrams and tabular values. As conclusion of this investigation, decreasing in velocity profile as numerical standards increased in major cases except few effects like absorption radiation parameter R, Schmidt number Sc over velocity flow. The same effects are investigated for temperature profile as well as concentration profile.

Effect of Heat Source/Sink on Free Connective MHD Flow past an Exponentially Accelerated Infinite Plate with Mass Diffusion and Chemical Reaction

The effects of heat source/sink and chemical reaction with mass diffusion on free convective incompressible viscous fluid flow past an accelerated vertical plate with magnetic field has been investigated. Laplace transformation method has been applied to solve the system of linear partial differential equations. The result is presented in form of complementary error function and exponential function. The effect of non dimensional parameters such as Schmidt number (Sc), Accelerated parameter (a), Chemical reaction parameter (K), Prandtl number (Pr), Magnetic field parameter (M), Mass Grashof number (Gm), Heat source/sink parameter (H), Thermal Grashof number (Gr) on temperature, concentration, velocity has been discussed with graphs.

Metachronal propulsion of a magnetised particle-fluid suspension in a ciliated channel with heat and mass transfer

Biologically-inspired pumping systems are of great interest in modern engineering since they achieve enhanced efficiency and circumvent the need for moving parts and maintenance. Industrial applications also often feature two-phase flows. In this article, motivated by these applications, the pumping of an electrically-conducting particle-fluid suspension due to metachronal wave propulsion of beating cilia in a two-dimensional channel with heat and mass transfer under a transverse magnetic field is investigated theoretically. The governing equations for mass and momentum conservation for fluid- and particle-phases are formulated by ignoring the inertial forces and invoking the long wavelength approximation. The Jeffrey viscoelastic model is employed to simulate non-Newtonian characteristics. The normalised resulting differential equations are solved analytically. Symbolic software is employed to evaluate the results and simulate the influence of different parameters on flow characteristics. Results are visualised graphically with carefully selected and viable data. With increasing wave number (β) fluid velocity is accelerated in the core region whereas it is decelerated near the channel wall, for the Newtonian case. With increasing eccentricity of cilia elliptic path (α), a similar response is computed as for the wave number. The size of the bolus is enhanced (and quantity of boluses is reduced) with increasing eccentricity of the cilia elliptic path (α) and Hartmann (magnetic) number (M) whereas bolus size is decreased (and quantity of boluses is increased) with increasing wave number (β) and particle volume fraction (C). It is also noted that increasing Schmidt number (Sc) and Soret number (Sr) diminish the concentration magnitudes. Furthermore, Brinkman number (which represents viscous heating effects) significantly boosts the temperature magnitudes. The current analysis provides a useful benchmark for more general computational simulations.

Indoor air performance and irreversibility analysis of a slot-ventilated mechanical system with wall heater and thermosolutal exchanger

A numerical simulation is performed for fluid flow, heat and mass transfer in a slot-ventilated enclosure to optimize the removal rate of heat and contaminants due to wall heater and a thermosolutal exchanger. Cold fresh air is infiltrated through the inlet port located along right vertical wall and flush out through the chimney shaped outlet port located along the upper wall. Vertical walls of the chimney are considered to be inclined at different angles with horizontal axis. Two dimensional analysis is made for flow, temperature and concentration in terms of streamlines, isotherms and isoconcentrations with the variation of Richardson number (Ri) from 0.0 to 10.0, Reynolds number (Re) from 50 to 300 and inclination angle of chimney (450 ≤ δ ≤ 900) with the fixed value of Prandtl number (Pr=0.71) and Schmidt number (Sc=1.14). The impact of inlet port locations, Reynolds number, inclination angle and Richardson number on average rate of heat transfer and mass transfer, average temperature, entropy generation, Bejan number, cooling efficiency, air change per hour and performance evaluation criterion inside the system is evaluated.

Numerical and Analytical Investigation of an Unsteady Thin Film Nanofluid Flow over an Angular Surface

In the present study, we examine three-dimensional thin film flow over an angular rotating disk plane in the presence of nanoparticles. The governing basic equations are transformed into ordinary differential equations by using similarity variables. The series solution has been obtained by the homotopy asymptotic method (HAM) for axial velocity, radial velocity, darning flow, induced flow, and temperature and concentration profiles. For the sake of accuracy, the results are also clarified numerically with the help of the BVPh2- midpoint method. The effect of embedded parameters such as the Brownian motion parameter Nb, Schmidt number Sc, thermophoretic parameter and Prandtl number Pr are explored on velocity, temperature and concentration profiles. It is observed that with the increase in the unsteadiness factor S, the thickness of the momentum boundary layer increases, while the Sherwood number Sc, with the association of heat flow from sheet to fluid, reduces with the rise in S and results in a cooling effect. It is also remarkable to note that the thermal boundary layer increases with the increase of the Brownian motion parameter Nb and Prandtl number Pr, hindering the cooling process resulting from heat transfer.

Evaluation of mass transfer coefficient for gas condensates in porous systems: Experimental and modeling

The gas condensate reservoirs are significant resources of energy for various municipal and industrial purposes. An unfavourable phenomenon attributed to this kind of reservoirs is liquid drop-out due to excessive near-wellbore pressure drop during production. Gas injection is normally employed to recover the liquid loss in the underground formation. The amount of condensate recovery is determined by assuming a thermodynamic local equilibrium, which seems irrational due to the limited contact area, high velocity, and low residence time for fluids around the wellbore. In this work, a series of experiments are conducted based on the Taguchi design of experiment (DOE) to study the steady-state mass transfer during gas injection. Three injection gases (CO2, N2, and CH4), three liquids to represent the liquid condensate (C5, C6, and C7), and three mean grain sizes within the range of 150–300 μm are the vital design variables of the experiments where a broad range of gas velocity (0.00472–0.0283 cm/s) is employed. Results of Taguchi DOE approach are then analyzed to find the optimum design levels and influence/contribution of each factor. The experimental data are utilized to develop new models for estimation of the mass transfer coefficient in terms of Schmidt number (Sc), Peclet number (Pe), normalized velocity, and mean grain size. The comparison between the modeling results and real data confirms the reliability and precision of the proposed correlations. Based on the research outputs, the injection rate (60% contribution factor) and grain size (nearly 10% contribution factor) have the highest and lowest effects on the mass transfer coefficient in porous systems, respectively. It is also found that the difference between the equilibrium concentration and the actual concentration of volatile component in the gas phase increases as the gas velocity increases. Based on the DOE, the optimal design levels for the injection rate, gas type, liquid type, and mean grain size are 12 cm3/min, C1, C5, and 300 μm, respectively. The new models provide accurate/reliable mass transfer coefficient (R2 = 0.9906) for non-equilibrium mass transfer cases to simulate re-vaporization of condensate into the gas phase, while implementing gas injection into the gas condensate reservoirs.

The effects of coupled heat and mass transfer in the fractional Jeffrey fluid over inclined plane

The flow of fractional Jeffrey fluid due to time-dependent motion of plate has been investigated. An inclined plate is considered, and thermal effects with mass diffusivity in flow are also taken into account. The set of governing equations is operated by integral transform namely Laplace transform technique. Caputo–Fabrizio time-fractional derivative is considered in energy and diffusion equations. Moreover, exact analytical solutions are achieved. In the limiting cases, the general solutions for accelerating and oscillating motion of Jeffrey fluid are obtained. Effects of involved physical parameters, fractional parameter $$\alpha$$, inclination of plate $$\theta$$, Prandtl number Pr and Schmidt number Sc on the flow, are graphically detected.

Phase separation in binary fluid mixtures with symmetric and asymmetric Schmidt numbers: A DPD study.

We investigate the effect of the Schmidt number (Sc) on phase separation dynamics of two immiscible fluids in a two-dimensional periodic box using dissipative particle dynamics. The range of Sc investigated spans liquid-liquid separation processes. Phase separation is characterized by a domain size r(t), which typically follows a power law tβ in time t, where β is a characteristic exponent corresponding to the coarsening mechanism at play. The phase separation dynamics is studied for strongly (deep quench) separating mixtures. We consider cases of critical (ϕ ∼ 0.5) and off-critical (ϕ < 0.5) mixtures of fluids A and B for both ScA = ScB and ScA ≠ ScB. In all cases, the growth dynamics slow down with the increasing Schmidt number of either fluid. We observe the power law exponent β = 0.5 for symmetric (ScA = ScB) critical mixtures and β = 0.33 for all other cases. However, for off-critical mixtures, the exponent is 0.33 irrespective of the Schmidt number ratio of the two fluids. We explain these results from an analysis of the competition between diffusive effects vis-á-vis dynamical forces.