Showing papers on "Schmidt number published in 2017"

On the Values for the Turbulent Schmidt Number in Environmental Flows

Abstract: Computational Fluid Dynamics (CFD) has consolidated as a tool to provide understanding and quantitative information regarding many complex environmental flows. The accuracy and reliability of CFD modelling results oftentimes come under scrutiny because of issues in the implementation of and input data for those simulations. Regarding the input data, if an approach based on the Reynolds-Averaged Navier-Stokes (RANS) equations is applied, the turbulent scalar fluxes are generally estimated by assuming the standard gradient diffusion hypothesis (SGDH), which requires the definition of the turbulent Schmidt number, Sct (the ratio of momentum diffusivity to mass diffusivity in the turbulent flow). However, no universally-accepted values of this parameter have been established or, more importantly, methodologies for its computation have been provided. This paper firstly presents a review of previous studies about Sct in environmental flows, involving both water and air systems. Secondly, three case studies are presented where the key role of a correct parameterization of the turbulent Schmidt number is pointed out. These include: (1) transverse mixing in a shallow water flow; (2) tracer transport in a contact tank; and (3) sediment transport in suspension. An overall picture on the use of the Schmidt number in CFD emerges from the paper.

Stratified flow of an Oldroyd-B nanoliquid with heat generation

Abstract: Here modeling and computations are made to explore the characteristics of mixed convection flow of Oldroyd-B nanoliquid. Linear stretchable surface creates the flow. Brownian motion and thermophoretic aspects in nanoliquid modeling are retained. Thermal and solutal stratifications along with heat generation/absorption are considered for heat and mass transfer processes. Boundary layer approach is implemented in the mathematical formulation. The resulting problems are computed by homotopic algorithm. Salient features of Deborah numbers, mixed convection parameter, ratio of thermal to concentration buoyancy forces, Brownian motion parameter, Prandtl number, thermophoretic parameter, thermal/concentration stratification parameter, heat generation/absorption parameter and Schmidt number on the velocity, temperature, nanoparticles concentration and Nusselt and Sherwood numbers are reported through graphs and tables. Besides this the results of presented analysis have been compared with the available works in limiting situations and good agreement is noted.

On Cattaneo–Christov heat flux model for Carreau fluid flow over a slendering sheet

Abstract: The underlying intentions of this article are to investigate the impact of non-Fourier heat flux model on the stagnation-point flow of non-Newtonian Carreau fluid. In this study, the innovative Cattaneo–Christov constitutive model is introduced to study the characteristics of thermal relaxation time. The flow is impelled by a slendering surface which is of the variable thickness. In the model, the physical mechanism responsible for homogeneous–heterogeneous reactions are further taken into account. Also, the diffusion coefficients of the reactant and auto catalyst are considered to be equal. The governing non-linear partial differential equations consisting of the momentum, energy and concentration equations are reduced to the coupled ordinary differential equations by means of local similarity transformations. The transformed ODEs are tackled numerically by employing an effective shooting algorithm along with the Runge–Kutta Fehlberg scheme. The physical characteristics of the fluid velocity, temperature and concentration profiles are illuminated with the variation of numerous governing factors and are presented graphically. For instance, our result indicates that the temperature and thermal boundary layer thickness are lower in case of Cattaneo–Christov heat flux model when compared to classical Fourier’s heat model. Meanwhile, the rate of heat transfer is significantly improved by a high wall thickness parameter and an opposite influence is found due to the thermal relaxation parameter. We further noticed that a higher value of homogeneous and heterogeneous reaction parameter corresponds to a deceleration in the concentration field and it shows an inverse relation for the Schmidt number. A correlation with accessible results for specific cases is found with fabulous consent.

Chemically reactive species in the flow of a Maxwell fluid

Abstract: This article presents a research for boundary layer flow and heat transfer of a Maxwell fluid over an exponential stretching surface with thermal stratifications. The effect of homogeneous and heterogeneous reaction are incorporated. Cattaneo–Christov heat flux model is used instead of Fourier law of heat conduction, which is recently proposed by Christov. This model predicts the impacts of thermal relaxation time on boundary layer. The transformed boundary layer equations are solved analytically by using Optimal homotopy analysis method. The effect of non-dimensional fluid relaxation time, thermal relaxation time, Prandtl number, Schmidt number and strength of homogeneous and heterogeneous reaction are demonstrated and exhibited graphically. The comparison of Cattaneo–Christov heat flux model and the Fourier’s law of heat conduction is also displayed.

Effects of mass transfer on MHD three dimensional flow of a Prandtl liquid over a flat plate in the presence of chemical reaction

Abstract: The present study addresses the three-dimensional flow of a Prandtl fluid over a Riga plate in the presence of chemical reaction and convective condition. The converted set of boundary layer equations are solved numerically by RKF four-fifth method. Obtained numerical results for flow and mass transfer characteristics are discussed for various physical parameters. Additionally, the skin friction coefficient and Sherwood number are also presented. It is found that, the momentum boundary layer thickness is dominant for higher values of α and solutal boundary layer is low for higher Schmidt number and chemical reaction parameter.

Radiation effects on the mixed convection flow induced by an inclined stretching cylinder with non-uniform heat source/sink.

Abstract: This study investigates the mixed convection flow of Jeffrey liquid by an impermeable inclined stretching cylinder. Thermal radiation and non-uniform heat source/sink are considered. The convective boundary conditions at surface are imposed. Nonlinear expressions of momentum, energy and concentration are transformed into dimensionless systems. Convergent homotopic solutions of the governing systems are worked out by employing homotopic procedure. Impact of physical variables on the velocity, temperature and concentration distributions are sketched and discussed. Numerical computations for skin friction coefficient, local Nusselt and Sherwood numbers are carried out. It is concluded that velocity field enhances for Deborah number while reverse situation is observed regarding ratio of relaxation to retardation times. Temperature and heat transfer rate are enhanced via larger thermal Biot number. Effect of Schmidt number on the concentration and local Sherwood number is quite reverse.

Chemically reactive flow of upper-convected Maxwell fluid with Cattaneo–Christov heat flux model

Abstract: This attempt concentrates on impact of chemically reactive flow of upper-convected Maxwell liquid Nonlinear slip condition for Maxwell fluid is employed The processes of heat and mass transfer through theory of Cattaneo–Christov flux are studied Ordinary differential systems have been considered Convergent solutions are constructed for the governing equations Incoming nonlinear modeled problems have been computed for the velocity, temperature and concentration The impact of emerging variables, namely Deborah number (β), Schmidt number (Sc), Thermal relaxation parameter (γ), Prandtl number (Pr) and chemical reaction parameter (δ) on quantities of interest is graphically investigated Both temperature and concentration fields decay when thermal relaxation and chemical reaction parameters are increased

Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction

Abstract: The goal of the present study is: (i) to demonstrate the two-dimensional nature of the elasto-inertial instability in elasto-inertial turbulence (EIT), (ii) to identify the role of the bi-dimensional instability in three-dimensional EIT flows and (iii) to establish the role of the small elastic scales in the mechanism of self-sustained EIT. Direct numerical simulations of FENE-P fluid flows are performed in two- and three-dimensional channels. The Reynolds number is set to $\mathrm{Re}_\tau = 85$ which is sub-critical for 2D flows but beyond transition for 3D ones. The polymer properties correspond to those of typical dilute polymer solutions and two moderate Weissenberg numbers, $\mathrm{Wi}_\tau = 40, 100$, are considered. The simulation results show that sustained turbulence can be observed in 2D sub-critical flows, confirming the existence of a bi-dimensional elasto-inertial instability. The same type of instability is also observed in 3D simulations where both Newtonian and elasto-inertial turbulent structures co-exist. Depending on the Wi number, one type of structure can dominate and drive the flow. For large Wi values, the elasto-inertial instability tends to prevail over the Newtonian turbulence. This statement is supported by (i) the absence of the typical Newtonian near-wall vortices and (ii) strong similarities between two- and three-dimensional flows when considering larger Wi numbers. The role of the small elastic scales is investigated by introducing global artificial diffusion in the hyperbolic transport equation for polymers. The study results show that the introduction of large polymer diffusion in the system strongly damps a significant part of the elastic scales that are necessary to feed turbulence, eventually leading to the flow laminarization. A sufficiently high Schmidt number is necessary to allow self-sustained turbulence to settle.

Impact of melting heat transfer and nonlinear radiative heat flux mechanisms for the generalized Burgers fluids

Abstract: The present paper deals with the analysis of melting heat and mass transfer characteristics in the stagnation point flow of an incompressible generalized Burgers fluid over a stretching sheet in the presence of non-linear radiative heat flux. A uniform magnetic field is applied normal to the flow direction. The governing equations in dimensional form are reduced to a system of dimensionless expressions by implementation of suitable similarity transformations. The resulting dimensionless problem governing the generalized Burgers is solved analytically by using the homotopy analysis method (HAM). The effects of different flow parameters like the ratio parameter, magnetic parameter, Prandtl number, melting parameter, radiation parameter, temperature ratio parameter and Schmidt number on the velocity, heat and mass transfer characteristics are computed and presented graphically. Moreover, useful discussions in detail are carried out with the help of plotted graphs and tables.

Magnetic field effect on nanofluid flow between two circular cylinders using AGM

Abstract: In this paper, uniform magnetic field impact on nanofluid flow between two circular cylinders is investigated analytically using AGM. Two phase model is applied for nanofluid. Analytical procedures are examined for various active parameters namely aspect ratio, Hartmann number, Eckert number, Reynolds number, thermophoresis and Brownian parameters and Schmidt number. Results indicate that velocity reduces with augment of Lorentz forces but it rises with augment of Reynolds number. Temperature gradient enhances with rise of Hartmann number but it decreases with augment of other parameters.

Numerical modeling of time-dependent bio-convective stagnation flow of a nanofluid in slip regime

Abstract: A numerical investigation of unsteady stagnation point flow of bioconvective nanofluid due to an exponential deforming surface is made in this research. The effects of Brownian diffusion, thermophoresis, slip velocity and thermal jump are incorporated in the nanofluid model. By utilizing similarity transformations, the highly nonlinear partial differential equations governing present nano-bioconvective boundary layer phenomenon are reduced into ordinary differential system. The resultant expressions are solved for numerical solution by employing a well-known implicit finite difference approach termed as Keller-box method (KBM). The influence of involved parameters (unsteadiness, bioconvection Schmidt number, velocity slip, thermal jump, thermophoresis, Schmidt number, Brownian motion, bioconvection Peclet number) on the distributions of velocity, temperature, nanoparticle and motile microorganisms concentrations, the coefficient of local skin-friction, rate of heat transport, Sherwood number and local density motile microorganisms are exhibited through graphs and tables.

Three dimensional MHD flow of couple stress Casson fluid past an unsteady stretching surface with chemical reaction

Abstract: The analysis of three dimensional MHD flow of couple stress Casson fluid past an unsteady stretching surface with the effect of chemical reaction and convective boundary condition has been considered. The governing partial nonlinear differential equations are treated with similarity variables reduced into them ordinary deferential equations. Runge Kutta Fehlberg fourth fifth order method is to employed to the resultant equation for numerical solution. The results are then discussed graphically in the form of velocity, temperature and concentration profiles for several physical parameters of interest. From the plotted results it is observed that the larger values of Casson parameter decrease velocity components. Whereas, solutal boundary layer thickness decreases for larger values of chemical reaction parameter and Schmidt number. The present results are compared with the existing limiting solutions, showing good agreement with each other.

Heat generation and solar radiation effects on Carreau nanofluid over a stretching sheet with variable thickness: Using coefficients improved by Cash and Carp

Abstract: Present work examines the effects of chemical reactive species and solar radiation on Carreau nanofluid induced by a stretching sheet with variable thickness. Heat generation effects are taken for exothermic reaction. In the boundary layer region, nanoparticles provides enhancement in the heat transfer phenomena. In the literature, most of the researchers used Runge Kutta Fehlberg method, but our main concentration here is to find the solution by improved form of Fehlberg method (Cash and Carp). The velocity, temperature and concentration profiles are plotted for different governing parameter, namely, wall thickness parameter, magnetic parameter, thermal conductivity parameter, chemical reaction parameter, Schmidt number and Prandtl number. It is found that the velocity profile increases by increasing Weissenberg numberWe, Hartmann number M and wall thickness parameter n. Moreover, temperature profile enhances by increasing heat generation parameter γ and radiative heat flux parameter R. The accuracy of the present method is checked with previously published work and excellent agreement is noticed.