Showing papers on "Schmidt number published in 2016"

Boundary layer flow of Maxwell fluid in rotating frame with binary chemical reaction and activation energy

Abstract: Here we study the heat/mass transfer effects on revolving flow of Maxwell fluid due to unidirectional stretching surface. Mass transfer process is modeled in terms of binary chemical reaction and activation energy. Modified Arrhenius function for activation energy is invoked. Traditional boundary layer approximations are utilized to simplify the governing equations. Using similarity method, self-similar form of boundary layer equations are derived which are solved numerically. The solutions depend on dimensionless numbers such as the rotation parameter λ , the Deborah number β , the Prandtl number Pr , the Schmidt number Sc , activation energy E , fitted rate constant n and temperature difference parameter δ . We found that the solute concentration in binary mixture is proportional to both rotation parameter λ and activation energy E . The reaction rate σ and fitted rate n both provide reduction in the solute concentration. Thermal boundary layer becomes thicker and heat transfer rate diminishes when fluid is subjected to a larger rotation rate.

Application of Caputo-Fabrizio derivatives to MHD free convection flow of generalized Walters’-B fluid model

Abstract: The present article applies the idea of Caputo-Fabrizio time fractional derivatives to magnetohydrodynamics (MHD) free convection flow of generalized Walters’-B fluid over a static vertical plate. Free convection is caused due to combined gradients of temperature and concentration. Hence, heat and mass transfers are considered together. The fractional model of Walters’-B fluid is used in the mathematical formulation of the problem. The problem is solved via the Laplace transform method. Exact solutions for velocity, temperature and concentration are obtained. The physical quantities of interest are examined through plots for various values of fractional parameter: $\alpha$ , Walters’-B parameter $\Gamma$ , magnetic parameter M , Prandtl number Pr, Schmidt number Sc, thermal Grashof number Gr and mass Grashof number Gm. As a special case, the published results from open literature are recovered.

Effects of Chemical Reaction and Nonlinear Thermal Radiation on Williamson Nanofluid Slip Flow over a Stretching Sheet Embedded in a Porous Medium

Abstract: The main emphasis of the present study is to discuss the effect of chemical reaction on flow, heat, and mass transfer of Williamson nanofluid over a stretching sheet. The flow is considered under the influence of nonlinear thermal radiation. To obtain the numerical results, the governing equations have been reduced to a set of nonlinear ordinary differential equations using appropriate similarity transformations. An efficient Runge-Kutta-Felhberg 45 order method along with a shooting technique is used to get the required solutions. The accuracy of the method used is verified with the existing results, and they are found to be in good agreement. Obtained numerical solutions are presented in the form of graphs and tables for a various range of slip boundary condition and for different values of flow pertinent parameters, such as permeability parameter, radiation parameter, Lewis number, Heat capacities ratio, diffusivity ratio, Schmidt number, chemical reaction parameter, volumetric volume expansion...

Convection heat and mass transfer of fractional MHD Maxwell fluid in a porous medium with Soret and Dufour effects

Abstract: This work is concerned with unsteady natural convection heat and mass transfer of a fractional MHD viscoelastic fluid in a porous medium with Soret and Dufour effects. Formulated boundary layer governing equations have coupled mixed time–space fractional derivatives, which are solved by finite difference method combined with L1-algorithm. Results indicate that the Dufour number (Du) , Eckert number (Ec) , Soret number (Sr) and Schmidt number (Sc) have significantly effects on velocity, temperature and concentration fields. With the increase of Du (Sr), the boundary layer thickness of momentum and thermal (concentration) increase remarkably. The average Nusselt number declines with the increase of Du and Ec. The average Sherwood number declines with the increase of Sr, but increases for larger values of Sc. Moreover, the magnetic field slows down the natural convection and reduces the rate of heat and mass transfer. The fractional derivative parameter decelerates the convection flow and enhances the elastic effect of the viscoelastic fluid.

Entropy generation analysis for non-Newtonian nanofluid with zero normal flux of nanoparticles at the stretching surface

Abstract: The primary objective of the present analysis is to investigate the entropy generation via two important slip mechanism Brownian motion and thermophoresis diffusion in non-Newtonian nanofluid flow. These effects are analyzed by momentum equation along with a newly formed equation for nanoparticle distribution. Conventional energy equation is modified for the nanofluid by incorporation nanoparticles effects. The condition for zero normal flux of nanoparticles at the stretching sheet is defined to impulse the particles away from surface. To measure the disorder in the thermodynamic system an entropy generation analysis is discussed for present Jeffery nanofluid model. In order to solve the governing equations, compatible similarity transformations are used to obtain a set of higher order non-linear differential equations. An optimal homotopy analysis method (OHAM) and Keller Box Method are used to solve the given system of higher order nonlinear differential equations. Effect of emerging parameters such as Prandtl number, Schmidt number, Brownian motion and thermophoresis on temperature and concentration are shown through graphs. Variations in the entropy generation for different emerging parameters are discussed in detail with the help of graphical results. Also, the coefficient of skin friction, Nusselt number, Sherwood number and characteristic entropy generation rate are presented through graphs.

Assessment on characteristics of heterogeneous-homogenous processes in three-dimensional flow of Burgers fluid

Abstract: An analysis is performed to explore the characteristics of heterogeneous-homogeneous processes for the steady three-dimensional flow of Burgers fluid over a bidirectional stretching surface. In this paper, we utilized the advanced model of a homogeneous-heterogeneous reactions with equal diffusivities for reactant and autocatalysis. Additionally, heat transfer analysis is carried out in the presence of nonlinear thermal radiation and convective boundary conditions. The basic governing non-linear problem is presented and reduced into self-similar form with the aid of suitable similarity approach. The advanced non-linear problem is then tackled analytically by employing the homotpy analysis method (HAM). The effectiveness of relevant physical parameters on temperature and concentration profiles are taken into consideration. It is evident from the graphs that the concentration distribution diminishes by uplifting the homogeneous process parameter while it enhances for strength of Schmidt number. Moreover, it is observed that the surface heat transfer rate enhances for larger values of the Prandtl number.

Lagrangian wall shear stress structures and near-wall transport in high-Schmidt-number aneurysmal flows

Abstract: The wall shear stress (WSS) vector field provides a signature for near-wall convective transport, and can be scaled to obtain a first-order approximation of the near-wall fluid velocity. The near-wall flow field governs mass transfer problems in convection-dominated open flows with high Schmidt number, in which case a flux at the wall will lead to a thin concentration boundary layer. Such near-wall transport is of particular interest in cardiovascular flows whereby haemodynamics can initiate and progress biological events at the vessel wall. In this study we consider mass transfer processes in pulsatile blood flow of abdominal aortic aneurysms resulting from complex WSS patterns. Specifically, the Lagrangian surface transport of a species released at the vessel wall was advected in forward and backward time based on the near-wall velocity field. Exposure time and residence time measures were defined to quantify accumulation of trajectories, as well as the time required to escape the near-wall domain. The effect of diffusion and normal velocity was investigated. The trajectories induced by the WSS vector field were observed to form attracting and repelling coherent structures that delineated species distribution inside the boundary layer consistent with exposure and residence time measures. The results indicate that Lagrangian WSS structures can provide a template for near-wall transport.

Nanofluid slip flow over a stretching cylinder with Schmidt and Péclet number effects

Abstract: A mathematical model is presented for three-dimensional unsteady boundary layer slip flow of Newtonian nanofluids containing gyrotactic microorganisms over a stretching cylinder. Both hydrodynamic and thermal slips are included. By applying suitable similarity transformations, the governing equations are transformed into a set of nonlinear ordinary differential equations with appropriate boundary conditions. The transformed nonlinear ordinary differential boundary value problem is then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple 18 symbolic software. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fractions and microorganism motile density functions have been illustrated graphically. Comparisons of the present paper with the existing published results indicate good agreement and supports the validity and the accuracy of our numerical computations. Increasing bioconvection Schmidt number is observed to depress motile micro-organism density function. Increasing thermal slip parameter leads to a decrease in temperature. Thermal slip also exerts a strong influence on nano-particle concentration. The flow is accelerated with positive unsteadiness parameter (accelerating cylinder) and temperature and micro-organism density function are also increased. However nano-particle concentration is reduced with positive unsteadiness parameter. Increasing hydrodynamic slip is observed to boost temperatures and micro-organism density whereas it decelerates the flow and reduces nano-particle concentrations. The study is relevant to nano-biopolymer manufacturing processes.

Thin Film Williamson Nanofluid Flow with Varying Viscosity and Thermal Conductivity on a Time-Dependent Stretching Sheet

Abstract: This article describes the effect of thermal radiation on the thin film nanofluid flow of a Williamson fluid over an unsteady stretching surface with variable fluid properties. The basic governing equations of continuity, momentum, energy, and concentration are incorporated. The effect of thermal radiation and viscous dissipation terms are included in the energy equation. The energy and concentration fields are also coupled with the effect of Dufour and Soret. The transformations are used to reduce the unsteady equations of velocity, temperature and concentration in the set of nonlinear differential equations and these equations are tackled through the Homotopy Analysis Method (HAM). For the sake of comparison, numerical (ND-Solve Method) solutions are also obtained. Special attention has been given to the variable fluid properties’ effects on the flow of a Williamson nanofluid. Finally, the effect of non-dimensional physical parameters like thermal conductivity, Schmidt number, Williamson parameter, Brinkman number, radiation parameter, and Prandtl number has been thoroughly demonstrated and discussed.

Effect of particle concentration on sediment and turbulent diffusion coefficients in open-channel turbulent flow

Abstract: To achieve a complete knowledge about the effect of particle concentration on sediment and turbulent diffusion coefficients in open-channel turbulent flow is a long-standing problem for the community of researchers. The effect of particle concentration is investigated on the sediment and turbulent diffusion coefficients through the inverse of turbulent Schmidt number or β which is defined by the ratio of sediment diffusion coefficient to turbulent diffusion coefficient. It is observed that with increasing particle concentration, the sediment diffusion coefficient decreases more in comparison with the turbulent diffusion coefficient for both dilute and non-dilute sediment-laden flows. The physical characteristics of β observed are expressed mathematically in terms of normalized settling velocity, reference level and reference concentration. The applicability of the mathematical formulae is confirmed by the agreement analysis between experimental data and particle concentration profile computed from the Rouse equations modified through the newly proposed expression of β. Apart from the better agreement between dilute particle concentration data and the developed Rouse equation, the striking observation is that the modified Rouse equation shows reasonable computational accuracy for non-dilute particle concentration data also. Minimum error is obtained from the present model when it is compared with the models proposed by the previous researchers.

A Lagrangian study of turbulent mixing: forward and backward dispersion of molecular trajectories in isotropic turbulence

Abstract: Statistics of the trajectories of molecules diffusing via Brownian motion in a turbulent flow are extracted from simulations of stationary isotropic turbulence, using a postprocessing approach applicable in both forward and backward reference frames. Detailed results are obtained for Schmidt numbers ( ) from 0.001 to 1000 at Taylor-scale Reynolds numbers up to 1000. The statistics of displacements of single molecules compare well with the earlier theoretical work of Saffman (J. Fluid Mech. vol. 8, 1960, pp. 273–283) except for the scaling of the integral time scale of the fluid velocity following the molecular trajectories. For molecular pairs we extend Saffman’s theory to include pairs of small but finite initial separation, which is in excellent agreement with numerical results provided that data are collected at sufficiently small times. At intermediate times the separation statistics of molecular pairs exhibit a more robust Richardson scaling behaviour than for the fluid particles. The forward scaling constant is very close to 0.55, whereas the backward constant is approximately 1.53–1.57, with a weak Schmidt number dependence, although no scaling exists if at the Reynolds numbers presently accessible. An important innovation in this work is to demonstrate explicitly the practical utility of a Lagrangian description of turbulent mixing, where molecular displacements and separations in the limit of small backward initial separation can be used to calculate the evolution of scalar fluctuations resulting from a known source function in space. Lagrangian calculations of the production and dissipation rates of the scalar fluctuations are shown to agree very well with Eulerian results for the case of passive scalars driven by a uniform mean gradient. Although the Eulerian–Lagrangian comparisons are made only for , the Lagrangian approach is more easily extended to both very low and very high Schmidt numbers. The well-known scalar dissipation anomaly is accordingly also addressed in a Lagrangian context.

Impact of thermophoresis particle deposition on three-dimensional radiative flow of Burgers fluid

Abstract: This paper explores the analytical solution to heat and mass transfer of a three-dimensional steady flow of Burgers fluid over a bidirectional stretching surface. Additionally, analysis is carried out in the presence of thermal radiation, heat generation/absorption and thermophoretic effects. The governing non-linear problem is developed and transformed into self-similar form by utilizing similarity approach. The resulting non-linear problem is solved analytically by employing the homotpy analysis method (HAM). The obtained results are plotted and discussed in detail for interesting physical parameters. It is seen that increasing values of the thermophoretic parameter leads to a decrease in the concentration field and the corresponding concentration boundary layer thickness. Also, it is noticed that the concentration field decays quickly corresponding with thermophoretic parameter in comparison to Schmidt number.

Heat and mass transfer in asymmetric channels during peristaltic transport of an MHD fluid having temperature-dependent properties

Abstract: Of concern in the paper is a study on the peristaltic transport of a magnetohydrodynamic fluid at low Reynolds number in an asymmetric channel The study is motivated by the phenomenon of peristalsis that is prominent in the flow of some physiological fluids in the human body The viscosity of the fluid is considered dependent on temperature The associated problems of heat and mass transfer during the flow of the fluid are also taken into account The study has been carried out for long wavelength of the peristaltic motion By using perturbation technique, series solutions have been obtained for stream function, velocity, pressure gradient, shear stress and pressure rise per wavelength Pumping characteristics and the phenomenon of trapping are also adequately discussed In order to illustrate the validity of the theoretical study, numerical results have been computed for a specific situation by using MATHEMATICA software The study reveals that the volume of the trapped bolus diminishes with increase in Hartmann number, Reynolds number, fluid viscosity and Schmidt number but decreases with increasing phase difference It is seen that the results of the study conform very well to those of previous studies reported in available scientific literatures

Lie group analysis for bioconvection MHD slip flow and heat transfer of nanofluid over an inclined sheet: Multiple solutions

Abstract: This paper considers numerical analysis of bioconvection boundary layer flow and heat transfer of electrically conducting nanofluid containing nanoparticles and gyrotactic microorganism over an inclined permeable sheet. Lie symmetry group transformations are used to convert the governing non-linear partial differential equations for continuity, momentum, energy, nanoparticles and microorganisms conservation into non-linear ordinary differential equations. The influences of important physical parameters such as mass transfer parameter s , Richardson number Ri , Buoyancy ratio Nr , bioconvection Rayleigh number Rb , velocity and thermal slip parameters, Brownian motion parameter Nb , thermophoresis parameter Nt , the bioconvection Schmidt number Sc b and the bioconvection Peclet number Pe , on the skin friction, the rate of heat transfer and microorganisms flux are discussed numerically in this study. The dual solutions are obtained for some critical range of mass transfer parameter s and stretching/shrinking parameter χ .

Heat and Mass Transfer on Squeezing Unsteady MHD Nanofluid Flow between Parallel Plates with Slip Velocity Effect

Abstract: Heat and mass transfer behavior of unsteady flow of squeezing nanofluids between two parallel plates in the sight of uniform magnetic field with slip velocity effect is investigated. The governing equations representing fluid flow have been transformed into nonlinear ordinary differential equations using similarity transformation. The equations thus obtained have been solved numerically using Runge-Kutta-Fehlberg method with shooting technique. Effects on the behavior of velocity, temperature, and concentration for various values of relevant parameters are illustrated graphically. The skin-friction coefficient and heat and mass transfer rate are also tabulated for various governing parameters. The results indicate that, for nanofluid flow, the rates of heat and mass transfer are inversely proportional to nanoparticle volume fraction and magnetic parameter. The rate of mass transfer increases with increasing values of Schmidt number and squeeze number.

Soret and Dufour effects on hydromagnetic flow of viscoelastic fluid over porous oscillatory stretching sheet with thermal radiation

Abstract: The thermal-diffusion and diffusion-thermo effects on magnetohydrodynamic viscoelastic flow of second grade fluid over porous oscillatory stretching sheet with thermal radiation are analyzed. The dimensionless nonlinear partial differential equations are solved by means of homotopy analysis method. The effects of various parameters on velocity, temperature and concentration distributions are investigated and discussed in detail. It is found that temperature increases by increasing Dufour number. The concentration field is enhanced by increasing Soret number while it decreases with Schmidt number. Moreover, the numerical values of effective local Nusselt number and local Sherwood number are calculated and illustrated through tables.

On the turbulence models and turbulent Schmidt number in simulating stratified flows

Abstract: Stratified flows are prevalent in indoor and outdoor environments. To predict these flows, this investigation evaluated the performance of seven turbulence models by comparing the simulation results with the experimental data of both weakly and strongly stratified jets. The models tested included six Reynolds-averaged Navier–Stokes models and one large eddy simulation (LES) model. The velocity, turbulent kinetic energy (TKE), and Reynolds stress distributions were examined. For the weakly stratified jet, all seven models could predict well the mean velocity, but for the strongly stratified jet, the Reynolds stress model and LES models overpredicted the velocity in the unstable stratification region. The Shear Stress Transport (SST) model was the best. This paper also introduced a new dynamic turbulent Schmidt number model which can improve the prediction of density distribution. In addition, this investigation analysed the computing costs of the models as well as the vorticity and entrainment ratios predi...

Mass transport by mode-2 internal solitary-like waves

Abstract: We present the first three-dimensional numerical simulations of the mass transport capabilities of mode-2 waves formed by a lock-release mechanism with both single and double pycnocline stratifications. Single pycnoclines and double pycnoclines with a small spacing between the pycnocline centres were found to exhibit large Lee instabilities which formed during the collapse of the intermediate density region. These instabilities led to the generation of vorticity dipoles across the mid-depth, and thereby contributed to the reduction in the mass transported by the wave. A double pycnocline with a separation of approximately 12% of the depth between the two pycnocline centres was found to transport a passive tracer optimally for the longest time-period. Increasing Schmidt number correlated with increasing mass transport, while decreasing the tracer diffusivity led to increasing mass transport, but only when a trapped core existed. Contrasted two-dimensional simulations reveal that in certain cases, most noticeably the optimal transport case, the mass transport is significantly different from the corresponding three-dimensional simulation.