Showing papers on "Schmidt number published in 2012"

Forced Convection Heat Transfer of Nanofluids in a Porous Channel

Abstract: This article is concerned with the effects of flow and migration of nanoparticles on heat transfer in a straight channel occupied with a porous medium. Investigation of force convective heat transfer of nanofluids in a porous channel has not been considered completely in the literature and this challenge is generally considered to be an open research topic that may require more study. The fully developed flow and steady Darcy–Brinkman–Forchheimer equation is employed in porous channel. The thermal equilibrium model is assumed between nanofluid and solid phases. It is assumed that the nanoparticles are distributed non-uniformly inside the channel. As a result the volume fraction distribution equation is also coupled with governing equations. The effects of parameters such as Lewis number, Schmidt number, Brownian diffusion, and thermophoresis on the heat transfer are completely studied. The results show that the local Nusselt number is decreased when the Lewis number is increased. It is observed that as the Schmidt number is increased, the wall temperature gradient is decreased and as a consequence the local Nusselt number is decreased. The effects of Lewis number, Schmidt number, and modified diffusivity ratio on the volume fraction distribution are also studied and discussed.

Double-diffusive natural convection in a rectangular cavity with partially thermally active side walls

Abstract: Double-diffusive natural convection in a rectangular cavity with partially thermally active side walls filled with air is studied numerically. The active part of the left side wall has a higher temperature and concentration than the right side one. The length of the thermally active part is equal to half of the cavity height. The top and bottom of the cavity and inactive part of the side walls are considered to be adiabatic and impermeable to mass transfer. Placement order of thermal active walls has significant effect on heat and mass transfer rate, to explore this effect and achieving the optimum rate inside the cavity, nine different relative positions of the active zones are considered. The non-dimensional forms of governing transport equations describing double-diffusive natural convection for laminar two-dimensional incompressible flow are functions of vorticity, temperature or energy, concentration and stream-function. Laminar regime is considered under steady state condition. The coupled differential equations are discretized by the finite difference method and are solved using the successive-over-relaxation (SOR) method. The results are obtained for different heating sections and different parameters such as aspect ratio, buoyancy ratio and Schmidt number. Also the heat and mass transfer rate in the cavity is measured in terms of the average Nusselt and Sherwood numbers.

Group theory and differential transform analysis of mixed convective heat and mass transfer from a horizontal surface with chemical reaction effects

Abstract: Viscous, laminar mixed convection boundary-layer flow over a horizontal plate, with chemical reaction, is considered. The governing equations are expressed in nondimensional form. Group theory is employed to determine the invariant solutions of these equations under a particular continuous one-parameter group. Series solutions of the transformed coupled system of equations are then generated for velocity, temperature, and concentration functions using the Differential Transform Method (DTM) with Pade approximants. The influence of thermal buoyancy parameter, species buoyancy parameter, chemical reaction parameter, order of chemical reaction, Prandtl number, and Schmidt number on the flow characteristics is evaluated in detail The obtained solutions are verified by comparison with the numerical shooting quadrature results. Applications of the study arise in sheet materials processing, bio-reactors, and catalytic systems in chemical engineering.

A Numerical Study on the Turbulent Schmidt Numbers in a Jet in Crossflow

Abstract: This work presents a numerical study on the turbulent Schmidt numbers in jets in crossflow. This study contains two main parts. In the first part the problem of the proper choice of the turbulent Schmidt number in the Reynolds-Averaged Navier-Stokes (RANS) jet in crossflow mixing simulations is outlined. The results of RANS employing the shear-stress transport (SST) model of Menter and its curvature correction modification and different turbulent Schmidt number values are validated against experimental data. The dependence of the “optimal” value of the turbulent Schmidt number on the dynamic RANS model is studied. Furthermore a comparison is made with the large-eddy simulation (LES) results obtained using the WALE (Wall-Adapted Local Eddy Viscosity) model. The accuracy given by LES is superior in comparison to RANS results. This leads to the second part of the current study, in which the time-averaged mean and fluctuating velocity and scalar fields from LES are used for the evaluation of the turbulent viscosities, turbulent scalar diffusivities, and the turbulent Schmidt numbers in a jet in crossflow configuration. The values obtained from the LES data are compared with those given by the RANS modeling. The deviations are discussed and the possible ways for the RANS model improvements are outlined.© 2012 ASME

Similarity solution of MHD boundary layer flow with diffusion and chemical reaction over a porous flat plate with suction/blowing

Abstract: Similarity analysis of diffusion of chemically reactive solute distribution in MHD boundary layer flow of an electrically conducting incompressible fluid over a porous flat plate is presented. The reaction rate of the solute is considered inversely proportional along the plate. Adopting the similarity transformation technique the governing equations are converted into the self-similar ordinary differential equations which are solved by shooting procedure using Runge-Kutta method. For increase of the Schmidt number the solute boundary layer thickness is reduced. Most importantly, the effects of reaction rate and order of reaction on concentration field are of conflicting natures, due to increasing reaction rate parameter the concentration decreases, but for the increase in order of reaction it increases. In presence of chemical reaction, the concentration profiles attain negative value when Schmidt number is large.

Radiation effects on mhd flow past an impulsively started vertical plate with variable heat and mass transfer

Abstract: Thermal radiation effect on a transient MHD flow with mass transfer past an impulsively fixed infinite vertical plate was studied by Ahmed and Sarmah (2009). Anjali and Kayalvizhi (2010) studied analytical solution of MHD flow with radiation over a stretching sheet embedded in a porous medium. Prasad et al. (2010) studied radiation and mass transfer effects on unsteady MHD free convection flow past a vertical porous plate embedded in a porous medium. Rajesh (2010) have considered MHD effects on free convection and mass transform flow through a porous medium with variable temperature. Radiation effects on MHD flow past an impulsively started vertical plate with variable heat and mass transfer is studied here. The temperature of plate is made to rise linearly with time. The fluid considered is gray, absorbing-emitting radiation but a non-scattering medium. The governing equations involved in the present analysis are solved by the Laplace-transform technique. The velocity, skin friction, Nusselt number and Sherwood number are studied for different parameters like radiation parameter, Schmidt number, Thermal Grashof number, mass Grashof number, magnetic field parameter and Prandtl number. Symbols used are given in appendix.

MHD flow over an inclined radiating plate with the temperature‐dependent thermal conductivity, variable reactive index, and heat generation

Abstract: We study the effects of higher-order chemical reaction and heat generation on coupled heat and mass transfer by MHD mixed convection from a permeable radiating inclined plate with the thermal convective boundary condition. The governing boundary layer equations are formulated and transformed into a set of similarity equations using dimensionless similarity variables developed by Lie group analysis. The resulting equations are then solved numerically using Maple 13 which uses a fourth–fifth order Runge–Kutta–Fehlberg algorithm for solving nonlinear boundary value problems. A representative set of numerical results are displayed graphically and discussed to show some interesting aspects of the parameters: convective heat transfer (γ), the angle of inclination (α), generation order of chemical reaction (n), reaction rate (λ), the Prandtl number (Pr), and the Schmidt number (Sc) on the dimensionless axial velocity, the temperature, and the concentration profiles. Also effects of pertinent parameters on the skin friction factor, the rate of heat, and the rate of mass transfer are obtained and displayed in tabular form. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20409

Dimensionality of the spatiotemporal entanglement of parametric down-conversion photon pairs

Abstract: In this work, the Schmidt number of the two-photon state generated by parametric down-conversion (PDC) is evaluated in the framework of a fully spatiotemporal model for PDC. A comparison with the results obtained in either purely spatial or purely temporal models shows that the degree of entanglement of the PDC state cannot be trivially reduced to the product of the Schmidt numbers obtained in models with lower dimensionality, unless the detected bandwidth is very narrow. This result is a consequence of the nonfactorability of the state in the spatial and temporal degrees of freedoms of twin photons. In the limit of a broad pump beam, we provide a geometrical interpretation of the Schmidt number as the ratio between the volume of the phase-matching region and of a correlation volume.

Double diffusive effects on pressure­driven miscible displacement flows in a channel

Abstract: The pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.

Effects of thermal radiation and mass diffusion on free convection flow near a vertical plate with newtonian heating

Abstract: The effects of thermal radiation and mass transfer on unsteady natural convection flow of an optically dense viscous incompressible fluid near a vertical plate with Newtonian heating have been investigated. Both physically important boundary conditions of uniform wall concentration (UWC) and uniform mass flux (UMF) are considered. Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. The governing dimensionless boundary layer equations are solved analytically using the Laplace transform technique. The effects of mass to thermal buoyancy ratio parameter (N), Prandtl number (Pr), Schmidt number (Sc), and the radiation parameter (R) as well as time (t) on the velocity field and skin friction are determined. It is found that velocity increases for aiding flows and it decreases for opposing flows in the cases of both UWC and UMF. The skin friction is reduced with increasing species concentration in the presence of aiding flows for both UWC and UMF. Also, the velo...

Soret and Dufour Effects on Natural Convection Flow Past a Vertical Surface in a Porous Medium with Variable Viscosity

Abstract: The heat and mass transfer characteristics of natural convection about a vertical surface embedded in a saturated porous medium subject to variable viscosity are numerically analyzed, by taking into account the diffusion-thermo (Dufour) and thermal-diffusion (Soret) effects. The governing equations of continuity, momentum, energy, and concentrations are transformed into nonlinear ordinary differential equations, using similarity transformations, and then solved by using Runge-Kutta-Gill method along with shooting technique. The parameters of the problem are variable viscosity, buoyancy ratio, Lewis number, Prandtl number, Dufour effect, Soret effect, and Schmidt number. The velocity, temperature, and concentration distributions are presented graphically. The Nusselt number and Sherwood number are also derived and discussed numerically.

Effects of surface mass transfer on steady mixed convection flow from vertical stretching sheet with variable wall temperature and concentration

Abstract: Purpose – The purpose of this paper is to study the effects of surface mass transfer on the steady mixed convection flow from a vertical stretching sheet in a parallel free stream with variable wall temperature and concentration.Design/methodology/approach – An implicit finite difference scheme in combination with the quasilinearisation technique is employed to obtain non‐similar solutions of the governing boundary layer equations for momentum, temperature and concentration fields.Findings – The numerical results are reported here to display the effects of mixed convection parameter, ratio of buoyancy forces, surface mass transfer (suction and injection), the ratio of free stream velocity to the composite reference velocity, Prandtl number and Schmidt number on velocity, temperature and concentration profiles as well as on skin friction, Nusselt number and Sherwood number.Research limitations/implications – Thermophysical properties of the fluid in the flow model are assumed to be constant except the dens...

MHD flow and mass transfer of chemically reactive upper convected Maxwell fluid past porous surface

Abstract: The magnetohydrodynamic (MHD) flow and mass transfer of an electrically conducting upper convected Maxwell (UCM) fluid at a porous surface are studied in the presence of a chemically reactive species. The governing nonlinear partial differential equations along with the appropriate boundary conditions are transformed into nonlinear ordinary differential equations and numerically solved by the Keller-box method. The effects of various physical parameters on the flow and mass transfer characteristics are graphically presented and discussed. It is observed that the order of the chemical reaction is to increase the thickness of the diffusion boundary layer. Also, the mass transfer rate strongly depends on the Schmidt number and the reaction rate parameter. Furthermore, available results in the literature are obtained as a special case.

A new definition of bejan number

Abstract: A new definition of Bejan number will be generated by replacing the thermal diffusivity with the mass diffusivity. For example, the Schmidt number is the mass transfer analog of the Prandtl number. For the case of Reynolds analogy (Sc = Pr = = 1), both current and new definitions of Bejan number are the same. This new definition is useful and needed for diffusion of mass (mass diffusion).

Internal bores: an improved model via a detailed analysis of the energy budget

Abstract: Internal bores, or internal hydraulic jumps, arise in many atmospheric and oceanographic phenomena. The classic single-layer hydraulic jump model accurately predicts the bore height and propagation velocity when the difference between the densities of the expanding and contracting layers is large (i.e. water and air), but fails in the Boussinesq limit. A two-layer model, which conserves mass separately in each layer and momentum globally is more accurate in the Boussinesq limit, but it requires for closure an assumption about the loss of energy across a bore. It is widely believed that bounds on the bore speed can be found by restricting the energy loss entirely to one of the two layers, but under some circumstances, both bounds overpredict the propagation speed. A front velocity slower than both bounds implies that, somehow, the expanding layer is gaining energy. We directly examine the flux of energy within internal bores using two- and three-dimensional direct numerical simulations and find that although there is a global loss of energy across a bore, a transfer of energy from the contracting to the expanding layer causes a net energy gain in the expanding layer. The energy transfer is largely the result of turbulent mixing at the interface. Within the parameter regime investigated, the effect of mixing is much larger than non-hydrostatic and viscous effects, both of which are neglected in the two-layer analytical models. Based on our results, we propose an improved two-layer model that provides an accurate propagation velocity as a function of the geometrical parameters, the Reynolds number, and the Schmidt number.

High-Schmidt-number mass transport mechanisms from a turbulent flow to absorbing sediments

Abstract: We have investigated the mechanisms involved in dissolved oxygen (DO) transfer from a turbulent flow to an underlying organic sediment bed populated with DO-absorbing bacteria. Our numerical study relies on a previously developed and tested computational tool that couples a bio-geochemical model for the sediment layer and large-eddy simulation for transport on the water side. Simulations have been carried out in an open channel configuration for different Reynolds numbers (Reτ = 180–1000), Schmidt numbers (Sc = 400–1000), and bacterial populations (χ* = 100–700 mg l−1). We show that the average oxygen flux across the sediment-water interface (SWI) changes with Reτ and Sc, in good agreement with classic heat-and-mass-transfer parametrizations. Time correlations at the SWI show that intermittent peaks in the wall-shear stress initiate the mass transfer and modulate its distribution in space and time. The diffusive sublayer acts as a de-noising filter with respect to the overlying turbulence; the instantaneo...

Cartesian and polar Schmidt bases for down-converted photons How high dimensional entanglement protects the shared information from non-ideal measurements

Abstract: We derive an analytical form of the Schmidt modes of spontaneous parametric down-conversion (SPDC) biphotons in both Cartesian and polar coordinates. We show that these correspond to Hermite-Gauss (HG) or Laguerre-Gauss (LG) modes only for a specific value of their width, and we show how such value depends on the experimental parameters. The Schmidt modes that we explicitly derive allow one to set up an optimised projection basis that maximises the mutual information gained from a joint measurement. The possibility of doing so with LG modes makes it possible to take advantage of the properties of orbital angular momentum eigenmodes. We derive a general entropic entanglement measure using the Renyi entropy as a function of the Schmidt number, K, and then retrieve the von Neumann entropy, S. Using the relation between S and K we show that, for highly entangled states, a non-ideal measurement basis does not degrade the number of shared bits by a large extent. More specifically, given a non-ideal measurement which corresponds to the loss of a fraction of the total number of modes, we can quantify the experimental parameters needed to generate an entangled SPDC state with a sufficiently high dimensionality to retain any given fraction of shared bits.

High-Schmidt-number mass transport mechanisms from a turbulent flow to absorbing sediments

Abstract: We have investigated the mechanisms involved in dissolved oxygen (DO) transfer from a turbulent flow to an underlying organic sediment bed populated with DO-absorbing bacteria. Our numerical study relies on a previously developed and tested computational tool that couples a bio-geochemical model for the sediment layer and large-eddy simulation for transport on the water side. Simulations have been carried out in an open channel configuration for different Reynolds numbers (Reτ = 180–1000), Schmidt numbers (Sc = 400–1000), and bacterial populations (χ* = 100–700 mg l−1). We show that the average oxygen flux across the sediment-water interface (SWI) changes with Reτ and Sc, in good agreement with classic heat-and-mass-transfer parametrizations. Time correlations at the SWI show that intermittent peaks in the wall-shear stress initiate the mass transfer and modulate its distribution in space and time. The diffusive sublayer acts as a de-noising filter with respect to the overlying turbulence; the instantaneo...

Unsteady mhd free convective mass transfer flow past an infinite vertical porous plate with variable suction and soret effect

Abstract: The MHD effects on the unsteady heat convective mass transfer flow past an infinite vertical porous plate with variable suction, where the plate temperature oscillates with the same frequency as that of variable suction velocity with the Soret effects. The governing equations of motion are solved to best possible classical solution by assuming at suitable trial solution. The flow phenomenon has been characterized with the help of flow parameters such as velocity, temperature and concentration profiles for different parameters such as Grashof number (Gr), modified Grashof number (Gm), Schmidt number (Sc), Prandtl number (Pr), Soret number (S0), Magnetic field (M) and variable suction parameter (A). The velocity, temperature and concentration profiles and ski-friction are shown graphically.

Transient Rayleigh-Bénard-Marangoni solutal convection

Abstract: Solutal driven flow is studied for a binary solution submitted to solvent evaporation at the upper free surface. Evaporation induces an increase in the solute concentration close to the free surface and solutal gradients may induce a convective flow driven by buoyancy and/or surface tension. This problem is studied numerically, using several assumptions deduced from previous experiments on polymer solutions. The stability of the system is investigated as a function of the solutal Rayleigh and Marangoni numbers, the evaporative flux and the Schmidt number. The sensitivity of the thresholds to initial perturbations is analyzed. The effect of viscosity variation during drying is also investigated. At last numerical simulations are presented to study the competition between buoyancy and Marangoni effects in the nonlinear regime.

Heat and mass transfer eects on mhd flow of viscous fluid through non-homogeneous porous medium in presence of temperature dependent heat source

Abstract: In this paper we have investigated the heat and mass transfer effects on MHD flow of viscous incompressible and electrically conducting fluid through a non� homogeneous porous medium in the presence of heat source, oscillatory suction velocity. A uniform transverse magnetic field is applied in the direction of the flow perpendicular to the plates. The equations governing the flow are solved by a simple perturbation technique the effects of various physical parameters viz., magnetic parameter M, modified Grashof number Gm., Schmidt number Sc etc., on primary and secondary velocity distributions. Temperature distribution, skinfriction and rate of heat transfer are discussed through graphs. It is observed that primary velocity increases with an increase in M, where as it shows reverse effect in case of the Gm .

Transient free convection flow between long vertical parallel plates with ramped wall temperature at one boundary in the presence of thermal radiation and constant mass diffusion

Abstract: The unsteady laminar free convection flow between two long vertical parallel plates with ramped wall temperature at one boundary has been investigated in the presence of thermal radiation and chemical species concentration. The exact solutions of the momentum, energy and concentration equations have been obtained using the Laplace transform technique. The velocity and temperature profiles, skin-friction and Nusselt number variations are shown graphically and the numerical values of the volume flow rate, the total heat rate and species rate added to the fluid are presented in a table. The influence of different system parameters such as the radiation parameter (R), buoyancy ratio parameter (N), Schmidt number (Sc) and time (t) has been analyzed carefully. A critical analysis of the coupled heat and mass transfer phenomena is provided. The free convective flow due to ramped wall temperature has also been compared with the baseline case of flow due to constant wall temperature.

X-entangled biphotons: Schmidt number for 2D model

Abstract: We calculate the Schmidt number for a two-dimensional model of the nonfactorable spatiotemporal wave-function of biphotons produced in type-I spontaneous parametric down-conversion with degenerate and collinear phase-matching taking into consideration a major part of the broad spectral and angular bandwidth of the down-converted light. We deduce an analytical expression for the Schmidt number as a function of the filter bandwidth in the limit of spectrally narrow pump and consider a possibility of tailoring a Gaussian model for the description of this kind of entanglement.