Showing papers on "Schmidt number published in 2019"

Sensitivity analysis of key parameters for population balance based soot model for low-speed diffusion flames

Abstract: In this article, the evolution of in-flame soot species in a slow speed, buoyancy-driven diffusion flame is thoroughly studied with the implementation of the population balance approach in association with computational fluid dynamics (CFD) techniques. This model incorporates interactive fire phenomena, including combustion, radiation, turbulent mixing, and all key chemical and physical formation and destruction processes, such as particle inception, surface growth, oxidation, and aggregation. The in-house length-based Direct Quadrature Method of Moments (DQMOM) soot model is fully coupled with all essential fire sub-modelling components and it is specifically constructed for low-speed flames. Additionally, to better describe the combustion process of the parental fuel, ethylene, the strained laminar flamelet model, which considers detailed chemical reaction mechanisms, is adopted. Numerical simulation is validated against a self-conducted co-flow slot burner experimental measurement. A comprehensive assessment of the effect of adopting different nucleation laws, oxidation laws, and various fractal dimension and diffusivity values is performed. The results suggest the model employing Moss law of nucleation, modified NSC law of oxidation, and adopting a fractal dimension value of 2.0 and Schmidt number of 0.9 yields the simulation result that best agreed with experimental data.

Numerical study of mixing in wavy micromixers: comparison between raccoon and serpentine mixer

Abstract: We numerically analyze the mixing and pressure drop characteristics for flow through wavy micromixer of two geometrical configurations, namely raccoon and serpentine for different values of amplitude of the waviness of the mixer (α), wavelength of the waviness (λ), Reynolds number(Re) and Schmidt number(Sc). Three different flow regimes are identified depending on the parameters influencing the mixing index. The mixing index for both the raccoon and serpentine mixer is very close to unity in the first regime (0.1

Darcy–Forchheimer flow of nanofluid due to a curved stretching surface

Abstract: Purpose The purpose of present communication is to analyze Darcy–Forchheimer flow of viscous nanofluid by curved stretchable surface. Flow in porous medium is characterized by Darcy–Forchheimer relation. Brownian diffusion and thermophoresis are considered. Convective heat and mass boundary conditions are also used at the curved stretchable surface. Design/methodology/approach The resulting nonlinear system is solved through shooting technique. Findings Skin friction coefficient is enhanced for larger porosity parameter and inertia coefficient while reverse trend is noticed for curvature parameter. Local Nusselt number is enhanced for higher Prandtl number and thermal Biot number, whereas the opposite trend is seen via curvature parameter, porosity parameter, inertia coefficient, thermophoresis parameter and Brownian motion parameter. Local Sherwood number is enhanced for Schmidt number, Brownian motion parameter and concentration Biot number, while reverse trend is noticed for curvature parameter, porosity parameter, inertia coefficient and thermophoresis parameter. Originality/value To the best of author’s knowledge, no such consideration has been given in the literature yet.

Effects of two-phase nanofluid model on MHD mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater

Abstract: This paper investigates a steady mixed convection in a lid-driven square cavity subjected to an inclined magnetic field and heated by corner heater with an inserted square solid block. Water–Al $$_2$$ O $$_3$$ nanofluid fills the cavity based on Buongiorno’s two-phase model. A corner heater is configured in the left lower corner of the cavity by maintaining 40% of the bottom and vertical walls at constant hot temperature. The top horizontal wall is moving and maintained at a constant low temperature. The remainder walls are thermally insulated. The governing equations are solved numerically using the finite element method. The governing parameters are the nanoparticles volume fraction ( $$0 \le \phi \le 0.04$$ ), Reynolds number ( $$1 \le Re \le 500$$ ), Richardson number ( $$0.01 \le Ri \le 100$$ ), Hartmann number ( $$0 \le Ha \le 50$$ ) and the size of the inner solid ( $$0.1 \le D \le 0.7$$ ). The other parameters: the Prandtl number, Lewis number, Schmidt number, ratio of Brownian to thermophoretic diffusivity and the normalized temperature parameter, are fixed at $$Pr=4.623$$ , $$Le=3.5\times 10^{5}$$ , $$Sc=3.55\times 10^{4}$$ , $$N_{\mathrm{BT}}=1.1$$ and $$\delta =155$$ , respectively. The inclination of the magnetic field is fixed at $$\gamma =\frac{\pi }{4}$$ . Results show that at low Reynolds number, the increase in nanoparticles loading more the 2% becomes useless. It is also found that a big size of the solid block can augment heat transfer in the case of high values of both the Reynolds and Richardson numbers.

Multiple Slip Effects on Magnetohydrodynamic Axisymmetric Buoyant Nanofluid Flow above a Stretching Sheet with Radiation and Chemical Reaction

Abstract: The present article investigates the effect of multiple slips on axisymmetric magnetohydrodynamics (MHD) buoyant nano-fluid flow over a stretching sheet with radiation and chemical effect. The non-linear partial differential equations were transformed to a non-linear control equation using an appropriate similarity transformation. The governing equations were solved through the finite element method. The influence of physical parameters such as multiple slips, magnetic, thermal radiation, Prandtl number, stretching, Brownian motion, thermophoresis, Schmidt number, Lewis number and chemical reaction on the radial velocity, temperature, solutal concentration and nano-fluid volume fraction profile were investigated. We noted that the boundary layers increases in the presence of multiple slip effects whereas, the effect of thermal slip on Nusselt number increases with the increasing values of magnetic and thermal radiation. To verify the convergence of the numerical solution, the computations were made by reducing the mesh size. Finally, our results are parallel to previous scholarly contributions.

Hall Effect on Couple Stress 3D Nanofluid Flow Over an Exponentially Stretched Surface With Cattaneo Christov Heat Flux Model

Abstract: A recent challenging task in the field of nanotechnology is nanofluids, which are potential heat transfer fluids. Numerous researchers worked on nanofluid with different physical conditions. In this research work, we presented the three-dimensional flow of couple stress nanofluid with Hall current, viscous dissipation and Joule heating impacts past an exponentially stretching sheet. The Cattaneo–Christov heat flux model is implemented to examine the thermal relaxation properties. The modeled equations have been transformed to nonlinear ordinary differential equations with the help of correspondence transformations. The homotopy analysis method is used to solve the proposed model. The effect of dimensionless parameters, which are couple stress, Hartmann number, the ratio of rates, and Hall on velocity fields in $x$ - and $y$ -directions has been scrutinized. The rise in Hall parameter, Hartmann number, the ratio of rates parameter, and couple stress parameter are reducing the velocity function in the $x$ -direction. The rise in Hall parameter, Hartmann number, and the ratio of rates parameter are improving the velocity function in the $y$ -direction. The influence of Prandtl number, thermal relaxation time, and temperature exponent on temperature field are presented in this paper. The rise in thermal relaxation parameter, Prandtl number, and temperature exponent are reducing the temperature function. The influence of thermophoresis, the Schmidt number, and Brownian motion on concentration field are presented. The rise in thermophoresis parameter is increasing the concentration function while the rise in Brownian motion parameter and Schmidt number are reducing the concentration function. The impacts of implanted factors on skin friction, Nusselt number, and Sherwood number are accessible through tables. The determined result of skin friction is compared with the previous study.

Three-Dimensional Casson Nanofluid Thin Film Flow over an Inclined Rotating Disk with the Impact of Heat Generation/Consumption and Thermal Radiation

Abstract: In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

Double diffusive effects on mixed convection Casson fluid flow past a wavy inclined plate in presence of Darcian porous medium

Abstract: The aim of this research paper is to study the effect of thermal diffusion (Soret) on unsteady magnetohydrodynamic mixed convection flow through an accelerated vertical wavy plate embedded in a darcian porous medium. Fundamental coupled non-linear partial differential equations with fitting boundary conditions control the flow problem. Efficient, stable, and finite element technique providing excellent convergence and versatility in accepting coupled systems of ordinary and partial differential equations is used to obtain numerical solutions for these partial differential equations. Graphical results for velocity, temperature, and concentration fields are discussed and displayed. The effects of emerging parameters on the Skin-friction are arrived at using comprehensive parametric tests. Rate of heat and mass transfer coefficients are graphically represented and examined. The results match with a special case of previously published work. From the present analysis it is reported that the presence of angle of inclination sustains a retarding effect on velocity. The velocity decreases with increasing magnetic field parameter, while the Dufour number and Soret number increase with increasing the same and the concentration field decrease as the Schmidt number increases while the temperature field decreases with increasing Prandtl number and Dufour number.

Effects of homogeneous-heterogeneous reactions and thermal radiation on magneto-hydrodynamic Cu-water nanofluid flow over an expanding flat plate with non-uniform heat source

Abstract: This study presents the effect of non-uniform heat source on the magneto-hydrodynamic flow of nanofluid across an expanding plate with consideration of the homogeneous-heterogeneous reactions and thermal radiation effects. A nanofluid’s dynamic viscosity and effective thermal conductivity are specified with Corcione correlation. According to this correlation, the thermal conductivity is carried out by the Brownian motion. Similarity transformations reduce the governing equations concerned with energy, momentum, and concentration of nanofluid and then numerically solved. The influences of the effective parameters, e.g., the internal heat source parameters, the volume fraction of nanofluid, the radiation parameter, the homogeneous reaction parameter, the magnetic parameter, the heterogeneous parameter and the Schmidt number are studied on the heat and flow transfer features. Further, regarding the effective parameters of the present work, the correlation for the Nusselt number has been developed. The outcomes illustrate that with the raising of the heterogeneous parameter and the homogeneous reaction parameter, the concentration profile diminishes. In addition, the outcomes point to a reverse relationship between the Nusselt number and the internal heat source parameters.

Wavelet analysis of stagnation point flow of non-Newtonian nanofluid

Abstract: The wavelet approach is introduced to study the influence of the natural convection stagnation point flow of the Williamson fluid in the presence of thermophysical and Brownian motion effects. The thermal radiation effects are considered along a permeable stretching surface. The nonlinear problem is simulated numerically by using a novel algorithm based upon the Chebyshev wavelets. It is noticed that the velocity of the Williamson fluid increases for assisting flow cases while decreases for opposing flow cases when the unsteadiness and suction parameters increase, and the magnetic effect on the velocity increases for opposing flow cases while decreases for assisting flow cases. When the thermal radiation parameter, the Dufour number, and Williamson’s fluid parameter increase, the temperature increases for both assisting and opposing flow cases. Meanwhile, the temperature decreases when the Prandtl number increases. The concentration decreases when the Soret parameter increases, while increases when the Schmidt number increases. It is perceived that the assisting force decreases more than the opposing force. The findings endorse the credibility of the proposed algorithm, and could be extended to other nonlinear problems with complex nature.

Simultaneous influence of thermo-diffusion and diffusion-thermo on non-Newtonian hyperbolic tangent magnetised nanofluid with Hall current through a nonlinear stretching surface

Abstract: In this article, the effect of thermo-diffusion and diffusion-thermo on hyperbolic tangent magnetised nanofluid with Hall current past a nonlinear porous stretching surface has been analysed numerically. The impact of thermal slip and chemical reaction are also examined in our current analysis. Runge–Kutta–Merson method and shooting method have been successfully employed to obtain numerical results for the governing nonlinear differential equations. The impact of Hartmann number, Hall parameter, porosity parameter, fluid parameter, Weissenberg number, Richardson number, concentration buoyancy parameter, Schmidt number, Dufour parameter, Soret number, Prandtl number, chemical reaction parameter, and power-law exponent are discussed and demonstrated graphically for the flow phenomena. Furthermore, the description for Sherwood number, rate of shear stress, and Nusselt number are displayed using tables against all the pertinent parameters. A detailed numerical comparison for the power-law exponent and Prandtl number has been elaborated via tables.

Unsteady reactive magnetic radiative micropolar flow, heat and mass transfer from an inclined plate with joule heating: a model for magnetic polymer processing

Abstract: Magnetic polymer materials processing involves many multi-physical and chemical effects. Motivated by such applications, in the present work a theoretical analysis is conducted of combined heat and mass transfer in unsteady mixed convection flow of micropolar fluid over an oscillatory inclined porous plate in a homogenous porous medium with heat source, radiation absorption and Joule dissipation. A first order homogenous chemical reaction model is used. The transformed non-dimensional boundary value problem is solved using a perturbation method and Runge-Kutta fourth order numerical quadrature (shooting technique). The emerging parameters dictating the transport phenomena are shown to be the gyro-viscosity micropolar material parameter, magnetic field parameter, permeability of the porous medium, Prandtl number, Schmidt number, thermal Grashof number, species Grashof number, thermal radiation-conduction parameter, heat absorption parameter, radiation absorption parameter, Eckert number, chemical reaction parameter and Eringen coupling number (vortex viscosity ratio parameter). The impact of these parameters on linear velocity, microrotation (angular velocity), temperature and concentration are evaluated in detail. Results for skin friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are also included. Couple stress is observed to be reduced with stronger magnetic field. Verification of solutions is achieved with earlier published analytical results.

Group theoretical analysis for MHD flow fields: a numerical result

Abstract: The physical phenomena having inhomogeneity subject to both the Newtonian and non-Newtonian fluid models yield the complex structured mathematical equations. It is well known that the exact solution in this direction is impossible. Therefore, the current pagination contains a systematic approach to present numerical solution of non-Newtonian fluid model. To be specific, the nonlinear mathematical problem is developed with the aid of fundamental laws involved in the field of fluid science. A group theoretic approach is implemented, and the obtained Lie point of transformation is used to step down the mathematical equations in terms of independent variables. The resultant system is solved by using shooting method conjectured with Runge–Kutta scheme. The impacts of involved parameters, namely power law index, magnetic field parameter, Weissenberg number, Prandtl number, Schmidt number, velocity slip parameter and thermal slip parameter are examined on dimensionless quantities in both the magnetized and non-magnetized flow fields. The obtained observations in this regard are provided by way of graphs. It is noticed that the fluid velocity is lesser in magnitude in a magnetized frame as compared to non-magnetized flow field.

Viscous Dissipation and Joule Heating Effects in Non-Fourier MHD Squeezing Flow, Heat and Mass Transfer Between Riga Plates with Thermal Radiation: Variational Parameter Method Solutions

Abstract: A Riga plate is an electromagnetic actuator which comprises permanent magnets and alternating electrodes placed on a plane surface. The present article investigates the influence of viscous and Joule heating (Ohmic dissipation) in the magnetohydrodynamic squeezing flow, heat and mass transfer between two Riga plates. A non-Fourier (Cattaneo–Christov) heat flux model is employed which generalizes the classical Fourier law to incorporate thermal relaxation time. Via suitable transformations, the governing partial differential conservation equations and boundary conditions are non-dimensionalized. The resulting nonlinear ordinary differential boundary value problem is well posed and is solved analytically by the variational parameter method (VPM). Validation of the solutions is included for the special case of non-dissipative flow. Extensive graphical illustrations are presented for the effects of squeeze parameter, magnetic field parameter, modified Hartmann number, radiative parameter, thermal Biot number, concentration Biot number, Eckert number, length parameter, Schmidt number and chemical reaction parameter on the velocity, temperature and concentration distributions. Additionally, the influence of selected parameters on reduced skin friction, Nusselt number and Sherwood number are tabulated. An error analysis is also included for the VPM solutions. Detailed interpretation of the results is provided. The study is relevant to smart lubrication systems in biomechanical engineering and sensor design.

Impact of homogeneous–heterogeneous reactions and non-Fourier heat flux theory in Oldroyd-B fluid with variable conductivity

Abstract: This article scrutinizes the influence of chemical reactions on flow of an Oldroyd-B fluid due to stretched cylinder. In vision of non-Fourier heat flux model, the heat transfer phenomenon is scrutinized. This enhanced constitutive model anticipates the time space upper-convected derivative which is recycled to depicting heat conduction mechanism. Additionally, heat transfer scrutiny is considered with the influence of thermal conductivity which is temperature dependent. Apposite conversions are engaged to acquire ODEs which are then deciphered analytically via homotopic approach. To highlight their physical consequences, the graphical portrayal of diverse considerations on velocity, temperature and concentration fields is depicted and conferred. It is scrutinized from this study that all the profiles are higher in the instance of the cylinder as equated to a flat plate. This scrutiny also reported that the thermal relaxation parameter decreases the temperature field while the Schmidt number and homogeneous response parameter display the conflicting performance on concentration field. In addition, an assessment in restrictive instance is also presented in this exploration, which ensures us that our outcomes are more precise.

Chemical Convection and Stratification in the Earth's Outer Core

Abstract: Convection in the Earth's outer core is driven by buoyancy sources of both thermal and compositional origin. The thermal and compositional molecular diffusivities differ by several orders of magnitude, which can affect the dynamics in various ways. So far, the large majority of numerical simulations have been performed within the codensity framework that consists in combining temperature and composition, assuming artificially enhanced diffusivities for both variables. In this study, we use a particle-in-cell method implemented in a 3D dynamo code to conduct a first qualitative exploration of pure compositional convection in a rotating spherical shell. We focus on the end-member case of infinite Schmidt number by totally neglecting the compositional diffusivity. We show that compositional convection has a very rich physics that deserves several more focused and quantitative studies. We also report, for the first time in numerical simulations, the self-consistent formation of a chemically stratified layer at the top of the shell caused by the accumulation of chemical plumes and blobs emitted at the bottom boundary. When applied to likely numbers for the Earth's core, some (possibly simplistic) physical considerations suggest that a stratified layer formed in such a scenario would be probably weakly stratified and may be compatible with magnetic observations.

Analysis of mixing performances in microchannel with obstacles of different aspect ratios

Abstract: In this study, the mixing performance and pressure drop characteristics have been numerically analyzed for flow through rectangular microchannel with obstacles in the walls arranged in a staggered ...

Darcy-Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo-Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions

Abstract: In the last decade, nanoparticles have provided numerous challenges in the field of science. The nanoparticles suspended in various base fluids can transform the flow of fluids and heat transfer characteristics. In this research work, the mathematical model is offered to present the 3D magnetohydrodynamics Darcy–Forchheimer couple stress nanofluid flow over an exponentially stretching sheet. Joule heating and viscous dissipation impacts are also discussed in this mathematical model. To examine the relaxation properties, the proposed model of Cattaneo–Christov is supposed. For the first time, the influence of temperature exponent is scrutinized via this research article. The designed system of partial differential equations (PDE’s) is transformed to set of ordinary differential equations (ODE’s) by using similarity transformations. The problem is solved analytically via homotopy analysis technique. Effects of dimensionless couple stress, magnetic field, ratio of rates, porosity, and coefficient of inertia parameters on the fluid flow in x- and y-directions have been examined in this work. The augmented ratio of rates parameter upsurges the velocity profile in the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, and couple stress parameter diminishes the velocity field along the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, ratio of rates parameter, and couple stress parameter reduces the velocity field along the y-axis. The influences of time relaxation, Prandtl number, and temperature exponent on temperature profile are also discussed. Additionally, the influences of thermophoresis parameter, Schmidt number, Brownian motion parameter, and temperature exponent on fluid concentration are explained in this work. For engineering interests, the impacts of parameters on skin friction and Nusselt number are accessible through tables.