Showing papers on "Schmidt number published in 2020"

Heat transport and nonlinear mixed convective nanomaterial slip flow of Walter-B fluid containing gyrotactic microorganisms

Abstract: Here nonlinear mixed convective nanoliquid slip flow of Walter-B fluid is addressed subject to stretched surface with gyrotactic microorganisms. The flow is generated via nonlinear stretched surface. Important slip mechanisms i.e., Brownian and thermophoresis diffusions are considered for the modeling of energy equation. Flow behavior is examined subject to nanofluid with gyrotactic microorganisms. Chemical reaction with activation energy is considered for the analysis of concentration. Suitable transformations leads to nonlinear ordinary differential system. Analytical solutions are made via built-in-Shooting and plotted graphically. The impacts of pertinent variables like viscoelastic parameter, Prandtl number, thermophoresis diffusion, Brownian motion, Chemical reaction, Schmidt number, bio-convection Lewis number, microorganisms concentration difference variable and bio-convection Peclet number on the velocity, temperature, concentration, motile density, skin friction coefficient, Nusselt number and Sherwood number. It is observed that temperature is more subject to higher estimations of Brownian motion and thermophoresis diffusion while decays versus higher values of Prandtl number. Concentration field decays versus higher values of Schmidt number and enhances by increasing the values of activation energy parameter.

A fractional and analytic investigation of thermo-diffusion process on free convection flow: an application to surface modification technology

Abstract: It is worth noted that soft and hard inchromizing entirely depends upon high temperature on materials. Due to this fact, thermal diffusion process can enhance the life expectancy of tools based on surface modification technology. The main objective of this investigation is to explore the thermo-diffusion effects on unsteady-free convection flow in the presence of magnetic field. For developing the governing equations of thermal diffusion process in terms of fractional differentiation, a modern approach of Atangana–Baleanu differential operator is invoked for knowing the memory effects on thermal diffusion process. The temperature, velocity, and concentration are obtained through analytical calculation via Laplace and Fourier sine transform methods. A parametric study is focused for hidden phenomenon of thermo-diffusion process which exhibits typical and rheological properties such as optimal temperature ranges, temperature resistance, increase or decrease of temperature, and few others. Finally, the characteristics of thermal diffusion process are presented graphically based on some physical parameters such as heat transfer (Grashof number), heat capacity (Prandtl number), enthalpy (Dufour number), momentum and mass diffusivity (Schmidt number), magnetization (magnetic field), and few other embedded parameters.

A rheological analysis of nanofluid subjected to melting heat transport characteristics

Abstract: This work focuses on the characteristics of heat sink–source and melting phenomena for time-dependent Falkner–Skan flow of Cross nanofluid. Additionally, stagnation point flow features are accounted. Modeling is based on thermophoresis diffusion and Brownian moment slip mechanisms. Zero mass flux condition is used at stretchable surface. Compact form of cross fluid equations are converted to component form by employing boundary layer concept. Appropriate transformations are engaged to give rise ODEs. Moreover, system of ODEs is tackled numerically. Detailed discussion for velocity, temperature, concentration, local Nusselt and Sherwood numbers is presented through graphs. Obtained statistical data reveals that velocity of cross nanoliquid boosts for larger melting and velocity ratio parameters. Intensification in Schmidt number corresponds to rise in concentration distribution.

Numerical study of slip and radiative effects on magnetic Fe3O4-water-based nanofluid flow from a nonlinear stretching sheet in porous media with Soret and Dufour diffusion

Abstract: Increasingly sophisticated techniques are being developed for the manufacture of functional nanomaterials. A growing interest is also developing in magnetic nanofluid coatings which contain magnetite nanoparticles suspended in a base fluid and are responsive to external magnetic fields. These nanomaterials are “smart” and their synthesis features high-temperature environments in which radiative heat transfer is present. Diffusion processes in the extruded nanomaterial sheet also feature Soret and Dufour (cross) diffusion effects. Filtration media are also utilized to control the heat, mass and momentum characteristics of extruded nanomaterials and porous media impedance effects arise. Magnetite nanofluids have also been shown to exhibit hydrodynamic wall slip which can arise due to non-adherence of the nanofluid to the boundary. Motivated by the multi-physical nature of magnetic nanomaterial manufacturing transport phenomena, in this paper, we develop a mathematical model to analyze the collective influence of hydrodynamic slip, radiative heat flux and cross-diffusion effects on transport phenomena in ferric oxide (Fe3O4-water) magnetic nanofluid flow from a nonlinear stretching porous sheet in porous media. Hydrodynamic slip is included. Porous media drag is simulated with the Darcy model. Viscous magnetohydrodynamic theory is used to simulate Lorentzian magnetic drag effects. The Rosseland diffusion flux model is employed for thermal radiative effects. A set of appropriate similarity transformation variables are deployed to convert the original partial differential boundary value problem into an ordinary differential boundary value problem. The numerical solution of the coupled, multi-degree, nonlinear problem is achieved with an efficient shooting technique in MATLAB symbolic software. The physical influences of Hartmann (magnetic) number, Prandtl number, Richardson number, Soret (thermo-diffusive) number, permeability parameter, concentration buoyancy ratio, radiation parameter, Dufour (diffuso-thermal) parameter, momentum slip parameter and Schmidt number on transport characteristics (e.g. velocity, nanoparticle concentration and temperature profiles) are investigated, visualized and presented graphically. Flow deceleration is induced with increasing Hartmann number and wall slip, whereas flow acceleration is generated with greater Richardson number and buoyancy ratio parameter. Temperatures are elevated with increasing Dufour number and radiative parameter. Concentration magnitudes are enhanced with Soret number, whereas they are depleted with greater Schmidt number. Validation of the MATLAB computations with special cases of the general model is included. Further validation with generalized differential quadrature (GDQ) is also included.

Study of Heat and Mass Transfer in MHD Flow of Micropolar Fluid over a Curved Stretching Sheet.

Abstract: A comprehensive investigation of mass and heat transfer in magnetohydrodynamics (MHD) flow of an electrically conducting non-Newtonian micropolar fluid because of curved stretching sheet is presented. Flow is originated by stretching of curved sheet by means of linear velocity. Concentration and energy equations are incorporated to study repercussion of mass and heat transfer. To define basic equations of the model, curvilinear coordinates are used. The transformed BL (boundary layer) equations for the momentum, concentration, angular momentum and temperature with appropriate boundary conditions are numerically solved by SOR (successive over relaxation) algorithms combined with the quasi-linearization technique. Flow features such as temperature fields, micro rotation, velocity and concentration are appraised for manipulation of pertinent parameters. The radius of curvature enhances the temperature and concentration whereas it declines micro-rotation as well as velocities of the fluid. It is significant to notice that magnetic field interaction is caused counterproductive in increasing concentration distribution and fluid temperature while diminishing micro-rotation and velocities at all domain flow points. As schmidt number increases concentration of fluid reduces.

Radiative mixed convection flow of maxwell nanofluid over a stretching cylinder with joule heating and heat source/sink effects.

Abstract: This work analyses thermal effect for a mixed convection flow of Maxwell nanofluid spinning motion produced by rotating and bidirectional stretching cylinder. Impacts of Joule heating and internal heat source/sink are also taken into account for current investigation. Moreover, the flow is exposed to a uniform magnetic field with convective boundary conditions. The modeled equations are converted to set of ODEs through group of similar variables and are then solved by using semi analytical technique HAM. It is observed in this study that, velocity grows up with enhancing values of Maxwell, mixed convection parameters and reduces with growing values of magnetic parameter. Temperature jumps up with increasing values of heat source, Eckert number, Brownian motion,thermophoresis parameter and jumps down with growing values of Prandtl number and heat sink. The concentration is a growing function of thermophoresis parameter and a reducing function of Brownian motion and Schmidt number.

Effect of radiation on thermosolutal Marangoni convection in a porous medium with chemical reaction and heat source/sink

Abstract: Thermosolutal Marangoni boundary layer flows are of great interest due to their applications in industrial applications such as drying of silicon wafers, thin layers of paint, glues, in heat exchangers, and crystal growth in space. The present analysis deals with the effect of chemical radiation and heat absorption/generation of the viscous fluid flow on a thermosolutal Marangoni porous boundary with mass transpiration and heat source/sink. The physical flow problem is mathematically modeled into Navier–Stokes equations. These nonlinear partial differential equations are then mapped into a set of nonlinear ordinary differential equations using similarity transformation. The analytical solutions for velocity, temperature, and concentration profiles are rigorously derived. The solutions so obtained are analyzed through various plots to demonstrate the effect of various physical parameters such as mass transpiration parameter Vc, inverse Darcy number Da−1, Marangoni number Ma, Schmidt number Sc, chemical reaction coefficient (K), Prandtl number (Pr), thermal radiation parameter (NR), and the heat source/sink parameter (I) on the momentum/thermal boundary, and their physical insights are also reported.

Chemically reactive MHD micropolar nanofluid flow with velocity slips and variable heat source/sink.

Abstract: The two-dimensional electrically conducting magnetohydrodynamic flow of micropolar nanofluid over an extending surface with chemical reaction and secondary slips conditions is deliberated in this article. The flow of nanofluid is treated with heat source/sink and nonlinear thermal radiation impacts. The system of equations is solved analytically and numerically. Both analytical and numerical approaches are compared with the help of figures and tables. In order to improve the validity of the solutions and the method convergence, a descriptive demonstration of residual errors for various factors is presented. Also the convergence of an analytical approach is shown. The impacts of relevance parameters on velocity, micro-rotation, thermal, and concentration fields for first- and second-order velocity slips are accessible through figures. The velocity field heightens with the rise in micropolar, micro-rotation, and primary order velocity parameters, while other parameters have reducing impact on the velocity field. The micro-rotation field reduces with micro-rotation, secondary order velocity slip, and micropolar parameters but escalates with the primary order velocity slip parameter. The thermal field heightens with escalating non-uniform heat sink/source, Biot number, temperature ratio factor, and thermal radiation factor. The concentration field escalates with the increasing Biot number, while reduces with heightening chemical reaction and Schmidt number. The assessment of skin factor, thermal transfer, and mass transfer are calculated through tables.

Caputo–Fabrizio fractional order model on MHD blood flow with heat and mass transfer through a porous vessel in the presence of thermal radiation

Abstract: In this article we propose a fractional order time derivative model on blood flow, heat and mass transfer through an arterial segment having interaction with magnetic field in the presence of thermal radiation and body acceleration. The study focuses on the unidirectional blood flow through porous medium vessel by treating non-Newtonian Casson fluid model. The mathematical model of Caputo–Fabrizio fractional derivative has been used and the problem is solved by employing the Laplace transform as well as finite Hankel transform method. The analytical expressions for blood flow velocity, temperature and concentration are obtained. The effects of order of the Caputo–Fabrizio fractional derivative, external magnetic field, Reynolds number, Darcy number, thermal radiation, Peclet number, Schmidt number are presented graphically. The study shows that the fractional order parameter has reducing effect on blood velocity, temperature and concentration as well as on the skin-friction coefficient and Nusselt number. Moreover, Hartmann number, thermal radiation and Soret effect play an important role in controlling wall shear stress, Nusselt number and Sherwood number respectively. More precisely these results bear the significant applications in biomedical Engineering and pathology.

Numerical study of self-similar natural convection mass transfer from a rotating cone in anisotropic porous media with Stefan blowing and Navier slip

Abstract: A mathematical model is presented for laminar, steady natural convection mass transfer in boundary layer flow from a rotating porous vertical cone in anisotropic high-permeability porous media The transformed boundary value problem is solved subject to prescribed surface and free stream boundary conditions with a Maple 17 shooting method Validation with a Chebyshev spectral collocation method is included The influence of tangential Darcy number, swirl Darcy number, Schmidt number, rotational parameter, momentum (velocity slip), mass slip and wall mass flux (transpiration) on the velocity and concentration distributions is evaluated in detail The computations show that tangential and swirl velocities are enhanced generally with increasing permeability functions (ie, Darcy parameters) Increasing spin velocity of the cone accelerates the tangential flow, whereas it retards the swirl flow An elevation in wall suction depresses both tangential and swirl flow However, increasing injection generates acceleration in the tangential and swirl flow With greater momentum (hydrodynamic) slip, both tangential and swirl flows are accelerated Concentration values and Sherwood number function values are also enhanced with momentum slip, although this is only achieved for the case of wall injection A substantial suppression in tangential velocity is induced with higher mass (solutal) slip effect for any value of injection parameter Concentration is also depressed at the wall (cone surface) with an increase in mass slip parameter, irrespective of whether injection or suction is present The model is relevant to spin coating operations in filtration media (in which swirling boundary layers can be controlled with porous media to deposit thin films on industrial components), flow control of mixing devices in distillation processes and also chromatographical analysis systems

Fractional characterization of fluid and synergistic effects of free convective flow in circular pipe through Hankel transform

Abstract: Although heat transfer by transient free convection has been investigated with different cross sections such as elliptical cones, rectangular or square ducts, and triangular plates, none of the analytical study of a circular cylinder in free space via fractional calculus approaches with sinusoidal conditions is explored. This manuscript presents fractional modeling of a circular cylinder to observe the heat transfer by transient free convection flow subject to the sinusoidal boundary conditions. The fractionalized mathematical model is solved via Hankel and Laplace transforms through two types of fractional calculus approaches called Atangana–Baleanu and Caputo–Fabrizio differential operators. The governing equations of the circular cylinder have been coupled for the sake of thermally interacting effects for knowing the hidden role of a particular geometry, viz., circular cylinder. In the literature, the analytic solutions for concentration, temperature, and velocity have been explored by means of Mittage–Leffler functions. The comparative investigation of heat transfer based on embedded rheological parameters such as the Prandtl number (Pr), Schmidt number (Sc), thermal Grashof number (Gr), and mass Grashof number (Gc) has been depicted as graphs via Atangana–Baleanu and Caputo–Fabrizio differential operators.

Mass transfer through a concentric-annulus microchannel driven by an oscillatory electroosmotic flow of a Maxwell fluid

Abstract: In this work we develop a theoretical analysis for the mass transfer of an electroneutral solute in a concentric-annulus microchannel driven by an oscillatory electroosmotic flow (OEOF) of a fluid whose behavior follows the Maxwell model. The annular microchannel connects two reservoirs that have different concentrations of the solute. For the mathematical modeling of the OEOF, we assume the Debye-Huckel approximation and that the wall zeta potentials of the micro-annulus can be symmetric or asymmetric. The governing equations are nondimensionalized, from which the following dimensionless parameters appear: an angular Reynolds number, the ratio of the wall zeta potentials of the annular microchannel, the electrokinetic parameter, the dimensionless gap between the two cylinders, the Schmidt number and the elasticity number. The results indicate that the velocity and concentration distributions across the annular microchannel become non-uniform as the angular Reynolds number increases, and depend notably on the elasticity number. It is also revealed that with a suitable combination of values of the elasticity number and gap between the two cylinders, together with the angular Reynolds number, the total mass transport rate can be increased and the species separation can be controlled.

Heat and mass transfer of fractional second grade fluid with slippage and ramped wall temperature using Caputo-Fabrizio fractional derivative approach

Abstract: Unsteady free convection slip flow of second grade fluid over an infinite heated inclined plate is discussed. The effects of mass diffusions in the flow are also eligible. Caputo-Fabrizio fractional derivative is used in the constitutive equations of heat and mass transfer respectively. Laplace transform is utilized to operate the set of fractional governing equations for both ramped and stepped wall temperature. Expression for Sherwood number and Nusselt number with non-integer order are found by differentiating the analytical solutions of fluid concentration and temperature. Numerical results of Sherwood number, Nusselt number and skin friction are demonstrated in tables. Solutions are plotted graphically to analyze the impact of distinct parameters i.e. Caputo-Fabrizio fractional parameter, second grade parameter, slip parameter, Prandtl number, Schmidt number, thermal Grashof number and mass Grashof number to observe the physical behavior of the flow.

Instabilities driven by diffusio-phoretic flow on catalytic surfaces

Abstract: We theoretically and numerically investigate the instabilities driven by diffusiophoretic flow, caused by a solutal concentration gradient along a reacting surface. The important control parameter is the Peclet number Pe, which quantifies the ratio of the solutal advection rate to the diffusion rate. First, we study the diffusiophoretic flow on a catalytic plane in two dimensions. From a linear stability analysis, we obtain that for Pe larger than 8pi, mass transport by convection overtakes that by diffusion, and a symmetry-breaking mode arises, which is consistent with numerical results. For even larger Pe, non-linear terms become important. For Pe larger than 16pi, multiple concentration plumes are emitted from the catalytic plane, which eventually merges into a single larger one. When Pe is even larger, there are continuous emissions and merging events of the concentration plumes. This newly-found flow state reflects the non-linear saturation of the system. The critical Peclet number for the transition to this state depends on Schmidt number Sc. In the second part of the paper, we conduct three-dimensional simulations for spherical catalytic particles, and beyond a critical Peclet number again find continuous plume emission and plume merging, now leading to chaotic motion of the phoretic particle. Our results thus help to understand the experimentally observed chaotic motion of catalytic particles in the high Pe regime.

Adomain computation of radiative-convective bi-directional stretching flow of a magnetic non-Newtonian fluid in porous media with homogeneous-heterogeneous reactions

Abstract: In the present communication, laminar, incompressible, hydromagnetic flow of an electrically conducting non-Newtonian (Sisko) fluid over a bi-directional stretching sheet in a porous medium is studied theoretically. Thermal radiation flux, homogeneous-heterogeneous chemical reactions and convective wall heating are included in the model. Darcy’s model is employed for the porous medium and Rosseland’s model for radiation heat transfer. The governing partial differential equations for mass, momentum, energy and concentration are reduced into ordinary differential equations via similarity transformations. The resultant nonlinear ordinary differential equations with transformed boundary conditions are then solved via the semi-analytical Adomain decomposition method (ADM). Validation with earlier studies is included for the non-radiative case. Extensive visualization of velocity, temperature and species concentration distributions for various emerging parameters is included. Increasing magnetic field and inverse permeability parameter are observed to decelerate both the primary and secondary velocity magnitudes whereas they increase temperatures in the regime. Increasing sheet stretching ratio weakly accelerates the primary flow throughout the boundary layer whereas it more dramatically accelerates the secondary flow near sheet surface. Temperature is consistently reduced with increasing stretching sheet ratio whereas it is strongly enhanced with greater radiative parameter. With greater Sisko non-Newtonian power-law index the primary velocity and temperature are decreased whereas the secondary velocity is increased. Increasing both homogenous and heterogenous chemical reaction parameters is found to weakly and more strongly, respectively, deplete concentration magnitudes whereas greater Schmidt number enhances them. Primary and secondary skin friction and Nusselt number profiles are also computed. The study is relevant to electro-conductive (magnetic polymer) materials processing operations.

Internal energy change and activation energy effects on Casson fluid

Abstract: This paper examines the steady-state momentum heat and mass transfer flow of a Casson fluid flow in the existence of a pre-exponential factor. The velocity of the fluid over a vertical stretched pin changes linearly with the axial distance when a Casson model is supposed for the viscosity. A similarity transformation eases the Navier–Stokes partial differential equations that are converted into ordinary differential equations and solved numerically for concentration, velocity, and temperature fields. Moreover, viscosity and conductivity are assumed to be dependent on the temperature profile. Results are discussed for two boundary conditions of the pin, while diffusivity is dependent on concentration. A reaction in the form of a pre-exponential factor is taken on the surface of the pin. Parameters such as the mixed convection parameter, viscosity parameter, and viscoelastic parameter are considered for the control of the flow field. In addition, the internal energy change and the Prandtl number are found to examine the temperature field inside the stretched pin, while the Schmidt number, temperature relative parameter, concentration buoyancy parameter, activation energy parameter, and chemical reaction parameter control the concentration field.This paper examines the steady-state momentum heat and mass transfer flow of a Casson fluid flow in the existence of a pre-exponential factor. The velocity of the fluid over a vertical stretched pin changes linearly with the axial distance when a Casson model is supposed for the viscosity. A similarity transformation eases the Navier–Stokes partial differential equations that are converted into ordinary differential equations and solved numerically for concentration, velocity, and temperature fields. Moreover, viscosity and conductivity are assumed to be dependent on the temperature profile. Results are discussed for two boundary conditions of the pin, while diffusivity is dependent on concentration. A reaction in the form of a pre-exponential factor is taken on the surface of the pin. Parameters such as the mixed convection parameter, viscosity parameter, and viscoelastic parameter are considered for the control of the flow field. In addition, the internal energy change and the Prandtl number are found t...

Hydrodynamics rheological impact of an oscillatory electroosmotic flow on a mass transfer process in a microcapillary with a reversible wall reaction

Abstract: In this work, we carry out a theoretical analysis of the mass transport rate through a long microcapillary, with a reactive wall, connecting two reservoirs with different concentrations of some electro-neutral solute, caused by an oscillatory electroosmotic flow of a Jeffreys fluid. The mass transport enhancement relative to that caused only by molecular diffusion is found to be a function of the following dimensionless parameters: the angular Reynolds number Rω; the Deborah numbers De1 and De2, associated with the relaxation and retardation times, respectively; the Schmidt number Sc; the Damkohler number Da; the partition number σ; the tidal displacement ΔZ; and the ratio between the radius of the microcapillary and the Debye length κ. We find that for a viscoelastic fluid, there exists a resonant behavior of the mass transfer rate when the angular Reynolds number assumes specific values. In this context, we evidence that the interaction between the fluid elasticity and the oscillatory character of the flow enhances the mass transfer rate up to several orders of magnitude compared with that caused by an oscillatory electroosmotic flow of a Newtonian fluid. We also found that the microcapillary wall’s reactive characteristics, manifested through the Damkohler number and the dimensionless partitioning coefficient, could enhance or diminish the mass transfer rate depending on the interplay of the other dimensionless parameters involved in the analysis.

Ferro-advection aided evaporation kinetics of ferrofluid droplets in magnetic field ambience

Abstract: The present article discusses the physics and mechanics of evaporation of pendant, aqueous ferrofluid droplets, and modulation of the same by an external magnetic field. We show experimentally and by mathematical analysis that the presence of a horizontal magnetic field augments the evaporation rates of pendant ferrofluid droplets. First, we tackle the question of improved evaporation of the colloidal droplets compared to water and propose physical mechanisms to explain the same. Experiments show that the changes in evaporation rates aided by the magnetic field cannot be explained on the basis of changes in surface tension or based on classical diffusion driven evaporation models. Probing via particle image velocimetry shows that the internal advection kinetics of such droplets plays a direct role toward the augmented evaporation rates by modulating the associated Stefan flow. Infrared thermography reveals changes in thermal gradients within the droplet and evaluating the dynamic surface tension reveals the presence of solutal gradients within the droplet, both brought about by the external field. Based on the premise, a scaling analysis of the internal magneto-thermal and magneto-solutal ferroadvection behavior is presented. The model incorporates the role of the governing Hartmann number, the magneto-thermal Prandtl number, and the magneto-solutal Schmidt number. The analysis and stability maps reveal that the magneto-solutal ferroadvection is the more dominant mechanism, and the model is able to predict the internal advection velocities with accuracy. Furthermore, another scaling model to predict the modified Stefan flow is proposed and is found to accurately predict the improved evaporation rates.

Numerical simulation of the combined effects of thermophoretic motion and variable thermal conductivity on free convection heat transfer

Abstract: In the current research, the effect of thermophoretic motion combined with temperature-dependent thermal conductivity on natural convection flow around the surface of a sphere at several circumferential locations has been presented. The modeled nonlinear governing partial differential has been transformed into a dimensionless form with the help of appropriate non-dimensional variables. Later, the finite difference method is applied to solve the proposed model. The effect of controlling parameters, such as thermal conductivity variation parameter γ, Prandtl number Pr, Schmidt number Sc, thermophoretic coefficient k, and thermophoresis parameter Nt on the velocity field, temperature distribution, mass concentration, skin friction, rate of heat transfer, and rate of mass transfer has been highlighted. The estimations of the emerging parameters on the physical properties are displayed in graphical and in tabular forms. It has been predicted that the rise in γ, Nt, Sc, Pr, and k increases the velocity distribution, but the reverse behavior has been seen in the temperature field. The enhancement in Nt, Sc, Pr, and k boosts up the curves of mass concentration, and the rise in γ suppresses the concentration function. It has been observed that an increase in γ reduces the skin friction and the rate of mass transfer but opposite behavior of the rate of heat transfer occurs. Furthermore, increasing values of Sc cause the skin friction to lose the dominance in the rate of heat and mass transfer. It has been also noticed that increasing values of Nt strengthen the skin friction and rate of heat transfer, and attenuation occurs in the case of the rate of mass transfer.

Analysis of chemically reactive species with mixed convection and Darcy–Forchheimer flow under activation energy: a novel application for geothermal reservoirs

Abstract: In the present article, an analysis has been performed to discuss the impact of steady mixed convection with Darcy–Forchheimer flow towards linear surface. Investigation has been achieved in the presence of Arrhenius activation energy and radiative heat flux which are associated with the heat and mass transport analysis which has not been performed so far. Porous media features are elaborated by utilizing Darcy–Forchheimer relation. Boundary-layer idea is employed for the simplification of governing expressions. The resulting set of mathematical expression is now solved with the help of bvp4c MATLAB package which applies a three-stage Lobatto IIIa finite-difference collocation scheme. Diagrams are drawn against pertinent parameters such as buoyancy forces ratio parameter, mixed convection parameter, porosity parameter, local inertia coefficient, activation energy, chemical reaction rate constant, Schmidt number, temperature difference ratio, exponentially fitted constant, magnetic parameter, radiation parameter, first-order and second-order slip parameter, suction or injection parameter and Prandtl number. It is observed that both mixed convection and activation energy parameters have an opposite impact on species profile. Also the present results are compared with those available in the literature for some cases, and an excellent agreement is found between them.

Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary.

Abstract: A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

Solute transport and reaction in porous electrodes at high Schmidt numbers

Abstract: We present lattice Boltzmann pore-scale numerical simulations of solute transport and reaction in porous electrodes at a high Schmidt number, Sc=10^2. The three-dimensional geometry of real materials is reconstructed via X-ray computed tomography. We apply a volume-averaging upscaling procedure to characterise the microstructural terms contributing to the homogenised description of the macroscopic advection–reaction–dispersion equation. We firstly focus our analysis on its asymptotic solution, while varying the rate of reaction. The results confirm the presence of two working states of the electrodes: a reaction-limited regime, governed by advective transport, and a mass-transfer-limited regime, where dispersive mechanisms play a pivotal role. For all materials, these regimes depend on a single parameter, the product of the Damkohler number and a microstructural aspect ratio. The macroscopic dispersion is determined by the spatial correlation between solute concentration and flow velocity at the pore scale. This mechanism sustains reaction in the mass-transfer-limited regime due to the spatial rearrangement of the solute transport from low-velocity to high-velocity pores. We then compare the results of pre-asymptotic transport with a macroscopic model based on effective dispersion parameters. Interestingly, the model correctly represents the transport at short characteristic times. At longer times, high reaction rates mitigate the mechanisms of heterogeneous solute transport. In the mass-transfer-limited regime, the significant yet homogeneous dispersion can thus be modelled via an effective dispersion. Finally, we formulate guidelines for the design of porous electrodes based on the microstructural aspect ratio.

Numerical analysis of time-dependent flow of viscous fluid due to a stretchable rotating disk with heat and mass transfer

Abstract: In this paper we studied the time-dependent viscous fluid flow due to a rotating stretchable disk. Fluid filling porous medium. Darcy’s law is used for description of porous medium. Moreover, the effect of chemical reaction and heat generation/absorption are considered in concentration and temperature equations respectively. Governing PDE’s system is reduced to dimensionless form by appropriate parameters. Finite difference method is used to solve the dimensionless PDE’s system. Behaviors of pertinent variables on temperature, velocity, mass and heat transfer rates are shown through graphs. Obtained results guarantee that velocity decreases for porosity parameter. Temperature increases for higher Prandtl number and heat generation. Concentration decreases for larger Schmidt number and chemical reaction parameter.

Impacts of temperature-dependent viscosity and variable Prandtl number on forced convective Falkner–Skan flow of Williamson nanofluid

Abstract: Fluid viscosity is considered as constant in several boundary layer analyses, but this fluid property can change remarkably when the temperature difference exists in the boundary layer. The Prandtl number and Schmidt number can also change significantly as the fluid viscosity changes depending on temperature. Therefore, this framework is exploring the consequences of varying viscosity and varying Prandtl number on Falkner–Skan flow of Williamson nanofluid over a wedge, plate and stagnation point. The Buongiorno nanofluid model has been employed to manifest the fluid transport properties of the Williamson nanofluid. Similarity transformations are utilized to transform the governing equations into ordinary differential equation and solved numerically using Runge–Kutta (RK) Fehlberg method. Williamson fluid velocity, temperature, concentration, skin friction factor, rate of heat transfer and rate of mass transfer are investigated with emerging parameters, and the outcomes are presented graphically. Computed results manifest that the Williamson nanofluid expresses the opposite nature in velocity and temperature for higher values of Weissenberg number parameter. Positive values of variable viscosity parameter diminish the significance of variable Prandtl number and variable Schmidt number in the boundary layer. Furthermore, it is noticed that the Williamson nanofluid temperature is higher over a plate compared with wedge and stagnation point cases.

Inspection of Coriolis and Lorentz forces in nanomaterial flow of non-Newtonian fluid with activation energy

Abstract: The main purpose of this article is to investigate the flow of third grade nanofluid due to rotating stretchable disk. Moreover, the effects of magnetohydrodynamic, nonlinear thermal radiation, Joule heating, activation energy, thermophoresis and Brownian movement are also accounted. By appropriate transformation transformed the governing PDE’s into ODE’s. The arising ODE’s are solved analytically by means of homotopy analysis method. The effects of different flow variables on temperature, velocities, concentration, skin frictions, Nusselt and Sherwood numbers are captured and analyzed graphically. The obtained results show that velocity is a decreasing function of material parameters as well as Hartmann number (magnetic parameter). Temperature increased with Brownian motion variables, thermal radiation parameter and thermophoresis parameter. Concentration reduced through chemical reaction and Schmidt number while enhanced with thermophoresis parameter, fitted rate constant and activation energy.