Concentration Boundary Layer Thickness Research Articles

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

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

RADIATION EFFECT ON MHD STAGNATION-POINT FLOW OF A NANOFLUID OVER A NONLINEAR STRETCHING SHEET WITH CONVECTIVE BOUNDARY CONDITION

The effect of radiation on the MHD stagnation-point fl ow of a nanofluid over a nonlinear stretching sheet with convective boundary condition is investigated numerically. A small magnetic Reynolds number and Rossel and approximation are also assumed in this study where the sheet is stretched with a power law velocity in the presence of a nonuniform magnetic field applied in the y direction normal to the fl ow on the sheet. A highly nonlinear problem is modeled using the modified Bernoulli equation for an electrically conducting nano fluid. The momentum, thermal, and concentration boundary-layer thicknesses are intensified with increasing values of the velocity ratio parameter. By using appropriate similarity transformation, the system of nonlinear partial differential equations is reduced to ordinary differential equations. These equations subjected to the boundary conditions are solved numerically using the Keller-box method. Numerical results are plotted and discussed for pertinent flow parameters. A comparison with previous results given in the literature is also made.

Unsteady Natural Convective Flow over an Impulsively Started Semi-Infinite Vertical Plate in the Presence of Porous Medium with Chemical Reaction

An investigation is carried out to analyze the effects of heat and mass transfer over an impulsively started vertical plate in the presence of porous medium with chemical reaction. The unsteady, non-linear, coupled partial differential equations are solved by implicit finite difference scheme of Crank Nicolson type. The influence of various parameters like Prandtl number, Schmidt number, first order chemical reaction on the velocity, temperature and concentration are analyzed. The local skin friction, local Nusselt number, local Sherwood number, average skin friction, average Nusselt number and average Sherwood numbers are investigated. It is observed that the velocity and concentration boundary layer decreases with increasing chemical reaction. An increase in the Schmidt number reduces the concentration boundary layer thickness.

Thermo Diffusion and Hall Current Effects on an Unsteady Flow of a Nanofluid under the Influence of Inclined Magnetic Field

In this paper, we investigated the effects of hall current and thermal diffusion on an unsteady flow of a nanofluid in the presence of inclined magnetic field and volume fraction of nanoparticles. We considered copper nanoparticles with base fluid as water and presented dual solutions for water and Cu-water cases. An analytical solution of the problem was performed using perturbation technique. The effects of various non-dimensional governing parameters on velocity, temperature and concentration fields along with the friction factor, local Nusselt and Sherwood numbers are discussed and presented through graphs and tables. To validate the results of the present study we compared the present results with the existed results and found an excellent agreement. Moreover, through this study we observed that an increase in the Hall current parameter increases the velocity profiles and depreciates the friction factor. It is also observed that an increase in Soret number causes to enhance the velocity and concentration boundary layer thicknesses.

Slip Effect on an Unsteady MHD Stagnation-Point Flow of a Micropolar Fluid towards a Shrinking Sheet with Thermophoresis Effect

The effect of slip and thermophoresis on an unsteady magnetohydrodynamic stagnation-point-flow micropolar fluid with heat and mass transfer towards a shrinking sheet has been investigated. The governing equations are reduced to a system of non-dimensional partial differential equations by using similarity transformation, before being solved numerically using the Keller-box method. The effects of various physical parameters on the velocity, microrotation, temperature, and concentration profiles as well as the reduced skin friction, the reduced Nusselt number, and the reduced Sherwood number are analyzed and discussed graphically. It is found that the concentration boundary layer thickness decreases with increasing values of the thermophoresis. Comparison with previously published results under the limiting cases is made and found to be in excellent agreement.

Investigation of Gas Seeding for Planar Laser-Induced Fluorescence in Hypersonic Boundary Layers

Numerical simulations of the gas-seeding strategies required for planar laser-induced fluorescence in a Mach 10 (approximately Mach 8.2 postshock) airflow were performed. The work was performed to understand and quantify the adverse effects associated with gas seeding and to assess various types of seed gas that could potentially be used in future experiments. In prior experiments, NO and NO2 were injected through a slot near the leading edge of a flat-plate wedge model used in NASA Langley Research Center’s 31 in. Mach 10 air tunnel facility. In this paper, nitric oxide, krypton, and iodine gases were simulated at various injection rates. Simulations showing the deflection of the velocity boundary layer for each of the cases are presented. Streamwise distributions of velocity and concentration boundary-layer thicknesses, as well as vertical distributions of velocity, temperature, and mass distributions, are presented for each of the cases. A comparison between simulated streamwise velocity profiles and experimentally obtained molecular tagging velocimetry profiles using a nitric oxide seeding strategy is performed to verify the influence of such a strategy on the boundary layer. The relative merits of the different seeding strategies are discussed. The results from a custom solver based on OpenFOAM version 2.2.1 are compared against results obtained from ANSYS® Fluent version 6.3.

Dual solutions for MHD stagnation-point flow of a nanofluid over a stretching surface with induced magneticfield

Present study deals with the buoyancy-driven MHD mixed convection stagnation-point flow, heat and mass transfer of a nanofluid over a non-isothermal stretching sheet in presence of induced magneticfield, radiation, chemical reaction, suction/injection and heat source/sink. The basic governing partial differential equations are reduced to a set of ordinary differential equations by using appropriate similarity transformation. The resulting system is solved numerically by bvp5c Matlab package. Numerical results are validated by comparing with the published results. The influence of non-dimensional governing parameters on velocity, induced magneticfield, temperature and concentration profiles along with coefficient of skin friction, local Nusselt and Sherwood numbers are discussed and presented with the help of graphs and tables. Comparisons are made with the existed studies. Results indicate that dual solutions exists only for certain range of suction/ injection parameter and injection parameter have tendency to enhance the momentum, thermal and concentration boundary layer thickness.

Unsteady convective heat and mass transfer in pseudoplastic nanofluid over a stretching wall

In this article, unsteady boundary layer flow of a power-law nanofluid over a stretching surface with a convective boundary condition is investigated numerically. A power-law model that incorporates the effects of Brownian motion and thermophoresis is used for non-Newtonian nanofluids. A set of similarity transformation is used to reduce Navier–Stokes, energy and nanoparticles concentration equations to a set of nonlinear ordinary differential equations which are then solved numerically by using a fourth order Runge–Kutta scheme coupled with a conventional shooting procedure. The effects of unsteadiness, suction/injection parameters, the generalized Prandtl and Lewis numbers and convective parameter on skin friction coefficient and reduced Nusselt number are investigated. Comparison with previously published work is performed and excellent agreement is observed for the limited case of existing literature. Numerical results show that dimensionless nanofluid concentration increases with the unsteadiness parameter whereas the values of dimensionless velocity and temperature decrease with it. Also, it is found that the effects of the unsteadiness parameter on the velocity boundary layer thickness are more pronounced compared to the concentration and temperature boundary layer thicknesses.

Unsteady MHD boundary layer stagnation point flow with heat and mass transfer in nanofluid in the presence of mass fluid suction and thermal radiation

The unsteady boundary layer stagnation point flow of heat and mass transfer in a nanofluid with magnetic field and thermal radiation is theoretically investigated. The resulting governing equations are nondimensionalized and are transformed using a similarity transformation and then solved numerically by the shooting method. Comparison with the previously published work is presented and the results are found to be in good agreement. The effects of unsteadiness parameter A , solid volume fraction \( \varphi\), magnetic field M, radiation parameter R, Schmidit number Sc and suction parameter w on the fluid flow, heat and mass transfer characteristic are discussed. Dual similarity solutions for the velocity, temperature and concentration profiles are obtained for some negative values of the unsteadiness parameter. It is found that the critical values of A for which the dual solution exists depend on the values of solid volume fraction parameter in the presence of the Schmidit number. Also, the magnetic field parameter as well as the mass fluid suction widen the range of A for which the solution exists. The results also indicate that momentum, thermal and concentration boundary layer thickness for the first solution are thinner than that of the second solution.

Reactive solute transfer in a stagnation-point flow over a shrinking sheet with a diffusive mass flux

Reactive solute transfer in a boundary-layer stagnation-point flow over a shrinking sheet with a uniform diffusive mass flux is investigated. The first-order chemical reaction is considered. By similarity transformations, the governing partial differential equations are converted into self-similar nonlinear ordinary differential equations. Then the transformed equations are solved numerically by using the shooting method. Dual solutions for the solute distribution are found. The study shows that the concentration at the point increases with increasing velocity ratio parameter for the first solution and decreases for the second solution. Due to an increase in the Schmidt number and reaction rate parameter, the concentration and concentration boundary layer thickness decrease in the presence of the mass flux.

Canopy macroalgae influence understorey corallines’ metabolic control of near-surface pH and oxygen concentration

Understorey macroalgae can alter pH at their surface via metabolic activity within the concentration boundary layer (CBL), but it is unknown to what degree the presence of larger macroalgal canopies can modify the pH micro-environment of understorey species. We examined whether flow reduction by a canopy-forming macroalga could alter the thickness of the CBL at the surface of understorey crustose coralline macroalgae (CCA). This could lead to a greater metabolic influence of macroalgae on the pH and oxygen environment at the coralline’s surface. Three experimental treatments were examined in a re-circulating flume: (1) a full canopy (consisting of Carpophyllum maschalocarpum ) and understorey ( Corallina officinalis and CCA), (2) a mimic (plastic/silk) canopy plus understorey, and (3) an understorey only. Profiles of seawater velocity and pH/O 2 concentration gradients were measured at 3 bulk seawater velocities (2, 4 and 8 cm s -1 ) above the CCA in both the light and dark. Canopy macroalgae altered the pH and O 2 environment encountered by understorey coralline algae via their physical presence rather than by directly altering bulk seawater chemistry through their metabolism. Reduced seawater velocities beneath Carpophyllum and mimic canopies resulted in increased CBL thicknesses, higher pH (up to 8.9) and O 2 concentrations in the light, and lower pH (down to 7.74) and O 2 concentrations in the dark. The ability of canopies to facilitate greater metabolic changes in pH at the surface of understorey species highlights a previously unrecorded species interaction that could play an important role in influencing the physiology and ecology of understorey assemblages.

Flow of Casson nanofluid with viscous dissipation and convective conditions: A mathematical model

The magnetohydrodynamic (MHD) boundary layer flow of Casson fluid in the presence of nanoparticles is investigated. Convective conditions of temperature and nanoparticle concentration are employed in the formulation. The flow is generated due to exponentially stretching surface. The governing boundary layer equations are reduced into the ordinary differential equations. Series solutions are presented to analyze the velocity, temperature and nanoparticle concentration fields. Temperature and nanoparticle concentration fields decrease when the values of Casson parameter enhance. It is found that the Biot numbers arising due to thermal and concentration convective conditions yield an enhancement in the temperature and concentration fields. Further, we observed that both the thermal and nanoparticle concentration boundary layer thicknesses are higher for the larger values of thermophoresis parameter. The effects of Brownian motion parameter on the temperature and nanoparticle concentration are reverse.

Flow Past a Sphere Buried in a Porous Media: Concentration Boundary Layer Thickness

In this work, consideration is given to the problem of dissolution of a buried solid sphere in the liquid flowing uniformly through the packed bed around it. The differential equations describing fluid flow and mass transfer by advection and diffusion in the interstices of the bed are presented and the method for obtaining their numerical solution is indicated.From the surface concentration fields, given by the numerical solution, the concentration boundary layer thickness as a function of the relevant parameters were undertaken. Mathematical expressions that relate the dependence with the Peclet number and d/d1 ratio of an immersed active sphere are proposed to describe the approximate size of the concentration boundary layer thickness.

Convective heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with heat source

Heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface were addressed. Analysis was performed in the presence of internal heat generation/absorption. Concentration and thermal buoyancy effects were accounted. Convective boundary conditions for heat and mass transfer analysis were explored. Series solutions of the resulting problem were developed. Effects of mixed convection, internal heat generation/absorption parameter and Biot numbers on the dimensionless velocity, temperature and concentration distributions were illustrated graphically. Numerical values of local Nusselt and Sherwood numbers were obtained and analyzed for all the physical parameters. It is found that both thermal and concentration boundary layer thicknesses are decreasing functions of stretching ratio. Variations of mixed convection parameter and concentration buoyancy parameter on the velocity profiles and associated boundary layer thicknesses are enhanced. Velocity profiles and temperature increase in the case of internal heat generation while they reduce for heat absorption. Heat transfer Biot number increases the thermal boundary layer thickness and temperature. Also concentration and its associated boundary layer are enhanced with an increase in mass transfer Biot number. The local Nusselt and Sherwood numbers have quite similar behaviors for increasing values of mixed convection parameter, concentration buoyancy parameter and Deborah number.

Analysis of Heat and Mass Transfer on MHD Flow of a Nanofluid Past a Stretching Sheet

In this work, a variational technique is applied to MHD, radiative nanofluid flow over a non-isothermal stretching sheet with Brownian motion and thermophoresis effects by Gyarmati's principle. The heat and mass transfer effects have been investigated and analyzed by this technique. The flow fields inside the boundary layer are approximated as polynomial functions. Euler-Lagrange equations for the functional of variational principle are constructed. The non-linear boundary layer equations are simplified as simple polynomial equations in terms of momentum, thermal and concentration boundary layer thicknesses. The temperature, concentration profiles, local heat and mass transfer rates are analyzed and are compared with existing numerical results. The comparison shows remarkable accuracy.

Concentration Boundary Layer in Membrane Degumming: A CFD Model and Neural Network Approach

The use of crude vegetable oils without degumming, during biodiesel production, might decrease the conversion rate and be difficult to separate glycerol from biodiesel. Ultrafiltration is promising technology for gum removal from crude vegetable oils. However, since the oil constituents have very close molecular weight, degumming process by membrane is relatively difficult. In order to understand the membrane degumming process of corn-oil, a prediction of concentration boundary layer thickness was calculated using a CFD model. An artificial neural network is developed to learn the relationship between Reynolds and Schmidt numbers of feed solution which affects the boundary layer thickness along the membrane tube.

Three-dimensional flow of an Oldroyd-B nanofluid towards stretching surface with heat generation/absorption.

This article addresses the steady three-dimensional flow of an Oldroyd-B nanofluid over a bidirectional stretching surface with heat generation/absorption effects. Suitable similarity transformations are employed to reduce the governing partial differential equations into coupled nonlinear ordinary differential equations. These nonlinear ordinary differential equations are then solved analytically by using the homotpy analysis method (HAM). Graphically results are presented and discussed for various parameters, namely, Deborah numbers and , heat generation/absorption parameter Prandtl parameter , Brownian motion parameters, thermophoresis parameter and Lewis number . We have seen that the increasing values of the Brownian motion parameter and thermophoresis parameter leads to an increase in the temperature field and thermal boundary layer thickness while the opposite behavior is observed for concentration field and concentration boundary layer thickness. To see the validity of the present work, the numerical results are compared with the analytical solutions obtained by Homotopy analysis method and noted an excellent agreement for the limiting cases.

Effect of thermal radiation on magnetohydrodynamics nanofluid flow and heat transfer by means of two phase model

In this study, effect of thermal radiation on magnetohydrodynamics nanofluid flow between two horizontal rotating plates is studied. The significant effects of Brownian motion and thermophoresis have been included in the model of nanofluid. By using the appropriate transformation for the velocity, temperature and concentration, the basic equations governing the flow, heat and mass transfer are reduced to a set of ordinary differential equations. These equations, subjected to the associated boundary conditions are solved numerically using the fourth-order Runge–Kutta method. The effects of Reynolds number, magnetic parameter, rotation parameter, Schmidt number, thermophoretic parameter, Brownian parameter and radiation parameter on heat and mass characteristics are examined. Results show that Nusselt number has direct relationship with radiation parameter and Reynolds number while it has reverse relationship with other active parameters. It can also be found that concentration boundary layer thickness decreases with the increase of radiation parameter.

Unsteady nanofluid flow and heat transfer in presence of magnetic field considering thermal radiation

In this study, heat and mass transfer characteristic of unsteady nanofluid flow between two parallel plates is investigated considering thermal radiation. Two phase model is considered in order to simulate nanofluid. The basic partial differential equations are reduced to ordinary differential equations which are solved numerically using the fourth-order Runge–Kutta method. The effects of the squeeze number, radiation parameter, Schmidt number, Brownian motion parameter, thermophoretic parameter and Eckert number on flow, heat and mass transfer are considered. Results indicate that concentration boundary-layer thickness increases with increase of Radiation parameter. Also it can be found that Nusselt number has direct relationship with Eckert number, Schmidt number, squeeze parameter and Radiation parameter.

Three dimensional flow of viscoelastic fluid by an exponentially stretching surface with mass transfer

Abstract Objective: This paper investigates the three-dimensional MHD flow of viscoelastic fluid with mass transfer over an exponentially stretching surface. Method: Nonlinear partial differential equations are reduced into ordinary differential equations by employing similarity variables. The corresponding nonlinear expressions for velocity and concentration are solved by homotopy analysis method. Results: Convergence analysis is performed graphically and numerically. Results for velocities, concentration and Sherwood number are displayed and discussed in detail. Conclusions: The momentum boundary layer thicknesses are reduced whereas the concentration boundary layer thickness is increased for the larger values of the Hartman number. The local Sherwood number is an increasing function of the Hartman number and viscoelastic parameter. Practice implications: Flows of non-Newtonian fluids have an extensive applications in the industry and technology, for example in petroleum drilling, manufacturing of foods and paper, polymers extrusion and many others.