Concentration Boundary Layer Thickness Research Articles

Analysis of entropy generation for MHD flow of third grade nanofluid over a nonlinear stretching surface embedded in a porous medium

The main focus of present research work is to elaborate magnetohydrodynamic flow of third grade nanofluid with activation energy and binary chemical reaction. Fluid flow is generated by a nonlinearly stretched surface. Temperature and nano-concentration distributions are analyzed in the presence of Brownian motion and thermophoresis effects. The effects of Joule heating, thermal radiation and porous medium are further investigated for current analysis. Thermodynamic second mechanism is utilized to explore entropy generation rate of the system. Newly developed condition having zero mass flux of nanoparticles at the boundary is also incorporated. Partial differential equations governing the flow problem has been converted into ordinary ones using appropriate similarity variables. Builtin Shooting technique via NDsolve has been used to construct the numerical solution of the resulting problem. Impacts of various physical flow parameters are presented graphically for temperature, nano-concentration, surface drag coefficient and rates of heat trasnfer and entropy generation. It is found that impacts of third grade parameters on the thermal and nano-concentration fields are quite similar. Temperature, concentration and associated layer thicknesses are reduced via higher third grade parameters. It is established that the magnetic field restricts the flow strongly and serves as a potent control mechanism. It can be concluded that an applied magnetic field will play a major role in applications like micropumps, actuators and biomedical sensors. The activation energy aspect reduces the concentration boundary layer thickness. Total entropy of the entire system increases against higher values temperature difference variable, Brinkman number, porosity parameter, radiation parameter and magnetic parameter.

SQLM for external yield stress effect on 3D MHD nanofluid flow in a porous medium

The aim of this paper is to study of the impact of yield stress and convective conditions on the 3D mixed convection magnetohydrodynamics boundary layer flow of two-phase Casson nanofluid past a stretching plate in a porous medium. The regulating partial differential equations are converted into a system of nonlinear ordinary differential equations with the proper boundary conditions by picking local similarity conversions, and is resolved numerically through the spectral quasi-linearization method with Maple 13.0 software. The implications of different parameters are demonstrated via tables and graphs for velocity, energy and nanoparticle volume distributions. Also, heat and mass transfer rates in diverse situations and the accessories of various parameters are scrutinized through tables. The results obtained are substantiated against the relevant numerical results in previously-published research. The external yield stress has a more significant influence on thermal boundary-layer thickness than on concentration boundary-layer thickness and improves the flow velocity in the same direction.

Free convection boundary layer flow on a solid sphere in a nanofluid with viscous dissipation

Present study considers the mathematical model of free convection boundary layer flow and heat transfer in a nanofluid over a solid sphere with viscous dissipation effect. The transformed partial differential equations are solved numerically using the Keller-box method. The numerical values for the reduced Nusselt number, reduced Sherwood number and the reduced local skin friction coefficient are obtained, as well as concentration profiles, temperature profiles and velocity profiles are illustrated graphically. Effects of the pertinent parameters, which are the Prandtl number, buoyancy ratio parameter, Brownian motion parameter, thermophoresis parameter, Lewis number and Eckert number are analyzed and discussed. It is found that the increase of Brownian motion parameter promoted the reduce of concentration boundary layer thickness while thermophoresis parameter did oppositely. It is worth mentioning that the results reported here are important for the researchers working in this area which can be used as a reference and comparison purposes in the future.

Thermo-Solutal Chemically Reacting Micropolar Fluid Past a Permeable Stretching Porous Sheet

The boundary layer flow, heat and mass transfer over a permeable stretching sheet due to a chemically reacting micropolar fluid with slip and convective boundary conditions have been analyzed. Transverse magnetic field clubbed with electric field is also considered for the sake of brevity. Governing nonlinear coupled PDEs are transformed to nonlinear ODEs with the use of suitable similarity transformation. However, analytical solutions to these transformed equations are not useful therefore; numerical solution is carried out using Runge-Kutta fourth order with shooting technique. The characteristics of the embedded parameters are obtained and presented through graphs. Validation of the proposed work with earlier established results are shown in tables and these are in good agreement. From the careful observation the major outcomes are: induced magnetic field decelerates the flow, enhances the thickness of thermal boundary layer temperature whereas applied electric field decelerates the thickness of thermal boundary layer. Both electric field and slip parameter accelerates the angular momentum. Temperature and concentration magnitudes are accelerated at the sheet with an increase of slip parameter. Furthermore, Schmidt number and first order chemical reaction reduces the concentration boundary layer thickness. PACS Number: 05.45-a; 05.70-Ce.

A treatment for contaminated interfaces and its application to study the hydrodynamics of a spherical bubble contaminated by surfactants

A numerical model for the contaminated interface is discussed, and then it is applied to investigate detailedly the interfacial surfactant concentration, the interfacial properties and the wake flow of a contaminated spherical bubble. For the present model, the surfactant molecules adsorbed on the bubble surface are assumed to be distributed over the concentration boundary layer adjacent to the bubble. The thickness of concentration boundary layer is obtained through the revised value from a theoretical formula. Then, the interfacial surfactant concentration is evaluated by coupling the transport equations of interfacial and bulk surfactant concentrations with the Navier-Stokes equations. The connection between the tangential stress and the interfacial surfactant concentration is set through the Marangoni stress and the state equation. The current results show that the present numerical model is reliable. The convention from the main flow, the Marangoni effect and the wake vortex determine the distribution of interfacial surfactant concentration on the bubble surface. The gradient of interfacial surfactant concentration along the bubble surface further affects the interfacial properties which react on the surrounding flow as feedbacks. The gradient of interfacial surfactant concentration at the front edge of the “contaminated” interface (FECI) is closely related to the location of FECI to the strongest convection position in the bulk around the bubble. The peak point on the curves of tangential stress and interfacial vorticity corresponds to the inflection point on the curve of interfacial surfactant concentration. The vortex size is affected by the positive pressure gradient at the bubble rear in bulk and the abrupt change of interfacial vorticity at FECI.

Thermal radiation and slip effects on magnetohydrodynamic (MHD) stagnation point flow of Casson fluid over a convective stretching sheet

Current study examines the combined effect of thermal radiation and velocity slip along a convective heated stretching sheet. magnetohydrodynamic (MHD) effect near the stagnation point is also under consideration. The main structure of partial differential equations attained in the form of momentum, energy and concentration equations. For a self-similar solution, the system of governing PDEs assimilated into the set of nonlinear ordinary differential equations by applying suitable similarity transformation. Resulting nonlinear ODEs are successfully solved via Runge-Kutta-Fehlberg method. All obtained unknown functions are discussed in detail after plotting the numerical results against different arising physical parameters. The validations of numerical results have been taken into account with two different numerical approaches and it is found to be in excellent agreement with the numerical results. The study reveals that concentration boundary layer thickness decreases by increasing the values of Schmidt number and increases by increasing the chemical reaction parameter.

Solute convection effects on a bubble entrapped as a pore during unidirectional upward solidification

A transport model is proposed to predict entrapment of a bubble during unidirectional upward solidification. Pore formation and its shape in solid influence not only microstructure of materials, but also contemporary issues of various sciences of biology, engineering, foods, geophysics and climate change, etc. In this study, COMSOL computer code is used to solve conservation equations of mass, momentum, energy and solute concentration in liquid, gas and solid phases satisfied by their interfacial conditions. It shows that strong convection deflects the pore growth toward the downstream direction. Time for bubble entrapment, however, depends on the ratio between square of concentration boundary layer thickness and solute diffusivity. Concentration boundary layer thickness is proportional to solute diffusivity divided by difference in bubble growth rate and vertical component of fluid velocity at the bubble cap. The latter is almost independent of incoming horizontal flow. Solute diffusion is therefore the mechanism responsible for bubble entrapment, where the bubble growth rate and vertical velocity component of fluid at the bubble cap are of the same order of magnitude. A triangle region with local high concentration is also found to occur in solid region near the triple-phase line. Predicted contact angle agrees with that obtained from the Abel’s equation of the first kind during solidification. This work provides a general model for a fundamental and systematical understanding of mechanisms of a bubble entrapped as a pore in solid.

Mathematical Modelling of Hydromagnetic Casson non-Newtonian Nanofluid Convection Slip Flow from an Isothermal Sphere

Abstract In this article, the combined magnetohydrodynamic heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid from an isothermal sphere surface with convective condition under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. magnetic parameter (M), Buoyancy ratio parameter (N), Casson fluid parameter (β), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr) and thermal slip (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Increasing viscoplastic (Casson) parameter decelerates the flow and also decreases thermal and nano-particle concentration. Increasing Brownian motion accelerates the flow and enhances temperatures whereas it reduces nanoparticle concentration boundary layer thickness. Increasing thermophoretic parameter increasing momentum (hydrodynamic) boundary layer thickness and nanoparticle boundary layer thickness whereas it reduces thermal boundary layer thickness. Increasing magnetohydrodynamic body force parameter decelerates the flow whereas it enhances temperature and nano-particle (species) concentrations. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

Magneto-hydrodynamics (MHD) Bioconvection Nanofluid Slip Flow over a Stretching Sheet with Thermophoresis, Viscous Dissipation and Brownian Motion

The bioconvection Magneto-Hydrodynamics (MHD) flow of nanofluid over a stretching sheet with velocity slip and viscous dissipation is studied. The governing nonlinear partial differential equations of the flow are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformation. These coupled ordinary differential equations are solved using fourth order Runge Kutta-Fehlberg integration method along with shooting technique. Solutions showing the effects of pertinent parameters on the velocity temperature, nanoparticles concentration, skin friction, Nusselt number and microorganism density are illustrated graphically and discussed. It is observed that there is enhancement of the motile microorganism density as thermal slip and Eckert number increase but microorganism density slip parameter have the opposite effect on the microorganism density. It is also found that an increase in Lewis number results in reduction of the volume fraction of nanoparticles and concentration boundary-layer thickness. Brownian motion, Nb and Eckert number, Ec decrease both local Nusselt number and local motile microorganism density but increases local Sherwood number. In addition, as the values of radiation parameter R increase, the thermal boundary layer thickness increases. Finally, thermophoresis parameter, Nt decreases both local Sherwood number, local Nuseselt number and local motile microorganism density. Comparisons of the present result with the previously published results show good agreement.

Heat and Mass Transfer of Magnetohydrodynamics (MHD) Boundary Layer Flow using Homotopy Analysis Method

Heat and mass transfer of MHD boundary-layer flow of a viscous incompressible fluid over an exponentially stretching sheet in the presence of radiation is investigated. The two-dimensional boundary-layer governing partial differential equations are transformed into a system of nonlinear ordinary differential equations by using similarity variables. The transformed equations of momentum, energy and concentration are solved by Homotopy Analysis Method (HAM). The validity of HAM solution is ensured by comparing the HAM solution with existing solutions. The influence of physical parameters such as magnetic parameter, Prandtl number, radiation parameter, and Schmidt number on velocity, temperature and concentration profiles are discussed. It is found that the increasing values of magnetic parameter reduces the dimensionless velocity field but enhances the dimensionless temperature and concentration field. The temperature distribution decreases with increasing values of Prandtl number. However, the temperature distribution increases when radiation parameter increases. The concentration boundary layer thickness decreases as a result of increase in Schmidt number

Numerical simulation for solar energy aspects on unsteady convective flow of MHD Cross nanofluid: A revised approach

A numerical analysis for unsteady magnetohydrodynamic (MHD) flow of Cross nanofluid subject to non-linear thermal radiation is carried out. The Buongiorno’s nanofluid model involving Brownian motion and thermophoresis is adopted. Two more realistic conditions namely convective condition and zero nanoparticles mass flux condition are implemented on the boundary. Mathematical problem is modelled with the aid of momentum, temperature as well as nanoparticles concentration equations adopting suitable transforming variables. The resulting highly nonlinear differential systems are solved numerically with the help of shooting Runge-Kutta-Fehlberg method. Numerical computations for Nusselt number as well as skin friction coefficient are performed. Variations of velocity, temperature as well as nanoparticles concentration profiles are examined by varying the involved parameters. A comparative analysis is conducted between existing study and present investigation in limiting case and found to be in excellent agreement. It is interesting to note that thermal as well as nanoparticles concentration boundary layer thicknesses are the upgrading functions of unsteadiness parameter. Additionally, rate of heat transfer is depreciated by upgrading the values of radiation parameter as well as thermophoresis parameter. Furthermore, the magnitude of wall shear stress is an enhancing function of the magnetic parameter. It is also noted that rate of heat transfer enhance with the enhancement of temperature ratio parameter as well as Biot number.

Entropy generation analysis for non-similar analytical study of nanofluid flow and heat transfer under the influence of aligned magnetic field

The present semi-analytical investigation covers the impact of aligned magnetic field, Ohmic dissipation and viscous dissipation on a non-similar nanofluid flow over a plate with no flux condition. The system of equations is transformed into the non-dimensional system of nonlinear partial differential equations to get solution using homotopy analysis method (HAM). The entropy generation analysis measuring disorderness of the system is also presented. The influence of physical parameters on momentum, temperature and concentration boundary layer thickness is discussed. The secondary variables (Cf,Nu) and entropy generation number (Ns) are also explored for present MHD model. The angle of inclination of magnetic field is found be controlling parameter for the minimization of skin friction.

Thermo diffusion effects on MHD Casson fluid flow over non-flatness stretching surface: Keller box method

ABSTRACT This paper numerically analyses thermo diffusion effects on MHD Casson fluid flow over a stretching sheet with variable thickness. Cattaneo–Christov heat flux model is imposed to predict the effects of thermal relaxation time. Similarity transformation is employed to normalise the governing boundary layer equations. Keller box method is applied to solve the system of equations. The behaviour of emerging parameters, such as Casson parameter (), Magnetic parameter (), power index (), variable viscosity parameter (), Prandtl number (), Soret number ( ) and Schmidt number () on velocity, temperature and concentration distributions, are discussed and analysed graphically. It is found that temperature profile decreases for large entries of thermal relaxation parameter. The concentration boundary layer thickness increases for large entries of Soret number.

Oscillating Electromagnetic Force Effect on Concentration Distribution near Liquid Solid Interface

Mass transfer near the reaction interface is often rate determining step in a high temperature process. Traditional agitation method reduces concentration boundary layer formed near the reaction interface from its outside by increasing the velocity in the bulk region. On the other hand, agitation in the concentration boundary layer is another way for intensification of the chemical reaction rate. For this purpose, excitation of flow in the concentration boundary layer is essential. Thus, effect of the static magnetic field on the solute concentration distribution near an electrode under the AC current imposition has been experimentally examined in this study. In the experiment, brightness near the interface between the copper electrode with the triangle shape and the mixed solution of 0.5mol/L CuSO4 aqueous solution with 0.1mol/L H2SO4 aqueous solution was measured under the imposition of the AC electrical current of 4Vp-p and 0.5Hz. And the aqueous solution motion was estimated using polystyrene particles. As the results, the concentration boundary layer thickness decreased and the AC current concentrated around the top of the lower electrode by imposing the static magnetic field.

(Invited) Development of Concentration Profile of Li+ Ion Accompanied with Electrodeposition of Li Metal in Solvated Ionic Liquid

Li metal is promising anode candidate for next-generation batteries because Li metal has very large specific capacity and Li/Li+ potential is the lowest. It is indispensable to control the surface morphological variation during cycles in order to utilize Li metal anode in next-generation batteries. In this study, the morphological variation of Li metal electrode in the electrodeposition is discussed from the viewpoint of Li+ ionic mass transfer rate in the vicinity of the electrode surface. In general, the metal electrodeposition and the morphology of electrodeposits are strongly affected by the electrode surface concentration. However, there are only a few researches focused on the relationship between the morphological variations of electrodeposited Li metal and the ionic mass transfer phenomenon. A digital holographic microscope (DHM) was utilized in order to visualize the Li+ concentration profile during the electrodeposition of Li metal. Our previous researches used a holographic interferometry to in-situ measure the surface concentration and concentration boundary layer thickness during the electrodeposition of Li metal. The principle of the technique is same, but the resolution of DHM was drastically improved. Figure 1 shows the DHM image in solvated ionic liquid electrolyte (LiTFSA:tetraglyme(G4) = 1:1). A working electrode was Cu plate, and a counter electrode was Li metal. Applied current density was 3.0 mA cm-2. The image was recorded at 100 seconds after the electrodeposition started. The color variation indicates the Li+ concentration profile near the working electrode, and the image shows that very uniform concentration profile was formed in this case (the precursor of Li dendrite was not detected.). Not only Li+ surface concentration but also concentration boundary layer thickness are focused to discuss the Li+ ionic mass transfer phenomenon. Especially, solvated ionic liquids are new electrolytes for batteries and then it is very important to understand the ionic mass transfer in the solvated ionic liquids. We would like to discuss the relationship between the morphological variations of electrodeposited Li metal and the developing the concentration profile in solvated ionic liquids systems. Figure 1

Chemical reaction and Newtonian heating effects on steady convection flow of a micropolar fluid with second order slip at the boundary

In this paper, asymptotic analysis of the chemical reaction and the Newtonian heating parameters is carried out. A mathematical model of a convective micropolar fluid flow over a permeable stretching/shrinking sheet is taken into account in the presence of the slip flow regime. A nonlinear system of transformed equations is solved by a semi-analytical technique called Homotopy Analysis Method (HAM). The current investigation is in a good agreement with the already published analytical and the numerical results with the help of tabular and graphical representations. In comparison with the stretching sheet, it is observed that the shrinking sheet produces a wider concentration boundary layer thickness by a small change in the chemical reaction parameter. In contrast to the stretching sheet, the Newtonian heating parameter raises the thermal boundary layer thickness by 39.93% for the shrinking sheet. The chemical reaction with the Newtonian heating effect is an important consideration in the solidification process of the liquid crystals and the polymeric suspensions.

Triple diffusive mixed convection from an exponentially decreasing mainstream velocity

Current paper deals with the numerical study on steady triple diffusive mixed convection boundary layer flow for exponentially decreasing external flow velocity in presence of suction/injection. Such exponentially decreasing external flows have specific applications in diverging channel flows. The temperature of the vertical surface is assumed to be higher compared to the surrounded fluid temperature. In the triple diffusive flow, the solutal components are chosen as Sodium chloride and Sucrose and the components are added in the flow stream from below with various concentration levels. The concentrations of NaCl-Water and Sucrose-Water are assumed to be lower within the free stream compared to the species concentrations of NaCl-Water and Sucrose-Water near the wall. The coupled nonlinear partial differential equations governing the flow, thermal and species concentration fields are transformed using the non-similarity variables and solved numerically by an implicit finite difference scheme with quasi-linearization technique. The effects of wall suction/injection, Richardson number, decelerating parameter, ratio of buoyancy parameters and Schmidt numbers of both the solutal components on the fluid flow, thermal and species concentration fields are analyzed and discussed. Results indicate that the thickness of the momentum boundary layer is lower for suction compared to injection for the buoyancy opposing flow. The decelerating parameter has significant impact on the flow fields. Also, the species concentration boundary layer thickness decreases with the increase of Schmidt numbers and that increases with the ratio of buoyancy parameters for both the species components. Overall, the mass transfer rate is found to increase with Schmidt numbers approximately 10% and 64% for NaCl and Sucrose, respectively.

Effect of thermal radiation and chemical reaction on non-Newtonian fluid through a vertically stretching porous plate with uniform suction

Abstract In this work, we discuss the unsteady flow of non-Newtonian fluid with the properties of heat source/sink in the presence of thermal radiation moving through a binary mixture embedded in a porous medium. The basic equations of motion including continuity, momentum, energy and concentration are simplified and solved analytically by using Homotopy Analysis Method (HAM). The energy and concentration fields are coupled with Dankohler and Schmidt numbers. By applying suitable transformation, the coupled nonlinear partial differential equations are converted to couple ordinary differential equations. The effect of physical parameters involved in the solutions of velocity, temperature and concentration profiles are discussed by assign numerical values and results obtained shows that the velocity, temperature and concentration profiles are influenced appreciably by the radiation parameter, Prandtl number, suction/injection parameter, reaction order index, solutal Grashof number and the thermal Grashof. It is observed that the non-Newtonian parameter H leads to an increase in the boundary layer thickness. It was established that the Prandtl number decreases thee thermal boundary layer thickness which helps in maintaining system temperature of the fluid flow. It is observed that the temperature profiles higher for heat source parameter and lower for heat sink parameter throughout the boundary layer. Fromm this simulation it is analyzed that an increase in the Schmidt number decreases the concentration boundary layer thickness. Additionally, for the sake of comparison numerical method (ND-Solve) and Adomian Decomposition Method are also applied and good agreement is found.

Combined effects of Brownian motion and thermophoresis parameters on three-dimensional (3D) Casson nanofluid flow across the porous layers slendering sheet in a suspension of graphene nanoparticles

The present study emphases on the three-dimensional (3D) Casson nanofluid flow across a slendering sheet in porous layers by considering the thermophoresis and Brownian motion effect. The proposed mathematical model has a tendency to characterise the effect of the non-uniform heat source/sink. In the present simulation, the graphene–water-based nanoparticles have been used at two different temperatures namely 10 and 50 °C. The nonlinear ordinary differential equations are solved using the Runge–Kutta Feldberg integration method. The characteristics of velocity, temperature and concentration boundary layers in the presence of graphene–water nanoparticles are presented for different physical parameters such as heat source/sink parameter, thermophoresis parameter, Brownian motion parameter, Casson fluid parameter, porosity parameter, volume fraction and velocity power index parameter. Moreover, the friction factor coefficients, Nusselt number and Sherwood number are also estimated and discussed for aforesaid physical parameters. It is found that there is a significant increase in the thermal and concentration boundary layer thickness when the strength of the thermophoresis parameter is increased. In contrast, thermal boundary layer increases with the rise in the Brownian motion parameter, while the reverse trend holds true for concentration field. In addition, the rate of heat and mass transfer rate are higher in case of graphene–water nanoparticle at 50 °C compared to 10 °C temperature.

Numerical investigation of magnetohydrodynamic (MHD) radiative flow over a rotating cone in the presence of Soret and chemical reaction

Present study is a numerical investigation of the flow, heat and mass transfer behaviour of magnetohydrodynamic flow over a vertical rotating cone through porous medium in the presence of thermal radiation, chemical reaction and Soret effects. Further, the numerical solutions are elucidated by using Runge-Kutta based shooting technique. Obtained results are validated with open literature and found an excellent agreement. The influence of non-dimensional governing parameters on velocity, temperature and concentration profiles along with the friction factor, local Nusselt and Sherwood numbers are determined and discussed with the help of graphs and tables. Results proved that the variable porosity parameter have tendency to enhance the heat and mass transfer rate. An increase in the buoyancy parameter depreciates the thermal and concentration boundary layer thicknesses.