Concentration Boundary Layer Research Articles

Assessment of a subgrid‐scale model for convection‐dominated mass transfer for initial transient rise of a bubble

AbstractThe mass transfer between a rising bubble and the surrounding liquid is mainly determined by an extremely thin layer of dissolved gas near the bubble interface. Resolving this concentration boundary layer in numerical simulations is computationally expensive and limited to low Péclet numbers. Subgrid‐scale (SGS) models mitigate the resolution requirements by approximating the mass transfer near the interface. In this contribution, we validate an improved SGS model with a single‐phase simulation approach, which solves only the liquid phase at a highly resolved mesh. The mass transfer during the initial transient rise of moderately deformed bubbles in the range Re = 72–569 and Sc = 102–104 is carefully validated. The single‐phase approach is able to mirror the two‐phase flow field. The time‐dependent local and global mass transfer of both approaches agree well. The difference in the global Sherwood number is below than 2.5%. The improved SGS model predicts the mass transfer accurately and shows marginal mesh dependency.

Hall and Rotation Effects on Radiating and Reacting MHD Flow past an Accelerated Permeable Plate with Soret and Dufour Effects

This article investigates numerically the effects of Hall current and rotation effects on radiating and chemically reacting unsteady MHD natural convection flow past an accelerated infinite vertical permeable plate in the presence of Soret and Dufour effects. The dimensionless coupled non-linear governing partial differential equations of the problem are solved numerically by employing finite element method. The influence of various physical parameters influencing the flow on the primary velocity, secondary velocity, temperature and the species concentration are displayed graphically whilst the numerical results of the primary skin friction, secondary skin-friction, Nusselt number and the Sherwood number are presented in tabular form. Results reveals that magnetic parameter, radiation parameter and chemical reaction rate tends to depreciate both primary and secondary velocity components whilst Hall, Soret and Dufour effects have reverse trend. Rotation parameter tends to retard fluid flow in the primary flow direction and accelerate fluid flow in the secondary flow direction. Thermal boundary layer thickness decreases with increasing radiation parameter whilst the reverse trend is noticed with increasing Dufour effect. Thermal diffusion effect causes to improve concentration boundary layer thickness whilst chemical reaction rate has reverse impact. These parameters have similar effect on the primary and secondary skin-frictions whilst opposite effect was noticed on the Nusselt and Sherwood numbers. This model problem finds an important in engineering and industrial application such as MHD generators, food processing, heat exchangers devices and internal rotation rate of the sun.
 HIGHLIGHTS
 
 The problem investigate the effects of Hall current and rotation effects on radiating and reacting on unsteady magnetohydrodynamics (MHD) natural convection heat and mass transfer flow over an infinite vertical porous plate embedded in a uniform porous medium taking Soret and Dufour effects into account
 The resulting partial differential equations governing the fluid flow are solved numerically using the finite element method. In order to determine the effects of various pertinent parameters and to investigate the important flow features, the numerical calculations for fluid velocity, temperature and species concentration are computed and shown graphically whereas skin friction, Nusselt number and Sherwood number at the plate are evaluated and depicted in tabular form
 The model problem finds an important in engineering and industrial application
 
 GRAPHICAL ABSTRACT

Heat and mass transfer exploration of non-Newtonian fluid flow induced by the exponentially stretching Riga surface with the application of Generalized Fourier’s and Fick’s law

In the present article, the analysis of the transportation of thermal and solutal energy of a3D flow on second- grade fluid with porous medium by an exponentially stretching surface is presented. The chemical reaction and heat generation/absorption are considered the dominating agents for the transportation of mass and heat in the second-order fluid. Furthermore, slip boundary conditions are considered on the boundary of the surface. A novel concept of the Cattaneo-Christov heat flux theory of the flow of second-order fluid is used under the effects of the Joule heating across the Riga surface for this research examination. The prevailing nonlinear PDEs are changed into the nonlinear coupled ordinary differential equations by choosing the suitable similarity transformations. The Matlab approach Bvp4c is applied to solve the nonlinear ODEs. Physical consequences of the different emerging parameters on the thermal, concentration, and momentum boundary layer thickness are examined by graphs. The thermal and concentration profiles are decreased by enhancing the values of (thermal relaxation parameter of time) and the (parameter of solutal relaxation time), respectively.

Study of thin layer film evolution near bacterial cellulose membrane by Ag|AgCl electrodes in chamber with lower concentration.

We used the method of measuring potential difference between two Ag|AgCl electrodes immersed directly into electrolyte solution with lower concentration and at different distances from membrane. The bacterial cellulose membrane was placed in horizontal plane in the membrane system with configurations with higher NaCl concentration and density under (A) and over the membrane (B). In both configurations at the initial moment the voltage between electrodes amounted to zero. After turning off mechanical stirring of solutions, in configuration A we observed the monotonic increase and next stabilization of voltage while in configuration B after short time dependent on the initial quotient of NaCl concentrations on the membrane we observed appearance of pulsations of measured voltage and gradual decrease of mean voltage over time. Smooth changes of voltage are connected with diffusional reconstruction of Concentration Boundary Layers (CBLs) while fast increase and subsequent pulsations of voltage are connected with the appearance of hydrodynamic instabilities (gravitational convection) near membrane imposed on diffusive reconstruction of thin layer. The time needed for the appearance of hydrodynamic instabilities in CBL depended nonlinearly on the initial ratio of electrolyte concentrations on the membrane.

Mathematical Simulation of Casson MHD Flow through a Permeable Moving Wedge with Nonlinear Chemical Reaction and Nonlinear Thermal Radiation.

The influence of the chemical interaction and dynamic micropolar convective heat transfer flow of Casson fluid caused by a moving wedge immersed in a porous material was explored. The Joule heating owing to magnetized porous matrix heating was also deliberated. The mathematical formulation for mass conservation, momentum, energy, and concentration profiles was expressed in the form of partial differential equations. The dimensionless set of ordinary equations was reduced from modeled equations via a transformation framework and then solved by the RK4 built-in function in MATLAB SOFTWARE by taking a step size of . The existing work was compared with the published work. The iteration procedure was stopped until all of the nodes in the η-direction met the convergence condition 10−5. The physical appearance of material parameters on the flow field, temperature, concentration, drag force, and Nusselt number was discussed through plots. The numerical results were obtained for limiting circumstances. The unsteadiness factor thinned the velocity boundary layer but decreased the thermal and concentration boundary layers. By increasing the Eckert number, the nondimensional temperature profile was enhanced. The novelty of the present study is that no one has numerically investigated the magnetized Casson fluid over a moving wedge in the presence of a chemical reaction and thermal radiation.

Double Stratified MHD Stagnation Point Slip Flow Over a Permeable Shrinking/Stretching Surface in A Porous Medium

The intention of this article is to investigate the impact of slip of MHD stagnation point flow over a permeable shrinking/stretching sheet with double stratification in a porous medium. Employing the appropriate similarity transformations and non-dimensional variables, the governing partial differential equations were reduced into a set of nonlinear ordinary differential equations. These equations were solved using shooting method and influence of pertinent variables on velocity, temperature and concentration are computed and analyzed. It was found that the slips have the propensity to control boundary layer flow and as the velocity slip increases, the momentum, thermal, and concentration boundary layer thickness become thinner for velocity slip. Therefore, velocity slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the velocity slip. It is also shown that the skin friction coefficient has decreased as the values of velocity slip increase while the It was found that the slips have the propensity to control boundary layer flow and as the velocity slip increases, the momentum, thermal, and concentration boundary layer thickness become thinner for velocity slip. Therefore, velocity slip acts as a boost for enhancement of the velocity profile in the boundary layer region, whereas temperature and concentration profiles decelerate with the velocity slip. It is also shown that the skin friction coefficient has decreased as the values of velocity slip increase while the local Nusselt number and the local Sherwood number are increasing. A comparison with previous studies available in the literature has been done and found an excellent agreement by comparing the numerical results in two decimal places which supports the validity of the present analysis.

Modelling of the Electrical Membrane Potential for Concentration Polarization Conditions.

Based on Kedem–Katchalsky formalism, the model equation of the membrane potential () generated in a membrane system was derived for the conditions of concentration polarization. In this system, a horizontally oriented electro-neutral biomembrane separates solutions of the same electrolytes at different concentrations. The consequence of concentration polarization is the creation, on both sides of the membrane, of concentration boundary layers. The basic equation of this model includes the unknown ratio of solution concentrations ( at the membrane/concentration boundary layers. We present the calculation procedure ( based on novel equations derived in the paper containing the transport parameters of the membrane (, , and ), solutions (, ), concentration boundary layer thicknesses (, ), concentration Raileigh number (), concentration polarization factor (), volume flux (), mechanical pressure difference (), and ratio of known solution concentrations (). From the resulting equation, was calculated for various combinations of the solution concentration ratio (), the Rayleigh concentration number (), the concentration polarization coefficient (), and the hydrostatic pressure difference ). Calculations were performed for a case where an aqueous NaCl solution with a fixed concentration of 1 mol m−3 () was on one side of the membrane and on the other side an aqueous NaCl solution with a concentration between 1 and 15 mol m−3 (). It is shown that () depends on the value of one of the factors (i.e., , , and ) at a fixed value of the other three.

Numerical investigation on heat and mass transfer of slit finned tube heat exchanger with humid flue gas

AbstractVery few studies have been reported on the fundamental mechanism analysis the augmentation of heat and mass transfer for the convection and condensation processes in the slit finned tube heat exchanger under dehumidifying conditions. By developing a 3D numerical model for the condensation of the slit finned tube heat exchanger under dehumidifying conditions, the heat and mass transfer characteristics were investigated under different the geometrical and operational parameters. The models neglecting convective mass flux or neglecting the water vapor loss can greatly enlarge the deviations of numerical results with respect to experimental data. The synergy angles are smaller in the windward and leeward sides of slits where the velocity field has a better synergy with both temperature field and the mass field. The slits on the fin not only increase the disturbance of fluid but continuously destroy the developments of thermal and mass concentration boundary layers, greatly enhancing the heat and mass transfer. The latent heat transfer is significantly greater than the sensible heat transfer, which accounts for 71.7% of the total heat transfer rate when inlet velocity is 1 m·s−1 and volume fraction of water vapor is 15%. The increases in the inlet velocity, and the volume fraction of water vapor can enhance the heat and mass transfer coefficient of wet flue gas. Whereas, the increase in inlet velocity can reduce the difference of synergy for the velocity field and the temperature or mass concentration gradient field of different fin tubes.

Biconvective transport of magnetized couple stress fluid over a radiative paraboloid of revolution

In the present study, the physical features of the bioconvective MHD flow of a couple stress fluid over an upper horizontal surface (i.e. surface shaped like a submarine or any ( uhsp) aerodynamical automobile) is analysed by considering radiation and viscous dissipation effects. In the fluid-saturated domain flow is induced due to the reaction of catalytic surface, double diffusion and stretching fluid layers. In fact, couple stress fluid is electrically conducted because non-uniform magnetic field is imposed. With the assistance of appropriate similarity transformations governing equations of the study are reduced to set of ordinary differential equations. Thereafter, built-in MATLAB solver bvp4c is implemented to solve the system numerically. By means of graphs and tables variations of the velocity, temperature, concentration, friction factor, local heat and mass transfer rates are observed thoroughly by varying the flow controlling parameters. From this analysis, main observations are, for rising values of couple stress and magnetic parameter velocity is decline, whereas temperature rises for the same parameters and increase in the thermal boundary layer is noted for the Brinkman number, whereas reverse trend is noted in the concentration boundary layer. Finally, comparison is done and a good correlation is identified between the present analysis and perversely recorded analysis.

Impact of osmotic pressure on the stability of Taylor vortices

We use linear stability analysis and direct numerical simulations to investigate the coupling between centrifugal instabilities, solute transport and osmotic pressure in a Taylor–Couette configuration that models rotating dynamic filtration devices. The geometry consists of a Taylor–Couette cell with a superimposed radial throughflow of solvent across two semi-permeable cylinders. Both cylinders totally reject the solute, inducing the build-up of a concentration boundary layer. The solute retroacts on the velocity field via the osmotic pressure associated with the concentration differences across the semi-permeable cylinders. Our results show that the presence of osmotic pressure strongly alters the dynamics of the centrifugal instabilities and substantially reduces the critical conditions above which Taylor vortices are observed. It is also found that this enhancement of the hydrodynamic instabilities eventually plateaus as the osmotic pressure is further increased. We propose a mechanism to explain how osmosis and instabilities cooperate and develop an analytical criterion to bound the parameter range for which osmosis fosters the hydrodynamic instabilities.

Thermal radiation and diffusion effects in MHD Williamson and Casson fluid flows past a slendering stretching surface

AbstractThe article is presented to analyze the magnetohydrodynamic Casson and Williamson fluids flow over a stretched surface of variable thickness by including the conditions of thermal radiation, velocity slip, temperature, and concentration slip. The equations governing the flow characteristics are transformed to ordinary differential equations by applying similarity transformations. The solution of the simplified equations is obtained by the numerical bvp5c Matlab package. The behavior for Williamson and Casson fluid cases is explored and discussed with the impact of sundry parameters on the flowing fluid, thermal, and diffusion fields. The profiles under the impact of parameters are depicted through graphs. Also, we evaluated the performance of local Nusselt and Sherwood numbers along with the friction of the wall and are displayed through tables. We found that the temperature and mass transfer distribution is low in Williamson fluid when compared to Casson fluid flow. The computed results indicate that the flow, thermal and concentration boundary layer characteristics of Williamson and Casson fluids are not unique.

Identification of airborne pollutant sources within a slot ventilated porous enclosure depending on backward model and downwind scheme

Identification of pollutant source, depending on the inverse computational fluid dynamics (CFD) methodology, within a slot-ventilated porous enclosure has been proposed in this paper. The whole fluid flow system is assumed to be two-dimensional, laminar and porous-saturated. As the inverse CFD modeling was ill-posed, a downwind scheme is employed to discretize the convection term to improve the accuracy and the corresponding time step range is derived to achieve numerical stability. Afterward, the downwind scheme simplifies the discretization process and its direct inversion algorithm. The effects of the Reynolds number (), the Darcy number (), the Schmidt number () and locations of pollutant source on the backward time CFD simulations are investigated, respectively. Results show that the temporal size/step is a critical factor of computational stability. In addition, the thickness of velocity or concentration boundary layer directly impacts the sensitivity of the inverse CFD simulation. The present research could aid in the safety of gas-supplying pipe network and relevant pollutant leakage accidents. Highlights Identification of prior-unknown sources was proposed regarding gas-supplying network. Original transport equations were maintained to enhance the accuracy and generality. The downwind convection scheme was implemented to enhance backward CFD procedures. Diverse influencing factors were numerically tested to recover pollutant sources. The proposed new algorithm was validated thoroughly by experiments and benchmark solutions.

Modelling the fluid mechanics in single-flow batteries with an adjacent channel for improved reactant transport

Redox flow batteries (RFBs) are an emerging electrochemical technology envisioned towards storage of renewable energy. A promising sub-class of RFBs utilizes single-flow membraneless architectures in an effort to minimize system cost and complexity. To support multiple functions, including reactant separation and fast reactant transport to electrode surfaces, electrolyte flow must be carefully designed and optimized. In this work, we propose adding a secondary channel adjacent to a permeable battery electrode, solving for the flow field and analysing the effects on the reactant concentration boundary layer at the electrode. We find that an adjacent channel with gradually changing thickness leads to a desired nearly uniform flow through the electrode to the adjacent channel. Consequently, the thickness of the concentration boundary layer is significantly reduced, increasing reactant transport to the electrode surface to 140% of the rate of a battery with a constant width adjacent channel, and 350% of the rate with no adjacent channel. Overall, this theory provides insight into the important role of flow physics for this promising sub-class of flow batteries, and can pave the way to improved energy efficiency of such flow batteries.

Thermophoresis and Brownian Effect for Chemically Reacting Magneto-Hydrodynamic Nanofluid Flow across an Exponentially Stretching Sheet

This comparative research investigates the influence of a flexible magnetic flux and a chemical change on the freely fluid motion of a (MHD) magneto hydrodynamic boundary layer incompressible nanofluid across an exponentially expanding sheet. Water and ethanol are used for this analysis. The temperature transmission improvement of fluids is described using the Buongiorno model, which includes Brownian movement and thermophoretic distribution. The nonlinear partial differential equalities governing the boundary layer were changed to a set of standard nonlinear differential equalities utilizing certain appropriate similarity transformations. The bvp4c algorithm is then used to tackle the transformed equations numerically. Fluid motion is slowed by the magnetic field, but it is sped up by thermal and mass buoyancy forces and thermophoretic distribution increases non-dimensional fluid temperature resulting in higher temperature and thicker boundary layers. Temperature and concentration, on the other hand, have the same trend in terms of the concentration exponent, Brownian motion constraint, and chemical reaction constraint. Furthermore, The occurrence of a magnetic field, which is aided by thermal and mass buoyancies, assists in the enhancement of heat transmission and wall shear stress, whereas a smaller concentration boundary layer is produced by a first-order chemical reaction and a lower Schmidt number.

Unified algebraic expression of lotus-type pore shape in solid

Algebraic expressions for the shapes of lotus-type or isolated pores after bubbles completely entrapped in solid during unidirectional solidification are provided in this study. Functional materials of lotus-type porous metals are fabricated by unidirectional solidification of molten metals dissolving gasses such as hydrogen, oxygen or nitrogen. In view of superior and anisotropic features of mechanical, thermal and electrical properties, unidirectional lotus-type pore materials have been widely used in bio-, micro- and nano-technologies. The present model is based on a previous work by accounting for transient gas pressure in the pore affected by solute transfer and balance of gas, capillary and hydrostatic pressures, and physico-chemical equilibrium at the bubble cap. Solute transport across the bubble cap during solidification can be in different directions as previously denoted by Cases 1 and 2 due to relative magnitude between height of bubble cap and thickness of the concentration boundary layer on the solidification front. Proposing the self-consistently unified model combining Cases 1 and 2 and introducing a solute transport parameter, algebraic expressions of lotus-type pores and isolated pore can be obtained. Predicted and measured maximum radius, total length, inter-pore spacing, aspect ratio and porosity of lotus-type pores subject to Henry's law and Sievert's law as well as shape of an isolated pore during unidirectional solidification of water containing oxygen gas, liquid copper containing hydrogen, and water containing carbon dioxide, respectively, agree quite well.

A PLIC-based method for species mass transfer at free fluid interfaces

A finite volume based method to govern mass transfer of a diluted transition component across moving fluid–fluid interfaces is presented. The concentration jump at the interface is described by a constant distribution coefficient, while Marangoni effects and volume changes due to mass transfer are neglected. The interface position is captured by means of a level set function and subsequently reconstructed using a PLIC (piecewise linear interface construction) algorithm. For the discretisation of the species transport equation, cells containing the interface are split at the reconstructed planes. The concentration of the transition component is represented by two variables, each being valid in one phase only. The cell splitting and the definition of two concentration fields is essential to avoid artificial mass transfer due to discretisation errors. The interfacial boundary conditions are the concentration jump and the continuity of species fluxes. They are implemented in a robust and fast converging algorithm.The method has been validated for two liquid–liquid systems and one gas-liquid system by simulating a single moving droplet/bubble. The results are in good agreement with reference data, even for the gas–liquid system with thin liquid-side concentration boundary layers. In contrast to one-field formulations, this method is suitable for convection-dominated mass transport and significant movement of the interface due to the prevention of non-physical effects.

Mixed convective transport in Maxwell hybrid nano-fluid under generalized Fourier and Fick laws

Generalized laws of Fourier and Fick based on thermal and solutal relaxation times are used in the development of the system of PDEs related to simultaneous transport of heat and species in Maxwell fluid with mono and hybrid nano particles. The developed systems of PDEs are solved numerically by using the finite element method (FEM). Implementation of the FEM algorithm is discussed. The parametric study is carried out by performing various theoretical and numerical experiments. Related outcomes are presented in the form of graphs and numerical data. Convergence is ensured and grid-independent solutions are derived. Thermal relaxation parameter tends to lower down the temperature of the fluid and thermal boundary layer becomes shorter for higher values of thermal relaxation parameter. Concentration relaxation parameter has shown a decreasing impact on the diffusion of species in Maxwell fluid. Deborah number has reduced the diffusion of momentum in Maxwell fluid. Convective transport of both heat and species is compromised when Deborah's number is increased. It is also noticed from simulations that Deborah number for mono nano-Maxwell fluid has greater value relative to that for hybrid nano-Maxwell fluid. The simulations have also confirmed that the effective thermal conductivity of the Maxwell fluid due to the simultaneous dispersion of copper and aluminium oxide is greater than the thermal conductivity of pure Maxwell fluid and mono nano-Maxwell fluid. Therefore, simultaneous dispersion of copper and aluminium oxide for optimized heat transfer. Thermal and concentration relaxation memory effects are responsible for reducing thermal and concentration boundary layer thickness respectively. It is also noted that heat transport rate in hybrid nano-Maxwell fluid is greater than that in mono nano-Maxwell fluid and pure Maxwell fluid. Thermal memory effects play significant role in increasing the wall heat flux.

Recent progress in Arrhenius activation energy for radiative heat transport of cross nanofluid over a melting wedge

A theoretical numerical communication is demonstrated to analyze the impact of Arrhenius activation energy and melting phenomena on chemically reactive Falkner-Skan flow of cross nanofluid over a moving wedge with viscous dissipation and nonlinear radiation impacts. The basic partial differential equations for nanoparticle concentration, energy, momentum and mass conservation are reduced to nonlinear ordinary differential equations with the help of appropriate transforming variables and then solved numerically via bvp4c Matlab solver. It is interesting to notice that nanoparticle concentration and concentration boundary layer thickness are uplifted for enhancing values of activation energy parameter. Additionally, magnitude of heat transfer rate is a growing function of the Eckert number.

CFD modelling of mass transfer in liquid–liquid core-annular flow in a microchannel

This work reports Computational Fluid Dynamics (CFD) modelling of mass transfer in liquid–liquid Core-Annular Flow (CAF) in a microchannel. The model solves Navier-Stokes and convection–diffusion equations after incorporating interfacial boundary conditions of velocity, shear stress, flux and concentration jump. The model has been validated with the analytical and previously reported results. The validated model has been used to understand and quantify the dependence of concentrations boundary layer thicknesses on the core side and annulus side on Reynolds number, Schmidt number, dimensionless length and distribution coefficient. Furthermore, the dependenceof local mass transfer coefficients on the core and annulus side on diffusivity and concentration boundary layer thicknesses is quantified and compared with the predictions of film theory and penetration theory. Finally, the results obtained from the CFD model have been used to obtain the correlations of Sherwood number on the core side and the annulus side.

Study on MHD Flow over a Stretching Surface with Convective Boundary Condition by Numerical Method

The thermal and mass diffusive MHD flow through a stretching sheet has been inspected in the presence of a chemically reactive solute under convective boundary conditions in the present paper. The non-linear PDEs of the system concerning the flow, temperature, and species are recasted into a set of non-linear ODEs using ST. The consequential system of the differential equations is numerically resolved by using an implicit FDS in combination with the QL technique. The velocity ratio factor plays an important role in reducing the thickness of the velocity boundary layer, whereas the presence of magnetic parameters decreases the thickness of the velocity boundary layer profile. The study reveals that the fluid moves away from the surface during injection, resulting in a fall of the velocity gradient, whereas the opposite effect is observed in suction. The thermal and concentration boundary layer thicknesses are influenced by non-dimensional numbers, namely Prandtl and Schmidt numbers. The reaction rate parameter acts as a decelerating agent, and it thins the solute boundary layer formed in the neighborhood of the sheet. An increase in the convective parameter leads to an increase in the plate surface temperature. The present results of the paper are compared with the existing one, and good agreement is found between them.