Concentration Boundary Layer Thickness Research Articles

Microchannel Modification in Membraneless Microfluidic Fuel Cell to Control the Concentration Boundary Layer

The concentration boundary layer thickness is one of the most important parameters used to characterize the performance of membraneless microfluidic fuel cells. Low concentration boundary layer thickness leads to a high electrochemical reaction over the electrodes, improving the performance of the fuel cell. For this purpose, this paper proposes a modified microchannel which directs the fuel and the oxidant to the electrode surfaces. According to the results obtained, the amount of concentration on the cathode electrode surface and therefore the amount of current density increased with the modified microchannel. At the same point of the cathode electrode surface, the oxidant concentration in the conventional microchannel was 0.055 mol/m3, while it was 0.19 mol/m3 in the modified microchannel. Since the concentration overpotential reduced, the limiting current density was 0.372 mA/cm2 in the conventional microchannel and 0.741 mA/cm2 in the modified microchannel. Thus, the limiting current density value increased by 91.5%.

Insight of Jeffrey flow over a stretching Riga plate with activation energy and viscous dissipation: Melting heat transfer regime

AbstractPresent article highlights the significance of Arrhenius activation energy along with viscous dissipation in Jeffrey fluid over a Riga plate. Riga plate is basically an actuator made up of array of magnets and electrodes scaled on a plane surface to tackle the weaker electrical conductivity during fluid flow. In order to ensure the novelty, a reliable melting heat surface condition has been incorporated on nonlinear stretching Riga plate of variable thickness to reconnoiter features of heat transfer. Moreover, stagnation point has been retained in this study. Adequate transformations are employed in order to attain system of nonlinear ordinary differential equations. A well known semi analytical technique (Homotopy analysis method) is utilized to obtain series solutions of prevailing dimensionless equations. Influence of several apposite parameters on velocity, thermal and concentration distributions is analyzed graphically. Physical evaluation and graphical sketch is presented for drag force coefficient and rate of heat transfer. Analysis of velocity as well as associated boundary layer thickness gives the growing up impact for the strength of modified Hartmann number. Enhancement of dimensionless reaction rate and endothermic/exothermic reaction parameter results in increment for heat flux over stretching Riga plate. Increase in thermal distribution takes place for higher Eckert number while thermal boundary layer thickness depicts opposite trend in this case. Concentration boundary layer thickness enhances while concentration profile declines for higher Schmidt number. Velocity distribution is found to be incremented for intense melting process. Higher dimensionless activation energy parameter is analyzed to be responsible for growing up concentration field.

Flow and heat transfer of nanofluids in a cylindrical permeable wavy channel embedded in porous medium using Buongiorno’s model

This investigation deals with the flow of Al2O3–water nanofluid in a wavy porous channel embedded in porous rocks. Fluid exchange takes place uniformly between porous rocks and the wavy channel. In this analysis, cylindrical and parallel plate wavy porous channels are considered. Consequences of Brownian motion and thermophoresis on the flow inside a wavy porous channel are elucidated. The modeled equations are made dimensionless by using dimensionless quantities. Impacts of flow parameters on the velocity, temperature, Nusselt number and friction factor are depicted through graphs. The numerical results with respect to parallel plate wavy porous channel are validated by comparing with the published results. The effectiveness of the cylindrical wavy porous channel as a heat transfer enhancement device in comparison to the parallel plate wavy porous channel is confirmed in this study. Designing devices at microlevels and understanding the heat transfer enhancement mechanism in wavy channels using the nanoparticle addition are the major outcomes from the results of this numerical investigation. The heat and mass transfer rate enhancements in the wavy porous channels are due to the higher Brownian motion in the boundary layer region and accelerated thermophoresis through thermal and concentration boundary layer thicknesses.

Magneto-Williamson nanofluid flow past a wedge with activation energy: Buongiorno model

The current investigation explores the effect of activation energy on the MHD radiative Williamson nanofluid flow across a wedge using heat generation and binary chemical reactivity. The flow model consists of partial differential equations (PDEs) by transforming them into ordinary differential equations (ODEs). Numerical computations have been carried out through the bvp4c MATLAB package. The most effective solutions for flow profiles have been displayed through graphs, while the numeric solutions for the drag friction, heat, and mass transport have been displayed via tables. Numerical findings demonstrate that the temperature field is accelerated by the increase in radiation parameter. In addition, it is intriguing to discover that the concentration boundary layer thickness improves as the activation energy increases. A fundamental study further reveals that the local skin friction coefficient is a rising function of thermal and concentration Grashof numbers. Moreover, it is concluded that the enhanced Brownian motion, thermophoresis, and Eckert number decline the heat transfer rate.

Particle Size, Dose, and Confinement Affect Passive Diffusion Flux through the Membrane Concentration Boundary Layer.

The authors present a steady-state-, particle-size-, and dose-dependent dissolution-permeation model that describes particle dissolution within the concentration boundary layer (CBL) adjacent to a semipermeable surface. It is critical to understand how particle size and dose affect the behavior of dissolving particles in the presence of a CBL adjacent to a semipermeable surface both in vivo and in vitro. Control of particle size is ubiquitous in the pharmaceutical industry; however, traditional pharmaceutical assumptions of particle dissolution typically ignore particle dissolution within the length scale of the CBL. The CBL does not physically prevent particles from traveling to the semipermeable surface (mucus, epithelial barrier, synthetic membrane, etc.), and particle dissolution can occur within the CBL thickness (δC) if the particle is sufficiently small (∼dparticle ≤ δC). The total flux (the time rate transport of molecules across the membrane surface per unit area) was chosen as a surrogate parameter for measuring the additional mass generated by particles dissolving within the donor CBL. Mass transfer experiments aimed to measure the total flux of drug using an ultrathin large-area membrane diffusion cell described by Sinko et al. with a silicone-based membrane ( Mol. Pharmaceutics 2020, 17, (7) 2319-2328, DOI: 10.1021/acs.molpharmaceut.0c00040). Suspensions of ibuprofen, a model weak-acid drug, with three different particle-size distributions with average particle diameters of 6.6, 37.4, and 240 μm at multiple doses corresponding to a range of suspension concentrations with dimensionless dose numbers of 2.94, 14.7, 147, and 588 were used to test the model. Experimentally measured total flux across the semipermeable membrane/CBL region agreed with the predictions from the proposed model, and at a range of relatively low suspension concentrations, dependent on the average particle size, there was a measurable effect on the flux due to the difference in δC that formed at the membrane surface. Additionally, the dose-dependent total flux across the membrane was up to 10% higher than the flux predicted by the standard Higuchi-Hiestand dissolution model where the effects of confinement were ignored as described by Wang et al. ( Mol. Pharmaceutics 2012, 9 (5), 1052-1066, DOI: 10.1021/mp2002818).

Study of Casson nanofluid flow over a wedge with variable magnetic effect, thermal radiation, and melting effects

In this article, we investigated the flow of a Casson nanofluid on a wedge considering the external effects of magnetic effects, thermal radiation, and melting effects. Also, thermophoretic and Brownian effects were being considered in our study. Similarity transformations were implemented to the governing set of nonlinear PDE’s to obtain coupled nonlinear set of ordinary differential equations. A fourth-order accurate MATLAB bvp4c routine was applied for solving the given boundary value problem. An excellent agreement to previously published results was found, which validates our study. Graphically, the consequences of pertinent parameters on dimensionless velocity, temperature, and nanoparticle concentration have been presented along with streamline visualizations for some of the parameters while the values for local skin friction, heat transfer, and mass transfer rates are presented in a tabular form. An augmentation in melting parameter augments momentum, thermal and concentration boundary layer thickness while skin friction, heat and mass transfer rates report a decrease. Wedge angle parameter, radiation, and Casson nanofluid parameters also enhance fluid velocity though the effects of magnetic field and permeability of the medium shows a reverse trend to their usual behavior.

Thermophoresis, Brownian Diffusion, Porosity, and Magnetic Parameters' Effects on Three-Dimensional Rotating Ag-CuO/H2O Hybrid Nanofluid Flow across a Linearly Stretched Sheet with Aligned Magnetic Field

Nanofluids are crucial to explore since they have substantial industrial applications and their rapid heat transfer rates. A brand-new category of nanofluid called "hybrid nanofluid" is now being employed to speed up heat transfer even further. The objective and novelty of this study investigates the impact of different parameters on the flow of a rotating, three-dimensional Ag-CuO/H2O hybrid nanofluid over a linearly stretched sheet with an aligned magnetic field. These parameters include thermophoresis, Brownian diffusion, porosity, magnetic parameter, and Forchheimer number. The study revealed that when temperatures decrease, CuO and Ag nanoparticle volume fractions lead to improved concentration and velocity profiles, correspondingly, momentum and concentration boundary layer thickness are enhanced while thermal boundary layer thickness is reduced. The investigation also reveals that while temperature rises with higher levels of some parameters, the velocity profile and concentration fall, correspondingly, momentum and concetration boundary layer thickness are reduced. The effects of different factors on the rates of skin friction, heat, and mass transmission can also be explored. Higher values of K and cause the Nusselt and Sherwood numbers to rise, whereas Fr,ϵ,M,α and Nb cause them to fall. The nonlinear ODEs formed from the governing system of nonlinear PDEs are solved in the study using MATLAB and the BVP-5C shooting method. The contribution of this work is to the understanding of the behaviour of hybrid nanofluids and its potential applications in the development and optimization of nanofluid-based systems for various engineering applications.

A numerical investigation of bio-convective electrically conducting water-based nanofluid flow on the porous plate with variable wall temperature

There is a awakening interest in applying bioconvective nanofluids in permeable media. As such, this article aims to numerically investigate boundary layer flow over a plate embedded in a porous medium filled with nanofluid with motile gyrotactic microorganisms. Consequence, mass and heat transmission efficiency in engineering, technological, and industrial domains is improved. Thus, heat and mass transmission with impacts of radiation and activation energy on the horizontal porous plate are analyzed with microorganisms. Ordinary differential equations are established from nonlinear leading Partial Differential Equations by implementing similarity variables. After that, the resultant ordinary differential equations are numerically tackled employing the BVP4C method, build-in package of MATLAB. From tables, it is evident that when the velocity parameter is one, skin friction is zero, which exhibits no opposition at the fluid-solid surface. The impacts of pertinent parameters upon nondimensional boundary layer outlines are deliberated. It is worth mentioning here that the impact of the magnetic field parameter () on velocity is drawn, and the graph depicts that the velocity is diminished by increasing the value of the magnetic parameter. It is because when the magnetic field is given perpendicular to the liquid’s surface, the generated magnetic impact causes the liquid to flow with a resistive form of force, which reduces its speed for the solutal resistance is increased by activation energy but decreased by Lewis number and chemical reaction constant Finally, current inquiry can helpfully enhance thermal conductivity, viscosity, convective heat transmission, and thermal diffusivity linked to those base fluids. The current investigation reveals that the Lewis number and chemical reaction constant tend to decay thickness of concentration boundary layer.

Hybrid Nanofluid Flow with Multiple Slips Over a Permeable Stretching/Shrinking Sheet Embedded in a Porous Medium

Including slip boundary conditions in the study involving the flow of foams, emulsions, polymer solutions, and suspensions over moving surfaces are crucial for real-life applications. The current study analysed the multiple slips effects on the magnetohydrodynamics (MHD) flow of Ag-CuO/water hybrid nanofluid past a permeable stretching/shrinking sheet embedded in a porous medium. Appropriate similarity variables are introduced for transforming the governing equations and boundary conditions into ordinary differential equations before being solved using the bvp4c solver. Dual solutions are yielded from the numerical computation of flow over a shrinking sheet, and the first solution is identified as stable through a stability analysis. It is found that the imposition of velocity, thermal, and mass slips promotes the reduction of momentum, thermal, and concentration boundary layer thickness, respectively. The hybrid nanofluid around the sheet is observed to flow at a different velocity from the sheet due to the imposition of velocity slip. Thermal and mass slips, meanwhile, obstruct the flow's ability to transport heat and mass. An increased suction parameter, however, can aid in enhancing the rates of heat and mass transfers.

Double diffusion and Hall effects on MHD sinusoidal natural convection flow of silver water-based nanofluid from a porous vertical plate

This paper scrutinizes Hall current, Soret and Dufour impacts on natural convective flow of nanofluid attributable to variation in sinusoidal surface temperature over a vertical plate through a porous medium with strong transverse magnetic field applied normally to the flow. In this regard, the silver metal is considered as nanoparticles with water as base fluid. The overlapping multi-domain bivariate spectral local linearization method (OMD-BSLLM) has been utilized to solve the dimensionless governing equations which are attained by means of appropriate transformations. The obtained results are portrayed via graphical and tabular formations to inspect flow fields, shear stresses, heat and mass transmission characteristics for varying thermo-physical parameters. We found that there is an enhancement in the flow fields, shear stresses and heat transportation with the use of silver nanoparticles. Thermal and concentration boundary layer thickness enhance by using porous material, whereas diminish with improvement in Hall effect and ratio of buoyancy forces. The flow characteristics decline with the inclusion of porous medium while elevates with increment in Hall parameter. Moreover, an upgrade in thermal-diffusion correspond to a substantial growth in concentration field along with mass transfer rate. Current analysis can be useful in MHD energy generators, and industrial applications such as heating and cooling procedures owing to the involvement of nanoparticles having superior thermal conductivity features.

Characterization of Mass Transfer within the Crystal-Solution Boundary Layer of l-Alanine {120} Faces Using Laser Interferometry during Growth and Dissolution.

Crystallization and dissolution are important processes to consider in drug development as well as many other industrial processes. Many current growth and dissolution models are based on bulk solution properties and do not implicitly consider concentration variation close to the crystal surface-solution interface and how this is mediated by solute diffusive mass transfer. Solution boundary layer thickness and concentration distribution, for the {120} crystal habit face of single crystals of l-alanine in saturated aqueous solutions during both growth and dissolution processes, is measured as a function of super/undersaturation using a Mach-Zehnder optical interferometer system. Further analysis allows determination of the diffusion coefficient and mass flux within the boundary layer as well as whether the processes are controlled by mass transfer or crystal interfacial kinetics. The measurement of this study revealed that the {120} face was not saturated at its surface during growth or dissolution meaning both processes were somewhat limited by their crystal interfacial kinetics. Growth was limited by crystal interfacial kinetics at all supersaturations to the same degree, whereas dissolution had a mixed dependency on crystal interfacial kinetics and mass transfer at lower undersaturations becoming more limited by mass transfer at higher undersaturations. Boundary layer thickness increased with super/undersaturation but to a lesser degree than the increase in the concentration difference between the crystal surface and bulk solution leading to a higher mass flux of solute molecules through the boundary layer. At the same relative super/undersaturation mass flux of solute molecules was faster during dissolution which was concurrent with its increased surface to bulk solution concentration difference and boundary layer thickness.

Thermal radiation and heat sink/source aspects on 3D magnetized Sutterby fluid capturing thermophoresis particle deposition

Investigating the characteristics and distinctive qualities of non-Newtonian fluids, the Sutterby model magnificently represents the dilute polymer solution. Different advantages of diluted polymeric solutions are found in polymerized melts, agricultural sprayers, clay coaters, cleansing products and many more. The purpose of this paper is to demonstrate a numerical solution of heat and mass transfer for a 3D study flow of Sutterby fluid over a bidirectional expansion surface. The heat generation/absorption, thermophoretic and thermal radiation effects are also analyzed. The nonlinear main problem is enhanced and transformed into a symmetrical model by using the similarity approach. To solve our creating problem numerically, we use the bvp4c technique. The effects of the obtaining results are discussed in detail and plotted on the basis of physical parameters. An increase in the stretching parameter values can indicate a decline in the concentration field and also decrease the consequent concentration boundary layer thickness. There is a rapid decay of the concentration field in accordance with the thermophoretic parameter compared to the Schmidt number.

Scrutiny of Carreau nanoliquid over rotating disk with radiation impacts and the Cattaneo–Christov flux theory

The purpose of this article is to execute an analytical approximation for the flow of magnetohydrodynamic Carreau nanoliquid over a heated stretchable rotating disk. An association between linear thermal radiations and the Cattaneo–Christov flux theory for heat and mass is discussed. The governed partial differential equations are first adapted to ordinary differential equations by engaging similarity transformations. The optimal homotopy analysis method (OHAM) is adopted to solve the model. The graphical and tabular illustrations are provided to analyze the impact of various physical parameters on flow properties. It is noticed that the enrichment of the radiation phenomenon results in enhancing the temperature. The thermal and concentration boundary layer thickness is contracted by strengthening thermal and solutal relaxation time parameters.

Significance of the third‐order slip flow of graphene‐(100% water, 70% water + 30% ethylene glycol, and 50% water + 50% ethylene glycol) nanofluids flow over a stretching surface with a Cattaneo–Christov heat and mass flux model

AbstractCommon conductive fluids include coolants (water and ethylene glycol [EG]), lubricants (oils), polymer solutions, paraffin, and biofluids. Compared with conventional fluids, the nanofluids have superior thermophysical properties like heat transmission, thermal conductivity, viscosity, and thermal diffusion. Such types of nanofluids have many biomedical, industrial, and engineering applications due to their enhanced properties like vehicle cooling, industrial cooling, heat transfer, electronics cooling, nanocryosurgery, magnetic drugs, etc. Therefore, in this analysis, the authors have investigated the significance of thermal and mass transmission mechanisms of the nanofluids on convective motion that happens through a stretching sheet with velocity slips. The nanofluid flow includes water (H2O) and EG (C2H6O2) which are used as a mixture of base fluid (water, 70%water + 30%EG, 50%water + 50%EG) and graphene nanomaterials (graphene nanoparticle [GP]) are used as nanoparticles. The governing equations are transformed with the help of suitable similarity variables and then solved by the means of homotopy analysis method (HAM). Validation of the present analysis has been performed and has found great agreement with previous results. The effects of physical factors developed during partial differential equation (PDE)‐to‐ordinary differential equation (ODE) transformations on flow profiles have been presented. The results show that the enhancing nanoparticle volume fraction shrinks the velocity boundary layer thickness and reduces the velocity profiles, while the thermal and concentration boundary layer thicknesses enhance, which consequently augment the thermal and concentration profiles. Additionally, the increasing nanoparticle volume fraction improves skin friction, heat transfer, and mass transfer rates. The augmenting thermal and mass relaxation times factors reduce the thermal and concentration profiles. Additionally, the thermal relaxation time factor shows prompt effect for the case of Fourier's law and the concentration relaxation time factor shows prompt effect for Fick's model. It is also found that the variations in the flow profiles are always dominant for the water + GP nanofluid as compared to 70% W + 30%EG + GP and 50% W + 50%EG + GP.

A computational study on diffusion-thermo and rotation effects on heat generated mixed convection flow of MHD Casson fluid past an oscillating porous plate

A finite element computational study is conducted to evaluate the impacts of diffusion-thermo and rotation on time-dependent heat generated MHD chemically reactive mixed-convection Casson fluid transport due to an oscillatory porous plate considering ramp surface temperature with thermal radiation and Hall effects. The boundary-layer equations describing the flow are formulated and altered into dimensionless form with aid of non-dimensional variables and parameters. The resulting governing boundary layer equations are numerically solved by a precise and robust finite element method. A representationary set of outcomes is exhibited graphically to exemplify the influent of emerging parameters on the profiles of temperature, concentration and velocity. The computed results of shearing stresses, Nusselt and the Sherwood numbers are displayed in the tables. We found that both velocity components decreased as magnetic field, rotation and Casson parameters increased whereas opposite result is discovered as heat generation and Hall parameter increased. Thickness of thermal and momentum boundary layers improve with increment in thermal radiation. Increasing chemical reaction parameter reduces both concentration and momentum boundary layer thickness. It is prominent to highlight in this investigation, in case of isothermal plate temperature, both velocity components, concentration and temperature are higher than in case of ramped surface temperature. Further, our results compared with earlier published works and established to be in excellent conformity.

Effect of unsteady relative thermal and concentration boundary layer thickness on mixed convection in a partially heated contaminated enclosure

Double diffusive flow under mixed convection has become a significant area of research. This study aims to evaluate the Lewis number effect in such a double-diffusive problem in a roof-based air-ventilated system. The Lewis number 0.01 ≤ Le ≤ 5 was chosen for the study, considering other parameters as constant to observe the impact of different heat and mass transfer properties varying the dimensionless time 0.1 ≤ τ ≤ 1. The Galerkin residual technique was chosen to generate the governing equations. The outcomes have been plotted in streamlines, isotherms, isoconcentration, heat and mass transfer, average fluid temperature and mass concentration. The major findings elucidate that heat and mass transfer rate augments when Lewis number goes higher and vice versa. Moreover, when the thermal diffusivity is higher than the mass diffusivity, the average fluid temperature and mass concentration become lower. Overall, this study will be a guide on double-diffusive system design, such as roof-based air ventilation systems.

Squeezing flow of Cu-TiO2/ H2Ohybrid nanofluid with activation energy and chemical reaction in a Darcy-Forchheimerporous medium

This paper presents numerical simulations of an unsteady squeezed flow of water-based hybrid incompressible nanofluid containing titanium oxide () and copper (Cu) as nanosolid particles between two parallel disks embedded in a Darcy-Forchheimer porous medium in presence of thermal slip and velocity slip together with a homogenous chemical reaction. The prime focus of the present investigation is to explore the velocity distribution, heat and mass transfer of the flow under the mentioned geometrical configurations. The leading PDEs is reduced into similarity non-linear ODEs with the help of relevant similarity transformation and then solved by the 4th order R-K integration technique accompanied with the shooting procedure. After numerical designs, the impact of diverse related factors on flow characteristics of the stream has been demonstrated via proper charts and graphs and described the consequences with apposite perspective. Some of the notable conclusions of the present study is that fluid temperature increases with growing values of activation energy and thermal slip, whereas the fluid velocity decrease with developing values of the porosity parameter, inertial parameter and squeezing number. Also thickness of concentration boundary layer leads to decrease with an intensification of squeezing number and chemical reaction parameter.

Flow and heat transfer analysis of a special third grade fluid over a stretchable surface in a parallel free stream

This paper aims to investigate a boundary layer flow with heat and mass transfer of a special third grade fluid over a stretchable surface in a parallel free stream. Using the similarity variables generated by the Lie group analysis, the governing nonlinear partial differential equations (PDEs) are transformed into a system of nonlinear ordinary differential equations (ODEs). The transformed equations are then solved numerically using the shooting technique. In addition, an attempt is made to carry the asymptotic solution behavior for large stretching and suction parameters, and the asymptotic results of skin friction coefficient are then compared with the direct numerical solutions, which shows a good agreement. It is observed that the similarity equations exhibit dual solutions in a certain range of shrinking strength. These two solution branches show different behavior on the skin friction coefficient, local Nusselt number, Sherwood number, velocity, and temperature profiles. Thus, emphasis has been given to carrying out a stability analysis to determine the physically reliable solution. The stability analysis shows that the upper branch solution is stable. It is observed that the suction parameter increases the range of dual solutions and the magnitude of the critical point from where the dual solutions bifurcate; however, the non-Newtonian parameter shows the opposite behavior. The momentum, thermal and concentration boundary layer thicknesses in the upper branch solution are lower than the lower branch solution.

A Simple Parameterization to Enhance the Computational Time in the Three Layer Dry Deposition Model for Smooth Surfaces

Optimization of dry deposition velocity calculation has been of great interest. Every time, determining the value of the concentration boundary layer (CBL) thickness led to a waste of numerical calculation time, which appears as a huge time in large-scale climate models. The goal of this study is to optimize the numerical calculation time in the three-layer deposition model for smooth surfaces through the development of a MATLAB code that can parameterize the appropriate concentration boundary layer height (y+cbl) and internal integral calculation intervals for each particle diameter Dp (0.01–100 µm) and friction velocity u* (0.01–100 m/s). The particle concentration, as a solution to the particle flux equation, is obtained and modeled numerically by performing the left Riemann sum using MATLAB software. On the other hand, the number of subdivisions N of the Riemann sum was also parameterized for each Dp and u* in order to lessen the numerical calculation time. From a numerical point of view, the new parameterizations were tested by several computers; about 78% on the average of the computation time was saved when compared with the original algorithm. In other words, on average, about 1.2 s/calculation was gained, which is valuable in climate models simulations when millions of dry deposition calculations are needed.

Numerical simulations of the effect of spacer filament geometry and orientation on the performance of the reverse osmosis process

Momentum and mass transfer in reverse osmosis membrane modules must be optimized to design efficient and economical designs. The feed spacers are used to improve mixing, to minimize fouling and concentration polarization. This computational study analyses fluid flow, mass transfer, concentration polarization and pressure drop in the feed channel of a reverse osmosis membrane module with different spacer filament geometry (cylindrical, diamond, pentagonal, and triangular), orientation and Reynolds numbers. The computational model solves three-dimensional fluid flow and mass transfer while considering the complex water and solute flux boundary conditions. The cylindrical spacer filaments configurations showed the lowest water flux, followed by pentagonal, diamond, and triangular spacer filaments configurations. The concentration boundary layer thickness was high near the spacer surface due to the stagnant velocity zone. The results indicated that the concentration polarization on the membrane surface increases with a decrease in Reynolds numbers. The channel containing triangular filament spacers gave the maximum water flux and minimum concentration polarization. The spacer configurations with an attack angle of 45° and a transverse angle of 135° showed the highest water flux; however, the pressure drop was also high. The channel containing triangular spacer filament (T1A0) showed the least CP. However, the concentration boundary layer thickness was higher at the bottom side of the channel. The developed model could be useful for predicting the reverse osmosis membrane process performance.