Concentration Boundary Layer Research Articles

Severe Californian wildfires in November 2018 observed from space: the carbon monoxide perspective

Abstract. Due to proceeding climate change, some regions such as California face rising weather extremes with dry periods becoming warmer and drier, entailing the risk that wildfires and associated air pollution episodes will continue to increase. November 2018 turned into one of the most severe wildfire episodes on record in California, with two particularly destructive wildfires spreading concurrently through the north and the south of the state. Both fires ignited at the wildland–urban interface, causing many civilian fatalities and forcing the total evacuation of several cities and communities. Here we demonstrate that the inherent carbon monoxide (CO) emissions of the wildfires and subsequent transport can be observed from space by analysing radiance measurements of the TROPOspheric Monitoring Instrument (TROPOMI) onboard the Sentinel-5 Precursor satellite in the shortwave infrared spectral range. From the determined CO distribution we assess the corresponding air quality burden in major Californian cities caused by the fires and discuss the associated uncertainties. As a result of the prevailing wind conditions, the largest CO load during the first days of the fires is found in Sacramento and San Francisco, with city area averages reaching boundary layer concentration anomalies of about 2.5 mg CO m−3. Even the most polluted city scenes likely comply with the national ambient air quality standards (10 mg CO m−3 with 8 h averaging time). This finding based on dense daily recurrent satellite monitoring is consistent with isolated ground-based air quality measurements.

Cell performance of passive paper-based microfluidic fuel cells with mini-hole array in the anode flow channel

Paper-based microfluidic fuel cells (PMFCs) exploit the capillary flow in paper porous media to enable passive transport of reactants, and also use the co-laminar flow nature to separate the fuel and oxidant, thereby eliminating the conventional proton exchange membrane and micro-pumps. PMFCs have been regarded as promising micro-power sources for next-generation paper-based electrochemical microfluidic assay for biomedical diagnosis. The PMFC performance is usually limited by fuel transport, failing to meet the power requirement. At present, the paper-based microfluidic fuel cells have been reported to improve the performance mainly by changing the operating parameters, the physical parameters of the paper channel and the absorption pad, and the cell structure. However, few studies have been reported to improve the cell performance by enhancing fuel transfer. In this paper, a new anode structure is proposed to enhance fuel transfer. That is, a mini-hole array is constructed in the paper-based channel on the anode to make part of the catalyst layer of the anode contact with the mini-hole array. It was expected that the fluid in the mini-hole array can not only enhance the convective fuel transport, but also improve the diffusive fuel transport due to the direct contact between the fluid in the paper-based flow channel and anode catalyst layer. Performance comparison was firstly conducted between paper-based microfluidic fuel cells with conventional flow channel and mini-hole array in the anode flow channel. Moreover, effects of operation conditions including anode/cathode interspace, electrode length, fuel and electrolyte concentration on the cell performance were investigated and discussed. The experimental results confirmed that the mini-hole array in the anode flow channel can enhance fuel transport and ion conduction. As compared to the PMFC with the conventional flow channel, the PMFC with mini-hole array in the anode flow channel yielded 41.2% higher maximum power density. In addition, the experimental data also indicated that the ion transfer resistance can be reduced by diminishing the anode/cathode interspace, leading to an improved cell performance. No obvious fuel crossover was observed even at the interspace of 1.0 mm, because the flow rate of catholyte was higher than that of the anolyte, impeding the fuel crossover towards the cathode. The maximum power density of the cell increased with the decrease in the electrode length. This was mainly due to electrochemical reaction consumption and slow diffusion on the anode surface, which would reduce the fuel concentration on the anode surface along the flow direction, forming a concentration boundary layer and limiting the cell performance. In addition, upon the increasement of fuel or electrolyte concentration, the cell performance was enhanced at relatively low concentration but then dropped at high concentration. The fuel transfer was enhanced at high concentration and the ion transfer resistance can be reduced by increasing the electrolyte concentration, leading to an improved cell performance. However, the viscosity and density of the fuel and electrolyte increase with the electrolyte concentration, which led to the decrease of the flow rate of the reactants, further resulting in fuel mass transfer limitation and performance reduction. The optimal power density reached 29.7 mW/cm2 by the proposed PMFC at the anode/cathode interspace of 1.0 mm, the electrode length of 5.0 mm, and the fuel and electrolyte concentrations of 2.0 mol/L.

Liquid-solid mass transfer in a rotating trickle-bed reactor: Mathematical modeling and experimental verification

Liquid-solid mass transfer model is significant but deficient for the design of a rotating trickle-bed reactor (RTBR), which has great potential for process intensification of heterogeneous catalytic reactions. In this work, a mathematical model considering the wetting efficiency was first established to describe the liquid-solid mass transfer process in the RTBR. External static liquid holdup was referred to give a reasonable initial value for calculation. The profile of concentration boundary layer was obtained by mass balance analysis of an Eulerian element on a single sphere. The above model was then extended to predict the liquid-solid mass transfer coefficient (kLS) in the RTBR. A copper dissolution method was employed to measure the kLS, considering the effects of particle diameter, rotational speed, and liquid superficial mass velocity. The comprehensive comparison between predicted and experimental values of kLS was conducted and deviations were within ±25%.

Thermal aspects of chemically reactive Oldroyd-B fluid flow over a rotating disk with Cattaneo–Christov heat flux theory

The current study explores the magnetized flow of an Oldroyd-B fluid by a rotating disk. In this analysis, we use the modified Fourier’s law instead of classical Fourier’s law to study the fluid thermal features. The impact of homogeneous–heterogeneous reactions for mass transport is also considered. The von Karman variables are used to convert the partial differential equations into non-dimensional ordinary differential equations. The BVP Midrich scheme is utilized to acquire the numerical solution. Diverse effects of various involved parameters on the velocities, temperature and concentration of the liquid are analyzed. Additionally, the comparison table is made for limiting case to see the validity of our numerical results with the past outcomes. It is observed that the fluid velocity reduces with the impact of relaxation time parameter. Further, higher values of thermal relaxation time decline the fluid temperature. Moreover, with an increase in homogenous reaction, the concentration boundary layer thickness becomes thinner. The reduction in wall concentration gradient is noticed against homogeneous reaction rate.

Slip flow of Carreau fluid over a slendering stretching sheet with viscous dissipation and Joule heating

The effects of Joule heating and viscous dissipation on the two-dimensional Carreau fluid flowing through a stretching sheet with variable thickness are inspected with the supposition of slip parameters. The leading equations are altered as a set of (nonlinear) ordinary differential equations by means of proper similarity alterations. With the assistance of shooting procedure, subsequent equations are unravelled numerically. The impacts of appropriate parameters such as Weissenberg number and slip parameters (related to velocity and temperature) on the common profiles (velocity, concentration and temperature) are analysed via graphs. And also, we have analysed the effects of the identical parameters on skin friction coefficient and rate of transfers (heat and mass) by means of tables. From the outcomes, we observed that (a) the velocity slip parameter lowers the velocity but boosts the friction factor, (b) Weissenberg number boosts the velocity but shows conflicting behaviour on temperature, and (c) all boundary layers are observed to be thinner against wall thickness parameter. So, it benefits to improve both transfer rates (heat and mass), (d) the concentration boundary layer is observed to be thinner during chemical reaction, (e) magnetic field parameter and Eckert number are both reduce the local Nusselt number, and (f) wall thickness parameter and chemical reaction parameter are both improve the rate of mass transfer.

Effects of pulsatile flow and straight length on low‐density lipoprotein transport in a curved arterial wall

Abnormal accumulation of macromolecules such as low‐density lipoproteins (LDLs) in the arterial wall causes narrowing and blockage of vessels, which leads to atherosclerosis. Effects of pulsatile nature of blood flows as well as the initial length on transport of the LDL species in the arterial boundary layer region are analyzed numerically in the present work. The set of governing equations consisting of continuity, Navier‐Stokes, and species transport is solved using a projection method based on the second‐order central difference discretization. The obtained results are in excellent agreement with the pertinent data. The computational results imply that the flow field and concentration distribution are time dependent but the variation of the filtration velocity can be ignored. The LDL concentration boundary layer thickness decreases in the outer part and increases in the inner part for both with or without straight length. Presence of initial straight length generates about 26% growth in the boundary layer thickness, although its effect on the LDL surface concentration (LSC) is negligible. The maximum LSC is related to the regions with minimum wall shear stress in the inner part of the curved artery, which have more potential for formation of atherosclerosis. A new numerical correlation between the LSC and boundary layer thickness is proposed and examined.

Evaporation of a liquid film in a microchannel under the action of a co-current dry gas flow

A joint motion of thin liquid film and dry gas in a microchannel is investigated numerically at different values of initial concentration of the liquid vapor in the gas phase, taking into account the evaporation process. Major factors affecting the temperature distribution in the liquid and gas phases are as follows: transfer of heat by liquid and gas flows, heat loses due to evaporation, diffusion and heat transfer. The velocity and temperature fields in the liquid and gas phases, as well as the vapor concentration in the gas, were calculated. It has been established that in the zone of entry of flows into the channel near the interface, thermal and concentration boundary layers are formed, whose properties differ from the classical ones. Comparisons of the numerical results for the case of the dry gas and for the case of equilibrium concentration of vapor in the gas have been carried out. It is shown that use of dry gas enhances the heat dissipation from the heater. It is found out that not only intense evaporation occurs near the heating areas, but also in both cases vapor condensation takes place below the heater in streamwise direction.

Entanglement of near-surface optical turbulence to atmospheric boundary layer dynamics and particulate concentration: implications for optical wireless communication systems.

Localized reduction in optical turbulence due to enhanced atmospheric heating caused by the solar absorption of aerosol black carbon (BC) is reported. Immediate response of atmospheric turbulence to BC-induced atmospheric warming strongly depends on the available solar radiation (time of the day), BC concentration, and atmospheric boundary layer dynamics. Besides the significant climate implications of a reduction in turbulence kinetic energy, a large reduction in the refractive index structure parameter (Cn2) resulting from BC-induced warming would affect the atmospheric propagation of laser beams. Interestingly, aerosols contribute significantly (up to 25%) to the signal deterioration in optical wireless communication systems during convectively stable atmospheric conditions when higher signal-to-noise ratios are expected otherwise due to the reduced thermal convection. Competing effects of the fractional contributions of aerosol extinction and scintillations on beam attenuation are reported; daytime being largely dominated by scintillation effects while the nighttime being dependent on the ambient aerosol concentration as well. We put forward the entanglement of optical turbulence to aerosol concentration, atmospheric boundary layer dynamics, and surface-reaching solar radiation, and discuss the possible implications for optical propagation.

Microbial growth rates and local external mass transfer coefficients in a porous bed biofilm system measured by 19 F magnetic resonance imaging of structure, oxygen concentration, and flow velocity.

19 F nuclear magnetic resonance (NMR) oximetry and 1 H NMR velocimetry were used to noninvasively map oxygen concentrations and hydrodynamics in space and time in a model packed bed biofilm system in the presence and absence of flow. The development of a local oxygen sink associated with a single gel bead inoculated with respiring Escherichia coli was analyzed with a phenomenological model to determine the specific growth rate of the bacteria in situ, returning a value (0.66 hr-1 ) that was close to that measured independently in planktonic culture (0.62 hr-1 ). The decay of oxygen concentration in and around the microbiologically active bead was delayed and slower in experiments conducted under continuous flow in comparison to no-flow experiments. Concentration boundary layer thicknesses were determined and Sherwood numbers calculated to quantify external mass transfer resistance. Boundary layers were thicker in no-flow experiments compared to experiments with flow. Whereas the oxygen concentration profile across a reactive biofilm particle was symmetric in no-flow experiments, it was asymmetric with respect to flow direction in flow experiments with Sherwood numbers on the leading edge (Sh = 7) being larger than the trailing edge (Sh = 3.5). The magnitude of the experimental Sh was comparable to values predicted by a variety of correlations. These spatially resolved measurements of oxygen distribution in a geometrically complex model reveal in innovative detail the local coupling between microbial growth, oxygen consumption, and external mass transfer.

Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids

In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

Numerical study of nonlinear mixed convection inside stagnation-point flow over surface-reactive cylinder embedded in porous media

Nonlinear mixed convection of heat and mass in a stagnation-point flow of an impinging jet over a solid cylinder embedded in a porous medium is investigated by applying a similarity technique. The problem involves a heterogenous chemical reaction on the surface of the cylinder and nonlinear heat generation in the porous solid. The conducted analysis considers combined heat and mass transfer through inclusions of Soret and Dufour effects and predicts the velocity, temperature and concentration fields as well as the average Nusselt and Sherwood number. It is found that intensification of the nonlinear convection results in development of higher axial velocities over the cylinder and reduces the thickness of thermal and concentration boundary layers. Hence, consideration of nonlinear convection can lead to prediction of higher Nusselt and Sherwood numbers. Further, the investigation reveals that the porous system deviates from local thermal equilibrium at higher Reynolds numbers and mixed convection parameter.

Time-dependent shapes of a dissolving mineral grain: Comparisons of simulations with microfluidic experiments

Experimental observations of the dissolution of calcium sulfate by flowing water have been used to investigate the assumptions underlying pore-scale models of reactive transport. Microfluidic experiments were designed to observe changes in size and shape as cylindrical disks (radius 10 mm) of gypsum dissolved for periods of up to 40 days. The dissolution flux over the whole surface of the sample can be determined by observing the motion of the interface. However, in order to extract surface reaction rates, numerical simulations are required to account for diffusional hindrance across the concentration boundary layer; the geometry is too complex for analytic solutions.We have found that a first-principles simulation of pore-scale flow and transport, with a single value of the surface reaction rate, was able to reproduce the time sequence of sample shapes without any fitting parameters. The value of the rate constant is close to recent experimental measurements but much smaller than some earlier values. The shape evolution is a more stringent test of the validity of the method than average measurements such as effluent concentration, because it requires the correct flux at each point on the sample surface.

Non-similar characteristics of mixed convective slip flow over a wedge with temperature-dependent thermo-physical properties

We examined heat and mass transfer characteristics of mixed convective slip flow over a wedge taking into account the effect of variable transport properties. Unlike other studies, we have utilized non-similar transformation to get the non-similar features of the mixed convective slip flow. For comparison, stream function formulation is used to reduce the governing equation into a convenient form for short- and long-time regimes. We have determined the series solutions by adopting the perturbation techniques. The agreement between the numerical and series solutions is found to be excellent. Numerical solutions reveal that the slip parameters augment the momentum, thermal and concentration boundary layers. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are found to decrease for higher value of slip parameters. For the increasing value of the variable viscosity parameter, the velocity is stronger, but the temperature and concentration lessen. Contrary to this, this parameter diminishes the local skin friction coefficient, local Nusselt number and local Sherwood number. Due to the increase of mass diffusivity parameter, the velocity and concentration significantly increase whereas the temperature remains almost unaffected. Moreover, the mass diffusivity variation parameter leads to an increase in the local skin friction coefficient and local Nusselt number, but it reduces the local Sherwood number.

3D radiative convective flow of ZnO-SAE50nano-lubricant in presence of varying magnetic field and heterogeneous reactions

A numerical simulation is presented to investigate the effect of an exponentially varying magnetic field on three dimensional flow of Zinc Oxide-Society of Automotive Engineers 50 nanolubricant (ZnO-SAE50nano-lubricant) past a stretching sheet. Subsequently the impact of homogenous and heterogeneous reactions on the flow of nanolubricant concerned has also taken into account. The study has been strengthened by introducing the convection mechanism and the effect of thermal radiation. Similarity transformations are employed to transform the set of partial governing equations into the set of ordinary differential equations. The suitable boundary conditions are used to obtain the numerical solution. The numerical results are simulated using Matlab bvp4c solver and validated with the existing results. The flow characteristics, thermal characteristics, nanoparticle concentration and some non-dimensional numbers are computed under the influence of the pertinent parameters. The valuable outcome of the current study is that augmented magnetic field strength is the root cause of diminishing axial as well as transverse velocities and growing trend of fluid temperature. Also, the coefficients of homogenous and heterogeneous reactions are boons for ascending concentration boundary layer.

Mixed convection flow of Oldroyd-B nano fluid with Cattaneo-Christov heat and mass flux model with third order slip

This study reports the three-dimensional mixed convection flow of an Oldroyd-B nanofluid past a bidirectional stretching surface. Nonlinear partial differential equations obtained from the flow problem were converted into nonlinear ordinary differential equations using similarity transformation, and then, the numerical solutions of these ODEs with corresponding boundary conditions were obtained by employing a bvp4c solver. The effect of governing parameters on nondimensional velocity along x- and y-directions, temperature, particle concentration, local Nusselt number, and Sherwood number was presented through graphs and tables. It can be seen that the increasing values of the Brownian motion parameter Nb and thermophoresis parameter Nt lead to an increase in the temperature field and thermal boundary layer thickness, while the opposite behavior is observed for concentration field and concentration boundary layer thickness. As the Deborah number β1 increases, the concentration profile as well as concentration boundary layer thickness increase. However, the effects of β2 on the concentration profile are opposite to those of β1. An increase in δt, Pr, and α results in a decrease in temperature. It is reported that the local Nusselt number increases when β and Pr increase, whereas it decreases when λ, Nb, Nt, and Sc increase. An increase in Biot number Bi results in an increase in the Nusselt number, and an increase in Nt results in an increase in the Sherwood number. The results of the present analysis were compared with the available works in particular situations, and more agreement has been noted.

Design Optimization for a Microfluidic Crossflow Filtration System Incorporating a Micromixer.

In this study, we report on a numerical study on design optimization for a microfluidic crossflow filtration system incorporated with the staggered herringbone micromixer (SHM). Computational fluid dynamics (CFD) and the Taguchi method were employed to find out an optimal set of design parameters, mitigating fouling in the filtration system. The flow and the mass transfer characteristics in a reference SHM model and a plain rectangular microchannel were numerically investigated in detail. Downwelling flows in the SHM model lead to backtransport of foulants from the permeable wall, which slows down the development of the concentration boundary layer in the filtration system. Four design parameters — the number of grooves, the groove depth, the interspace between two neighboring grooves, and the interspace between half mixing periods — were chosen to construct a set of numerical experiments using an orthogonal array from the Taguchi method. The Analysis of Variance (ANOVA) using the evaluated signal-to-noise (SN) ratios enabled us to identify the contribution of each design parameter on the performance. The proposed optimal SHM model indeed showed the lowest growth rate of the wall concentration compared to other SHM models.

Laminar boundary layer flow of a combustible gas over a semi-infinite porous surface

Laminar boundary layer flow of a combustible gas under mixed convection over a semi-infinite porous surface is analyzed theoretically and numerically. The governing equations are transformed into a set of partial differential equations which are solved numerically by using finite difference method. To assess the accuracy of numerical results, we also solve these equations by using perturbation method for low frequency range and asymptotic method for high frequency range. Numerical computations have been carried out for several values of parameters involved in the equations, namely the Prandtl number, the Schmidt number, the wall temperature and the mass flux for injected fuel. Results show that the momentum, thermal and concentration boundary layers increase owing to the increase in the mass flux, but increasing Prandtl number reduces the thermal boundary layer and thickens the momentum and concentration boundary layers. Moreover, an expression for the ignition distance involving the pertinent parameters is derived using large activation energy asymptotics. It is found that the ignition distance considerably diminishes upon increasing the above parameters.

Chemically reactive membrane crystallisation reactor for CO2–NH3 absorption and ammonium bicarbonate crystallisation: Kinetics of heterogeneous crystal growth

The feasibility of gas-liquid hollow fibre membrane contactors for the chemical absorption of carbon dioxide (CO2) into ammonia (NH3), coupled with the crystallisation of ammonium bicarbonate has been demonstrated. In this study, the mechanism of chemically facilitated heterogeneous membrane crystallisation is described, and the solution chemistry required to initiate nucleation elucidated. Induction time for nucleation was dependent on the rate of CO2 absorption, as this governed solution bicarbonate concentration. However, for low NH3 solution concentrations, a reduction in pH was observed with progressive CO2 absorption which shifted equilibria toward ammonium and carbonic acid, inhibiting both absorption and nucleation. An excess of free NH3 buffered pH suitably to balance equilibria to the onset of supersaturation, which ensured sufficient bicarbonate availability to initiate nucleation. Following induction at a supersaturation level of 1.7 (3.3 M NH3), an increase in crystal population density and crystal size was observed at progressive levels of supersaturation which contradicts the trend ordinarily observed for homogeneous nucleation in classical crystallisation technology, and demonstrates the role of the membrane as a physical substrate for heterogeneous nucleation during chemically reactive crystallisation. Both nucleation rate and crystal growth rate increased with increasing levels of supersaturation. This can be ascribed to the relatively low chemical driving force imposed by the shift in equilibrium toward ammonium which suppressed solution reactivity, together with the role of the membrane in promoting counter-current diffusion of CO2 and NH3 into the concentration boundary layer developed at the membrane wall, which permitted replenishment of reactants at the site of nucleation, and is a unique facet specific to this method of membrane facilitated crystallisation. Free ammonia concentration was shown to govern nucleation rate where a limiting NH3 concentration was identified above which crystallisation induced membrane scaling was observed. Provided the chemically reactive membrane crystallisation reactor was operated below this threshold, a consistent (size and number) and reproducible crystallised reaction product was collected downstream of the membrane, which evidenced that sustained membrane operation should be achievable with minimum reactive maintenance intervention.

On the effects of straight extremities on low-density lipoprotein transport in the concentration boundary layer of curved arteries

Purpose The purpose of this paper is to analyze the influence of curvature on the transport of low-density lipoprotein (LDL) through a curved artery and concentration boundary layer characteristics numerically. Design/methodology/approach By using a projection method based on the second-order central difference discretization, the authors solve the set of governing equations, which consists of Navier–Stokes, continuity and species transport. The effects of initial straight length, as well as the curvature and wall shear stress (WSS) on LDL transport in a curved artery are established in this paper. Findings The obtained numerical results imply that the LDL concentration boundary layer thickness decreases in the outer part of the curved artery and increases in the inner part for both with or without initial straight length. The effect of Reynolds number on the concentration distribution in a curved artery with initial straight length is more pronounced than that on a fully curved artery, although an opposite trend was seen for the curvature ratio. The maximum surface LDL concentration is related to the regions with minimum WSS in the inner part of the curved artery, which has more potential the formation of atherosclerosis. Originality/value The authors present a comprehensive concentration distribution of LDL in the concentration boundary layer of the curved artery. The authors also characterize and predict the influence of curvature on the formation and development of atherosclerosis within the arterial wall.

Combined heat and mass transfer and thermodynamic irreversibilities in the stagnation-point flow of Casson rheological fluid over a cylinder with catalytic reactions and inside a porous medium under local thermal nonequilibrium

The transport of heat and mass from the surface of a cylinder coated with a catalyst and subject to an impinging flow of a Casson rheological fluid is investigated. The cylinder features circumferentially non-uniform transpiration and is embedded inside a homogeneous porous medium. The non-equilibrium thermodynamics of the problem, including Soret and Dufour effects and local thermal non-equilibrium in the porous medium, are considered. Through the introduction of similarity variables, the governing equations are reduced to a set of non-linear ordinary differential equations which are subsequently solved numerically. This results in the prediction of hydrodynamic, temperature, concentration and entropy generation fields, as well as local and average Nusselt, Sherwood and Bejan numbers. It is shown that, for low values of the Casson parameter and thus strong non-Newtonian behaviour, the porous system has a significant tendency towards maintaining local thermal equilibrium. Furthermore, the results show a major reduction in the average Nusselt number during the transition from Newtonian to non-Newtonian fluid, while the reduction in the Sherwood number is less pronounced. It is also demonstrated that flow, thermal and mass transfer irreversibilities are significantly affected by the fluid’s strengthened non-Newtonian characteristics. The physical reasons for these behaviours are discussed by exploring the influence of the Casson parameter and other pertinent factors upon the thickness of thermal and concentration boundary layers. It is noted that this study is the first systematic investigation of the stagnation-point flow of Casson fluid in cylindrical porous media.