Permeable Surface Research Articles

Analysis of Nonlinear Convection-Radiation in Chemically Reactive Oldroyd-B Nanoliquid Configured by a Stretching Surface with Robin Conditions: Applications in Nano-Coating Manufacturing.

Motivated by emerging high-temperature manufacturing processes deploying nano-polymeric coatings, the present study investigates nonlinear thermally radiative Oldroyd-B viscoelastic nanoliquid stagnant-point flow from a heated vertical stretching permeable surface. Robin (mixed derivative) conditions were utilized in order to better represent coating fabrication conditions. The nanoliquid analysis was based on Buongiorno's two-component model, which features Brownian movement and thermophoretic attributes. Nonlinear buoyancy force and thermal radiation formulations are included. Chemical reactions (constructive and destructive) were also considered since coating synthesis often features reactive transport phenomena. An ordinary differential equation model was derived from the primitive partial differential boundary value problem using a similarity approach. The analytical solutions were achieved by employing a homotopy analysis scheme. The influence of the emerging dimensionless quantities on the transport characteristics was comprehensively explained using appropriate data. The obtained analytical outcomes were compared with the literature and good correlation was achieved. The computations show that the velocity profile was diminished with an increasing relaxation parameter, whereas it was enhanced when the retardation parameter was increased. A larger thermophoresis parameter induces an increase in temperature and concentration. The heat and mass transfer rates at the wall were increased with incremental increases in the temperature ratio and first order chemical reaction parameters, whereas contrary effects were observed for larger thermophoresis, fluid relaxation and Brownian motion parameters. The simulations can be applied to the stagnated nano-polymeric coating of micromachines, robotic components and sensors.

Irreversibility analysis in the hydrothermal flow of γAl2O3/H2O and γAl2O3/C2H6O2 over a permeable stretching surface with effective Prandtl number

This present article provides a mathematical model that unravels the effect of entropy production on the hydrothermal behavior and cooling/heating process on the hybrid nanofluid spraying on a vertical permeable stretched surface. γAl2O3 is considered as the nanoparticles while water and Ethylene Glycol served as the base fluids. The derived heat balance equation considers the viscous dissipation phenomenon in addition to the effective Prandtl number. The competence of γAl2O3/H2O hybrid nanofluid on the cooling process as compared to γAl2O3/C2H6O2 nanofluid is deliberated in detail. These combined effects are commonly employed in solar film collectors, heat exchanger technologies, and geothermal energy storage systems. Using sufficient similarity, the fundamental equations are converted into dimensionless forms and solved using the spectral collocation method. The residual errors are graphed to analyze the method’s speedy convergence. Results for the embedded parameter on the flow speed, thermal distribution, entropy production, and Bejan number are shown graphically in the presence of an effective Prandtl number while the plots for skin friction and Nusselt number are displayed with and without an effective Prandtl number. As the Reynolds number parameters are increased, the Bejan number decreases, resulting in the dominance of entropy formation owing to frictional heating and magnetic field irreversibility.

Augmentation of magnetohydrodynamic nanofluid flow through a permeable stretching sheet employing Machine learning algorithm

An incompressible MHD nanofluid boundary layer flow over a vertical stretching permeable surface employing Buongiorno’s design investigated by considering the convective states. The Brownian motion and thermophoresis effects are used to implement the nanofluid model. Operating the similarity transmutations, to transform the governing partial differential equations into ordinary differential equations consisting of the momentum, energy, and concentration fields and later worked by using a program written together with the stiffness shifting in Wolfram Language. The consequences of various physical parameters on the velocity, temperature, and concentration fields are analyzed, such as magnetic parameter M, Brownian motion parameter Nb, thermophoresis parameter Nt, Lewis number Le, temperature Biot number Biθ, concentration Biot number Biϕ, and suction parameter fw. Furthermore, the Skin friction coefficient, local Nusselt, and local Sherwood numbers concerning magnetic parameter for various values of physical parameters (i.e. fw, Nb) are obtained graphically, then the outcome is validated with other recent works. Finally, introduced a new environment to employ machine learning by performing the sensitivity analysis based on the iterative method for predicting the Skin friction coefficient, reduced Nusselt number, and Sherwood number with respect to magnetic parameter for suction parameter and Brownian motion parameter. Machine learning algorithms provide a strong and quick data processing structure to enhance the actual research procedures and industrial application of fluid mechanics. These techniques have been upgraded and organized for fluid flow characteristics. The present optimization process has the potential for a new perspective on the metallurgical process, heat exchangers in electronics, and some medicinal applications.

Year-round monitoring of chloride releases from three zero-exfiltration permeable pavements and an asphalt parking lot

Winter deicers, though essential for maintaining safe pavement conditions in winter, increase chloride (Cl−) concentrations in receiving water bodies above recommended environmental guidelines. Zero-exfiltration or lined permeable pavement is an important technological innovation for controlling particulate-bound pollutants at the source. As stormwater does not infiltrate into the ground, soluble pollutants like Cl− are ultimately discharged into receiving water bodies. Our aim was to examine Cl− concentrations in effluents from three zero-exfiltration permeable pavement cells (Permeable Interlocking Concrete Pavement (PICP), Pervious Concrete (PC), Porous Asphalt (PA)) and compare them with runoff from a Conventional Asphalt (ASH) cell. The study conducted at a parking lot in St. Catharines, Ontario, Canada, from January 2016 to May 2017 observed that the permeable pavements provided only temporary attenuation of Cl− during winter but exhibited a quick release during spring melt. Cl− concentrations and loadings were different for each permeable pavement system in terms of timing and magnitude. Cl− concentration in ASH runoff frequently had very high spikes (21,780 mg/L); however, the median winter Cl− concentration in ASH runoff was lower than Cl− levels in the permeable pavements' effluents and later declined drastically after spring melt, but in few instances, was above the chronic water quality guideline (120 mg/L). The average event mean concentration (EMC) of Cl− was 1600 and 120 mg/L in the permeable pavements’ effluents during salting and non-salting season, respectively. In one year, each permeable pavement system released approximately 67–81 kg of Cl− with significant differences being observed in Cl− loads between the 2016 and 2017 seasons. Therefore, a multi-year data collection and monitoring plan captured the variability in winter conditions. The study provided insights into the behaviour, retention and release of Cl− from traditional and permeable hardscape surfaces and possible avenues for Cl− attenuation, source control and aquatic habitat conservation.

Exact multiple solutions of 2-D bidirectional moving plate micropolar hybrid nanofluid flow with heat transfer

Consider a hybrid copper-aluminum oxide/water flow over a permeable deforming surface with constant wall and prescribed wall temperature of non-Newtonian micropolar hybrid nanofluid flow under velocity slip boundary condition. The main purpose is to assess the existence of unique or multiple exact solutions of governing system of nonlinear coupled ordinary differential equations that describe the flow and heat fields. Similarity transformation variables are used to reduce the micropolar hybrid nanofluid flow and heat transfer model into nonlinear differential equations, which are exactly solvable in explicit forms. The classification of solutions into physically meaningful solutions depends entirely on the domains of parameters. Critical values determined for mass transfer are definitive in positioning and bordering the solutions. The profiles of velocity, microrotation and temperatures in the micropolar fluid reveal monotonically decaying behavior. The cases when parameters attain special values, produce special as well as dual exact solutionsIn addition, the visual analysis showing the influences of state parameters on wall moving velocity, angular velocity, constant wall temperature, linearly growing wall temperature and rate of heat transfer is presented. • Multiple solutions for hybrid nanofluid flow of bidirectional deforming plane problem. • Parametric domains determine regions for unique and multiple solutions. • No solutions fall in the region 0 ≤ K ≤ 1 , and only one solution exists for K > 1 . • For large values of velocity slip, the stretching/shrinking velocity diminishes. • Larger temperature jump values abate heat transfer rate.

Urban Land Use Changes: Effect of Green Urban Spaces Transformation on Urban Heat Islands in Baghdad

Urban sprawl has led to changes in landscaping. For instance, open areas and green urban spaces (GUSs)11GUSs: Green Urban Spaces. are replaced by buildings, streets, and infrastructure. Permeable and wet surfaces have also been transformed into non-permeable and dry surfaces. This, unfortunately, creates a major problem known as Urban Heat Islands (UHI). The rise in temperature makes the urban centres warmer when compared to their rural outlying areas. This affects the environmental goodness, energy consumption demands, quality of wellbeing. However, there is limited knowledge concerning the change in the use of GUSs, the relationship between the area of ​​these spaces, and the buildings formation on the exacerbation of the UHI in the cities. The research study aim is to assess the impact of the area of GUSs and the building s formation on the exacerbation of the (UHI) in Baghdad city.The purpose of this study is to improve the understanding of an integrated approach for open green spaces by reviewing city‘s experience with a main focus of environmental sustainability, cooler temperature, and thermal comfort. The research selected three typical GUSs in Baghdad (Ziyouna) as a case study. Those spaces were transformed into various types of buildings for different uses. The UHI impact is identified and compared in two scenarios (GUSs and added building) using computer climate simulation (ENVI-met) tool. The tool also assessed and measured surfaces and air temperature (CLUHI & SUHI) at different points in the selection of three typical models. The results demonstrated several factors combined with the change of urban land uses that are responsible for exacerbation of UHI in terms of buildings‘ height, formation, ground coverage, and construction including pavement materials and colour.

The behavior of permeable interlocking concrete pavement under different rainfall intensities and design conditions

ABSTRACT This study investigated the behaviour of permeable interlocking concrete pavement (PICP) in terms of water infiltration volume, surface runoff volume, and load resistance, using a specific lab apparatus, designed and manufactured as a rainfall simulator. The connecting pattern of the surface blocks is a stretcher bond pattern with a joint spacing of (5 and 10 mm) between the block pavers to be filled with a small-sized open-graded aggregate to finalise the permeable surface of joints. The adopted pattern has been examined under three rainfall intensities of (20, 40, and 60 l/min), four longitudinal slopes (0, 2, 4, and 6%), and three transverse slopes (0, 2, and 4%). The results showed that at high rainfall intensities (60 l/min), high longitudinal slopes (6%), and high transverse slopes (4%), the stretcher-bonded PICP with 5 mm spacing between the blocks infiltrates less water than the one with 10 mm. Furthermore, PICP with 5 mm spacing has higher surface runoff than PICP with 10 mm spacing at high rainfall intensities (60 l/min), high longitudinal slopes (6%), and all transverse slope percentages (0, 2, and 4%). In addition, the load resistance of stretcher-bonded PICP with 5 mm spacing between the blocks is higher than that of 10 mm at all the subjected loads in the load-deflection test. Despite the shown differences between both types of PICP, they are strongly recommended as an alternative choice for ordinary dense-graded pavement.

Конвективный теплообмен и трение в тонком ламинарно-турбулентном пограничном слое на проницаемой поверхности затупленного конуса малого удлинения

Solving the problem of calculating convective heat transfer and friction in the laminar-turbulent boundary layer involves the need for numerical integration of differential equations, supplemented by those or other semiempirical models of apparent turbulent viscosity, which should be validated on the results of experimental studies, carried out in conditions, providing simulation of the gas dynamic picture of body flowing by a gas stream. Unfortunately, at present, there are no literature data on studies of laminar-turbulent heat exchange on the permeable surface of a blunted body, and under these conditions, one has to go by the way of comparing the calculated data with the results of experiments carried out on sharp bodies. Literature sources describe the results of studies carried out for a hemisphere, in which one of the semi-empirical models of apparent turbulent viscosity is used, tested on the results of experiments carried out on the impermeable surface of such shaped body. In this case, it was possible to obtain a physically consistent picture of the influence exerted by blowing gas through the wall on the degree of blocking of the convective heat flow. In the absence of qualitative experimental data on this issue, it seems reasonable to apply in practice the considered semi-empirical model of apparent turbulent viscosity to estimate the degree of blocking of convective heat flow and friction under the specified conditions. This article is devoted to the solution of a similar problem for the lateral surface of a blunted cone

Non-Newtonian Nano-Fluids in Blasius and Sakiadis Flows Influenced by Magnetic Field

Current study solves heat transfer and fluid flow problem in Newtonian and non-Newtonian nano-fluids through a permeable surface with a magnetic field effects which is done in the presence of injection and suction for the first time. In order to solve the governing partial differential equations numerically, we used the Runge-Kutta Fehlberg (RKF45) technique in which the similarity transformation method is applied. This approach converts the governing partial differential equations into ordinary differential equations. In this particular investigation nano-particles of copper, copper oxide, titanium dioxide, and aluminium oxide are studied by considering CMC/water as a base fluid with the effect of magnetic field on the classical Blasius and Sakiadis flows of nano-fluids. Validation is carried out using the previously obtained numerical findings. We looked at the power-law index (n), the volume fraction (φ) of nano-particles and the permeability parameter (fw) which affects the flow of nano-fluid and the transfer of heat. Non-Newtonian nano-fluid demonstrates superior performance in terms of heat transfer when compared to Newtonian nano-fluid in both the injection and the impermeable surfaces. Altering the nano-particles' composition, on the other hand, has a far greater impact on the heat transfer process that occurs during suction. Graphics show the impacts of governing physical parameters on Blasius and Sakiadis flow velocity, temperature, skin friction coefficient, and reduced Nusselt number. Physical and engineering interest are explored in detail.

Contribution of suction phenomenon and thermal slip effects for radiated hybrid nanoparticles (Al2O3 −Cu/H2O) with stability framework

This thermal case pronounced the stability framework for stagnation point flow of magnetized alumina and copper nanoparticles with due exponentially shrinking permeable surface. The thermal stability and enhancement of water base liquid had been taken into account with uniform impulsion of hybrid nanomaterials. The induced flow results via exponentially shrinking permeable surface. The similarity transformation simplifies the mathematical model where governing formulated system for hybrid nanofluid is altered into the nondimensional form. A numerical solver called bvp4c is employed in MATLAB software to aid in the problem-solving process, and dual branches have been found. The significance of pertaining parameters associated to the flow model is inspected in view of thermal properties. The findings show that there are two branches for suction strength [Formula: see text] and magnetic strength [Formula: see text]. The bifurcation values [Formula: see text] and [Formula: see text] reduce for the occurrence of dual branches as the solid volume percentages of copper increase. Furthermore, for the upper branch solutions, the skin friction and heat transfer rate rise as [Formula: see text] increases. The temporal stability analysis determines the stability of the dual branches, and it is discovered that only one of them is stable and physically applicable. The presence of suction parameter effectively controls the thermal transportation phenomenon.

Turbulent boundary layer on an elongated axisymmetric body with air blowing and permeable surface roughness

Turbulent boundary layer on an elongated axisymmetric body with air blowing and permeable surface roughness

A three-dimensional numerical study of laminar buoyancy-driven columnar vortices

This study deals with the development of a low momentum whirling laminar plume that results from the interaction between a plume and a circulating flow imposed by a cylindrical rotating screen. Numerical simulations were performed by direct simulation of the fully three-dimensional flow governed by the compressible Navier-Stokes and energy equations. The rotating thermal plume forms a columnar vortex governed by the Grashof (GR) and nondimensional rotation velocity (Reynolds number (ReR)), based on the cylindrical domain’s radius and the angular frequency of rotation of the permeable lateral surface. Numerical solutions were obtained in the range 102<Gr<106 and 10<ReR<150. The vortex generated bifurcates into a pair of steady co-rotating vortices within the range 104<Gr<2×105 and 30<ReR<100. The steady state configuration of the flow is described and analysed, showing the evolution of the vorticity contours in cross-sections that start out as circlets, gradually turn into an ellipse and end up bifurcating into a pair of co-rotating vortices. The role of the boundary layer is also described, showing an increase in the distance between the co-rotating vortex pair for a given Gr and ReR numbers but in the absence of a boundary layer. At last, the temporal evolution of the vortex splitting process is compared to measurements of merging of two co-rotating vortices available in the literature, uncovering that the two phenomena take similar timescales to occur.

Numerical simulation of melting heat transfer towards stagnation point region over a permeable shrinking surface

Numerical simulation of melting heat transfer towards stagnation point region over a permeable shrinking surface

Radiative and MHD Effects on Time-Dependent Thermal-Material Transfer by Micropolar Binary Mixture

Radiation is an important branch of thermal engineering which includes geophysical thermal insulation, ground water pollution, food processing, cooling of electronic components, oil recovery processes etc. An analysis of unsteady magneto-convective heat-mass transport by micropolar binary mixture of fluid passing a continuous permeable surface with thermal radiation effect has been introduced in this paper. The governing equations are transformed into coupled ordinary differential equations along with Boussinesq approximation by imposing the similarity analysis. Applying the shooting technique, the obtained non-linear coupled similarity equations are solved numerically with the help of “ODE45 MATLAB” software. The results of the numerical solutions to the problem involving velocity, temperature, concentration and micro-rotation are presented graphically for different dimensionless parameters and numbers encountered. With an increase of suction parameter, the velocity distributions very closed to the inclined permeable wall decrease slightly where 0 ≤ η ≤ 0.3 . But for the uplifting values of sunction, both micro-rotation profile and species concentration enhance through the boundary layer. The skin-friction coefficient increases about 61%, 13%, 27% for rising values of Prandtl number (0.71-7), radiation effect (0 - 1) and thermal Grashof number (5-10), respectively, but an adverse effect is observed for magnetic field (1 - 4), inclined angle 0 0 − 60 0 and Schmidt number (0.22 - 0.75). Heat transfer and mass transfer reduce about 82%, 53%, respectively, in increasing of Pr (0.71-1) and 36%, 11%, respectively, in increasing of thermal radiation (0 - 1). The surface couple stress increases about 26%, 49%, 64% and 30% with the increasing values of magnetic field (1-4), inclination angle 0 0 − 60 0 , suction (0-1) and Schmidt number (0.22-0.75), respectively. Finally, the present study has been compared with the earlier published results. It is observed that the comparison bears a good agreement.

The activation energy in the radiative flow of fourth-grade nanomaterial with convective conditions

The fourth-grade nanomaterial over a stretched permeable surface is intended in this article. The heat transport process is analyzed by thermal radiation and viscous dissipation. Convective heat-mass conditions at the surface are imposed. The Boungiorno model is utilized for nanofluid description. Furthermore, activation energy is accounted for. Flow expressions (PDEs) are modeled by the implementation of boundary layer approximations. These PDEs are expressed to ODEs by means of appropriate transformations. A technique, namely, OHAM is executed for solution development. Quantities of interest (skin fraction, velocity, Nusselt number, temperature, concentration, and Sherwood number) are evaluated for the influential variables. An increasing trend for velocity () is observed for increasing fourth-grade fluid parameters in the case of negative injection parameters, while an inverse behavior is noted for positive values of injection parameters. Eckert number and radiation increase heat transfer rate, while a decreasing trend is observed against higher Brownian and thermophoresis parameters.

One Case of Shock-free Deceleration of a Supersonic Flow in a Constant Cross Section Area Channel

Air flows with supersonic speeds are used in many cases, for example, as aircraft air intakes, wind tunnels, and energy separation devices. In many cases it is necessary to decelerate the flow to sonic speeds. Traditionally the deceleration realized through the shocks system, which leads to total pressure losses. The article considers the method of deceleration of supersonic flows using permeable surfaces. In this case, the deceleration process occurs without shocks and, therefore, with lower total pressure losses. We have considered the flow in a tube with permeable wall located behind a supersonic nozzle. One-dimensional and axisymmetric mathematical models of such a device are developed. The calculation results are compared with experimental data. It is shown that, depending on the ratio of pressure inside the tube and the ambient pressure, different flow regimes inside the tube are possible: pure subsonic, transitional from supersonic to subsonic, and pure supersonic. The transition from supersonic to subsonic flow occurs without shocks due to the suction and friction combined effects.

Impacts of Land Use and Land Cover Changes on Land Surface Temperature over Cachar Region, Northeast India—A Case Study

The promptness of industrialisation and expanding urbanisation to achieve targets of economics are resulting in the transfiguration of permeable surfaces into impervious ones through LULC adaptation, leaving a herculean footprint on the ecosystem. The LULC escalates land surface temperature (LST), which further stimulates urban heat islands (UHIs), ultimately remaining in tune with high levels of air pollution, energy use, and corresponding health hazards. The present evaluation first used Landsat TM/OLI satellite data to identify the labyrinth of the LULC rotation and, secondly, gauged its effects on the LST in the Cachar district of Assam, India, for the years 1990, 2000, 2010, and 2020. It embraces Cellular Automata (CA) and GIS methodologies to pull out the urbanization pattern and its ramifications in various LULC brackets of Cachar, India. It also embraces spatiotemporal LULC monitoring (1990–2020) and urban growth modelling (2030–2040). From the period 1990 to 2020, satellite-based LULC showed a net urban expansion of 269.43 km2 (7.13% increase). Some correlations were developed to show the relationship between spatial indices such as NDVI, NDBI, and NDWI with Land Surface Temperature (LST). Resultantly, a positive relation exists between LST and NDBI, but a negative correlation prevails between LST and NDVI, as well as NDWI. This evaluation will be of service to urban and environmental planners, providing them with detailed knowledge on how land cover is changing uniquely in northeast India.

Analysis of Mixed Convection on Two-Phase Nanofluid Flow Past a Vertical Plate in Brinkman-Extended Darcy Porous Medium with Nield Conditions

The rapid advancement in technology in recent years has shown that nanofluids are very vital to further development in science and technology. Moreover, many industrial specifications cannot be met by allowing natural convection only, hence the need to incorporate forced convection and natural convection into a single flow regime. The research aims to quantify the mixed convective two-phase flow past a vertical permeable surface in a Brinkman-Extended Darcy porous medium (BEDPM) induced by nanofluid, with heat and mass transfer. In addition, the Nield condition is also incorporated. The model of the problem was initially constructed in the vital form of leading governing equations (LGEs). These LGEs are specifically called partial differential equations (PDEs) (because of two or more independent variables) which were later converted into a set of the single independent variable of ordinary differential equations (ODEs) by implementing the similarity transformations. The set of single independent ODEs was numerically solved via the boundary value problem of fourth-order (bvp4c) technique. The bvp4c is one of the most frequently recommended built-in MATLAB subroutines based on the three-stage Labatto formula. The impact of several physically embedded influential parameters on the fluid flow, along with mass and thermal properties of the nanofluid in a Brinkman-Extended Darcy porous medium for the cases of buoyancy assisting flow (BAF) and buoyancy opposing flow (BOF), were investigated and argued. The numerical outcomes clarify that the porosity parameter reduces the velocity, whereas the concentration and the temperature enhance in the case of the buoyancy assisting and buoyancy opposing flows. In addition, the wall drag force elevates for the larger value of the dimensionless permeability parameter K1 and the buoyancy ratio parameter N, while it declines for the modified porosity parameter ε1.

Numerical Solution of Magnetized Williamson Nanofluid Flow over an Exponentially Stretching Permeable Surface with Temperature Dependent Viscosity and Thermal Conductivity.

This research work describes and investigates Williamson nanofluid flow over an exponentially stretching permeable vertical plate with temperature-dependent thermal conductivity and viscosity. The governing non-linear partial differential equations (PDEs) are metamorphosed into coupled non-linear ordinary differential equations (ODEs) by using similarity transformation. The succeeding equations were numerically solved using MATLAB function bvp4c for various values of parameters. For velocity, temperature, concentration, the skin friction coefficient, and the local Nusselt number, data are presented in the form of graphs and tables. It is noted that for increasing values of magnetic parameter , Williamson parameter and viscosity parameter , the boundary layer thickness of the velocity profile decreases, while it increases for the temperature profile. The findings of the present work are validated through the published results.

Study of an unsteady fluctuative MHD flow of elasticoviscous liquid past a vertical porous plate

AbstractMost flows which occur in nature/practical applications are fluctuating. The fluctuating motions superimposed on the main motion are complex. Further, the unsteadiness of the flow is an added reality to applications in various fields. The free convection flow of an electrically conducting fluid past different types of vertical bodies subjected to a magnetic field is studied because of its wide range of applications in astrophysics, geophysics, aerodynamics, electromagnetic pumps, the flow of liquid metals, and so forth. In the present analysis, an attempt has been made to study the thermal radiation effect on the unsteady magnetohydrodynamic flow of an incompressible elasticoviscous liquid (Walters‐B' fluid model) along an infinite hot vertical permeable surface embedded in a porous medium with heat source and chemical reaction. The governing equations of motion, energy, and concentration are solved by an approximate analytical method, that is, the successive perturbation technique and numerical method (Runge–Kutta with shooting). The solution procedure rests upon the basic assumption that the unsteady boundary layer involves a steady basic flow superimposed on an unsteady flow. The most striking outcome is that the combined effect of oscillation outflow, the elasticity of the fluid, and thermal as well as mass buoyancy overrides the resistive electromagnetic force and suction at the plate to enhance the velocity so that high values of magnetic strength are not desired. Further, a higher value of the heat source parameter accelerates the momentum diffusion resulting in the escalation of the velocity field. Fall of concentration is relatively faster in cases of heavier species as well as destructive reactions. The heat transfer coefficient assumes positive values indicating the heat flows from the plate to the fluid (cooling of the bounding surface and heating of the fluid). These observations may have industrial (design of heat exchanges) and therapeutic bearings.