Concentration Boundary Layer Thickness Research Articles

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.

Modeling the Effects of Coatings, Light Absorption, and Mass Transfer on Solar-to-Hydrogen Efficiencies in Z-Scheme Photocatalytic Reactors

Z-scheme photocatalytic particles in an aqueous solution with soluble redox shuttles present a promising pathway for solar water splitting to produce hydrogen. Tandem light absorbers more efficiently utilize the incident solar spectrum, and physically separating hydrogen and oxygen production sites offers a safe reactor design. Theoretically, these reactor designs are projected to achieve competitive solar-to-hydrogen efficiencies as large as 34% with idealized light absorbers, state-of-the-art hydrogen, and oxygen evolution catalysts, selective reactions, and rapid mass transfer rates1. However, practical demonstrations have been limited to significantly lower efficiencies that are less than 1%. In part, this effect is attributed to competing and undesired redox reactions occurring at the particle–cocatalyst–electrolyte interface. In this work, we develop and apply an expanded equivalent circuit model to test the effectiveness of coatings to achieve reaction selectivity by manipulating redox species transport to functional interfaces2. This model formulates light absorbers as photodiodes and accounts for the effects of kinetic and mass-transfer resistances for both the desired and competing redox reactions. Transport properties in the coatings are parametrized as a function of its thickness, species permeabilities, and solubility coefficients. Mass transport rates are computed as a function of species concentration and concentration boundary layer thickness. Additionally, spatial profiles of light intensity in a reactor with multiple light absorbers are evaluated for an ensemble of (a) optically thin semitransparent slabs, and (b) particles that can absorb and scatter incident light. Results reveal the interplay of light absorption behavior, coating transport and kinetic properties, and mass transfer rates on the predicted solar-to-hydrogen efficiencies. An optimum concentration of light absorbers is shown to maximize light absorption while minimizing the extent of competing reactions. Results are further interpreted to provide insight on design principles for selective coatings to maximize efficiency. Overall, the modeling framework provides new capabilities with a tractable approach to traverse the multidimensional dependencies of various parameters on the solar-to-hydrogen efficiencies for Z-scheme photocatalytic systems. References Keene, S., Bala Chandran, R. & Ardo, S. Calculations of theoretical efficiencies for electrochemically-mediated tandem solar water splitting as a function of bandgap energies and redox shuttle potential. Energy Environ. Sci. 12, 261–272 (2019).Barrera, L. & Bala Chandran, R. Harnessing Photoelectrochemistry for Wastewater Nitrate Treatment Coupled with Resource Recovery. ACS Sustain. Chem. Eng. 9, 3688–3701 (2021).

Cattaneo-Christov dual diffusive non-Newtonian nanoliquid flow featuring nonlinear convection

A theoretical study is presented of the transport characteristics in double diffusive tangent hyperbolic (non-Newtonian) nanofluid boundary layer flow from a stretching flat surface. The Cattaneo–Christov (non-Fourier and non-Fickian) double diffusion model is deployed in the formulations for energy and species conservation, to determine more precisely temperature and concentration distributions with thermal and solutual relaxation times. Non–linear mixed convection and heat generation/absorption are included. The nanofluid approach combines Brownian motion and thermophoresis. Suitable transformations are deployed to render the nonlinear partial differential system into a system of dimensionless coupled ordinary nonlinear differential equations. The non-dimensional boundary value problem is then solved with the homotopic analysis method (HAM). The distributions of velocity, temperature and concentration of nanoparticles are depicted and investigated for the effects of multiple emerging parameters. Velocity is reduced (and momentum boundary layer thickness elevated) with increasing power–law index and Weissenberg number whereas velocity is elevated (and momentum boundary layer thickness reduced) with increment in mixed convection variable. Temperature is suppressed (and thermal boundary layer thickness depleted) with increasing thermal relaxation variable, heat sink parameter, Prandtl number whereas temperature is enhanced (and thermal boundary layer thickness boosted) with greater heat source parameter, Brownian motion parameter and thermophoresis parameter. Nanoparticle concentration is depleted (and concentration boundary layer thickness reduced) with greater Schmidt number and Brownian motion parameter whereas the opposite effect is induced with greater thermophoresis parameter and solutal relaxation time. Skin friction is strongly reduced with increasing values of nonlinear thermal and concentration convection variables. The simulations are relevant to nano-polymer coating operations.

Gyrotactic microorganisms bioconvection in combined convective magnetohydrodynamic Casson nanofluid flow over a vertically surfaced saturated porous media with variable viscosity

AbstractThe current article focuses on mass and thermal transfer analysis of a two‐dimensional immovable combined convective nanofluid flow including motile microorganisms with temperature‐dependent viscosity on top of a vertical plate through a porous medium, and a model has been developed to visualize the velocity slip impacts on a nonlinear partial symbiotic flow. The governed equations include all of the above physical conditions, and suitable nondimensional transfigurations are utilized to transfer the governed conservative equations to a nonlinear system of differential equations and obtain numerical solutions by using the Shooting method. Numerical studies have been focusing on the effects of intricate dimensionless parameters, namely, the Casson fluid parameter, Brownian motion parameter, thermophoresis parameter, Peclet number, bioconvection parameter, and Rayleigh number, which have all been studied on various profiles such as momentum, thermal, concentration, and density of microorganisms. The concentration boundary layer thickness and density of microorganisms increased as the Casson fluid parameter, Brownian and thermophoresis parameters increased, whereas the bioconvection parameter, Peclet number, and Rayleigh number increased. The thermal boundary layer thickness, concentration boundary layer thickness, and density of microorganisms all decreased. The velocity distribution decreases as the Peclet number, bioconvection, and thermophoresis parameters rise but rises as the Rayleigh number, Brownian motion parameter, and Casson fluid parameter rise. These are graphed via plots along with divergent fluid parameters.

Effect of the anode to cathode surface area ratio on the concentration distribution near the solid-liquid interface

For the solid-liquid chemical reaction, the mass transfer near the solid-liquid interface is often the rate determining step, such as in an electroplating process and in a high temperature process. To enhance the chemical reaction, traditional methods reduce the concentration boundary layer thickness formed near the solid-liquid interface by exciting a macro-scale flow in the bulk region. However, traditional methods have limitation in reducing the concentration boundary layer, because the concentration boundary layer exists in the velocity boundary layer. This means that the excitation of flow in the concentration boundary layer is important. Based on this concept, direct imposition of a force near the solid-liquid interface by superimposing the magnetic field and current has been proposed. By this means, the flow can be directly excited in the concentration boundary layer. In the past research, a Cu anodic electrode was dissolved in a Cu2+ aqueous solution, and the increase of the Cu2+ concentration decreased under the imposition of a time-varying force compared to that without the time-varying force imposition just above the centre of the anode. In this experiment, the uniformity of the solute concentration distribution under the time-varying force imposition with a different anode to cathode surface area ratio was investigated. As a result, the uniformity of the Cu2+ concentration distribution increased, and the average Cu2+ concentration in the vicinity of the anode surface decreased by increasing the anode to cathode surface area ratio. Tables 2, Figs 3, Refs 13.

Chemically reactive Maxwell nanoliquid flow by a stretching surface in the frames of Newtonian heating, nonlinear convection and radiative flux: Nanopolymer flow processing simulation

AbstractThe effects of a chemical reaction and radiative heat flux in a nonlinear mixed thermo-solutal convection flow of a viscoelastic nanoliquid from a stretchable surface are investigated theoretically. Newtonian heating is also considered. The upper-convected Maxwell (UCM) model is deployed to represent the non-Newtonian characteristics. The model also includes the influence of thermal radiation that is simulatedviaan algebraic flux model. Buongiorno’s two-component nanofluid model is implemented for thermophoretic and Brownian motion effects. Convective thermal and solutal boundary conditions are utilized to provide a more comprehensive evaluation of temperature and concentration distributions. Dimensionless equations are used to create the flow model by utilizing the appropriate parameters. The computed models are presented through a convergent homotopic analysis method (HAM) approach with the help of Mathematica-12 symbolic software. Authentication of HAM solutions with special cases from the literature is presented. The impact of various thermophysical, nanoscale and rheological parameters on transport characteristics is visualized graphically and interpreted in detail. Temperatures are strongly enhanced with Brownian motion and thermophoresis parameters. Velocity is boosted with the increment in the Deborah viscoelastic number and mixed convection parameter, and the hydrodynamic boundary layer thickness is reduced. A stronger generative chemical reaction enhances concentration magnitudes, whereas an increment in the destructive chemical reaction reduces them and also depletes the concentration boundary layer thickness. Temperature and concentration are also strongly modified by the conjugate thermal and solutal parameters. Greater radiative flux also enhances the thermal boundary layer thickness. Increasing the Schmidt number and the Brownian motion parameter diminish the concentration values, whereas they elevate the Sherwood number magnitudes,i.e.enhance the nanoparticle mass transfer rate to the wall.

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

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

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

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

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

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

Modelling of the Electrical Membrane Potential for Concentration Polarization Conditions.

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

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

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

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

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

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

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

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

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

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

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

Simulation studies on a rotating ring disk electrode: Effects of ionic migration with kinetic complication‐disk results

AbstractIn continuation to my previous work (Guha S. AIChE J. 2013;59(4):1390‐1399), in this work, effects of ionic migration are evaluated for disk region of a rotating ring disk electrode system by numerically solving complex differential equations, developed for mass transfer along with kinetic complication in presence of ionic migration under limiting current condition. The system for simulation is 0.01 M Fe2(SO4)3 solution with H2SO4 as supporting electrolyte. Simulation cases are presence and absence of ionic migration with kinetic complication (oxidation of Fe2+ to Fe3+ under O2 pressure). Results show that concentration boundary layer thickness of reactant Fe3+ reduces appreciably and steady‐state disk current reduces substantially in presence of migration. Simulated steady‐state disk current in absence of migration case agrees well with published data. Results indicate higher Fe2+ concentration in presence of migration and thereby higher rate of oxidation of Fe2+ to Fe3+ at all rate constant values.

Spectral relaxation computation of electroconductive nanofluid convection flow from a moving surface with radiative flux and magnetic induction

Abstract A theoretical model is developed for steady magnetohydrodynamic viscous flow resulting from a moving semi-infinite flat plate in an electrically conducting nanofluid. Thermal radiation and magnetic induction effects are included in addition to thermal convective boundary conditions. Buongiorno’s two-component nanoscale model is deployed, which features Brownian motion and thermophoresis effects. The governing nonlinear boundary layer equations are converted to nonlinear ordinary differential equations by using suitable similarity transformations. The transformed system of differential equations is solved numerically, employing the spectral relaxation method (SRM) via the MATLAB R2018a software. SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation, and linearization for solving a nonlinear system of equations. Effects of embedded parameters such as sheet velocity parameter$\lambda$, magnetic field parameter$\beta$, Prandtl number$Pr$, magnetic Prandtl number$Prm$, thermal radiation parameter$Rd$, Lewis number$Le$, Brownian motion parameter$Nb$, and thermophoresis parameter$Nt$ on velocity, induced magnetic field, temperature, and nanoparticle concentration profiles are investigated. The skin-friction results, local Nusselt number, and Sherwood number are also discussed for various values of governing physical parameters. To show the convergence rate against iteration, residual error analysis has also been performed. The flow is strongly decelerated, and magnetic induction is suppressed with greater magnetic body force parameter, whereas temperature is elevated due to extra work expended as heat in dragging the magnetic nanofluid. Temperatures are also boosted with increment in nanoscale thermophoresis parameter and radiative parameter, whereas they are reduced with higher wall velocity, Brownian motion, and Prandtl numbers. Both hydrodynamic and magnetic boundary layer thicknesses are reduced with greater reciprocal values of the magnetic Prandtl number Prm. Nanoparticle (concentration) boundary layer thickness is boosted with higher values of thermophoresis and Prandtl number, whereas it is diminished with increasing wall velocity, nanoscale Brownian motion parameter, radiative parameter, and Lewis number. The simulations are relevant to electroconductive nanomaterial processing.

Material behaviour in micropolar fluid of Brownian motion over a stretchable disk with application of thermophoretic forces and diffusion-thermo

To study the material behavior of axisymmetric flow in micropolar fluid for heat and mass exchange over a stretchable disk placed in porous medium taking into account the effect of heat generation, diffusion thermo, Brownian motion and thermophoretic effect. A suitable similarity transformations is adapted to convert the governing PDEs to non-dimensional form. A well-tested, numerically stable MATLAB code in connection with Bvp4c is employed for the conservation of equations. The noticeable features of the relevant parameters on micropolar fluid flow for axial velocity, radial velocity, micro-rotation, temperature and species concentrations profiles are accentuated on the plots using MATLAB. It is found that angular velocity is enhanced for augmented values of micropolar parameter. Moreover, due the effect of thermophoretic force, the thickness of thermal and concentration boundary layer are enhanced. In addition, thermal diffusion becomes more due to the increase in the vortex viscosity of the fluid, and an amplified thermal and molar concentration boundary layer thicknesses can be found. This study incorporates numerous engineering applications on rotating machineries, spin-coating, centrifugal pumps, computer storage devices, chemical engineering and different aerodynamic issues. Also, this analysis signifies great impact on biomechanics and stenosis related issue in medical sciences.

A computational model for hybrid nanofluid flow on a rotating surface in the existence of convective condition

The current work aims to study heat transfer properties within the flow. A newly developed idea regarding hybrid nanofluid is utilized to obtain the desired outcomes. This study focused on hybrid base nano liquid flow past an exponentially stretching rotating surface in the presence of the convective condition. Ethylene glycol-water (50%–50%) mixture is taken as base fluid. Thermophysical properties are discussed. The probe of emerging parameters indicates that hybrid base nanofluid gives a preferable rating as compared to nanofluid. Appropriate choice of composition plays a vital role. Physical characteristics of essential parameters such as Prandtl number, convective parameter, stretching ratio, rotation parameter, and temperature exponent are evaluated. Graphical depiction reveals that the velocity curve decline by increasing rotation parameter for CuO-hybrid base fluid and TiO2 hybrid base fluid. By expanding the values of the stretching ratio the velocity profile p′(η) is decreasing while the velocity curve q′(η) increased for CuO as well as TiO2 hybrid base fluid. Concentration boundary layer thickness growing by enlarging rotation parameters for both types of nanofluid. Moreover, the influence of various parameters on skin friction factor and Nusselt numbers are also evaluated.