Micropolar Nanofluid Research Articles

Diversified characteristics of the dissipative heat on the radiative micropolar hybrid nanofluid over a wedged surface: Gauss-Lobatto IIIA numerical approach

The present examination focuses on the Falkner-Skan flow of micropolar hybridized nanofluid via a wedge surface. The proposed study examines thermal radiative fluxing and heat dissipation in hybridized nanoparticle aqueous solutions. Simulations of uni-directional radiative transport in optically dense fluids use Rosseland's diffusion model. This study created a Cu-TiO2/water hybrid nanofluid by mixing Cu and TiO2 nanomolecules with H2O. Partial differential equations from Naiver-Stokes theory are used to generate the regulating flow phenomena, then convert them into ordinary differentiation equations using an appropriate similarity approach. Additionally, the three-stage Lobatto IIIA method is used to compute the formulae. Calculations are done using MATLAB's built-in bvp5c function. We found that increasing material characteristics slows fluid flow because micropolar nanofluids minimize drag. These alterations alter fluid flow and boost temperature. However, boosting thermal radiation and Eckert number slows heat movement but improves temperature profiles. Much prior research ignored thermal radiative fluxing and heat dissipation in the aqueous solution of hybrid nanomolecules (Cu and TiO2) in Falkner-Skan micropolar flow via a wedge surface. Tables show wall frictional factor and Nusselt quantity results. Micropolar fluid characteristic decreases velocity but increases micro-rotational velocity. Power-law parameters, volume fractions, radiation, heat source, and Eckert amount affect thermal contours.

Numerical investigation of heat and mass transfer in micropolar nanofluid flows over an inclined surface with stochastic numerical approach

Numerical investigation of heat and mass transfer in micropolar nanofluid flows over an inclined surface with stochastic numerical approach

Free convective flow of micropolar nanofluid over a heated stretching sheet with the impact of dissipative heat and binary chemical reactions

Free convective flow of micropolar nanofluid over a heated stretching sheet with the impact of dissipative heat and binary chemical reactions

A computation analysis with heat and mass transfer for micropolar nanofluid in ciliated microchannel: With application in the ductus efferentes

Inherited heat enhancement capabilities and their significance in the field of medical sciences and industry make nanofluids the focus of research nowadays. Furthermore, due to the remarkable advancements in bionanotechnology and its significance in biomedical fields such as drug delivery systems, cancer tumor therapy, bioimaging, and many others, it has emerged as a key research area. Contribution of cilia for the flow in ductus efferentes of human male reproductive tract is elaborated. A novel mathematical scheme is presented for the heat and mass transfer of MHD micropolar nanofluid transport in an asymmetric channel lined with cilia. The pertinent equations of nanofluid transport are exposed to lubrication approximation theory and solution for the physical problem is examined with efficient bvp4c technique in MATLAB. Fluid rheology is explored with the variations of different transport parameters like Hartmann number, Grashof number, Brownian motion, buoyancy, thermophoresis and Darcy number. It is reported that nanofluid transport is affected with rise in the Lorentz force and show reverse behavior with rising permeability. The temperature of the nanofluid in ciliated microchannel is raised with enhanced value of Hartmann number, Grashof number, Prandtl number, and Darcy number while diffusion phenomenon of nanofluid is slowed down with these parameters. Spinning motion of the nanofluid is enhanced with Grashof number and slow down with nanoparticle Grashof number and different behavior is recorded for Darcy and viscosity parameters in different flow regime. Reported investigation presents crucial findings for ciliary transport of micropolar nanofluid and tackled with appropriate selection of micropolar parameter, Brownian motion parameter, thermophoresis and Grashof number. Moreover, this investigation will be handful for cilia-based actuators which work as micro-mixers in controlling the flow in minute bio-sensors and may prove their worth in micro-pumps employed in various drug-delivery systems.

Thermal analysis of hybrid nano-fluids: Modeling and non-similar solutions

The thermal analysis of hybrid nano-fluids is a significant research area with diverse applications in industries such as paint, electronics, and mechanical engineering. Existing literature provides limited solutions to the governing equations for the flow of these fluids. Modeling and deriving non-similar solutions for these equations pose interesting and challenging mathematical problems. This study focuses on investigating heat transfer in the flow of two types of nano-fluids, specifically Al2O3/H2O micropolar nano-fluid and Al2O3 + Ag/H2O hybrid nano-fluid, near an isothermal sphere. Conservation laws are employed to formulate the mathematical problem, and by normalizing the variables, the governing equations are converted into a set of dimensionless partial differential equations. Non-similar solutions are then obtained using numerical methods. A comparative analysis is carried out to assess the influence of various parameters on different profiles and engineering quantities for both types of nano-fluids. Both linear and rotational velocities fall down near the surface of sphere with rising microstructure in hybrid nanofluid. The micro-rotation parameter rises the temperature profile while reduces the Nusselt number of both traditional Al2O3/water based nanofluid as well as hybrid nanofluid.

Entropy generation in a chemically reactive magnetohydrodynamic unsteady micropolar nanofluid flow with activation energy over an inclined stretching sheet: A Buongiorno model approach

The goal of this research is to inspect the heat and mass transfer trends and entropy generation in a time-reliant stagnation point stream of a micropolar fluid across an inclined stretched surface. For this objective, a chemically reactive, electrically conducting fluid exposed to an orthogonal magnetic field is studied. The flow governing equations are modelled using Buongiorno model and are reformed to a system of higher order ordinary differential equations by administering appropriate similarity transformations. This system is quantitatively examined by employing the fourth-order Runge-Kutta scheme with shooting approach. The effects of thermal radiation, magnetic field, uniform heat source/sink, Brownian motion, thermophoresis, activation energy, and binary chemical reaction are studied on velocity, microrotation, temperature, and concentration profiles. It is observed that magnetic field and Brownian motion elevate the flow temperature. Increased activation energy spikes the fluid concentration while increase in binary chemical reaction reduces the particle concentration. Later, impact of various parameters on skin friction coefficient and heat and mass transfer rates are tabularised. Increasing values of thermophoretic diffusion parameter, Brownian diffusion parameter, and chemical reaction parameter improve the rate of mass transfer. Unsteadiness parameter triggers the skin friction coefficient 53.2% when the parameter value was increased from 0.7 to 1.0. Viscous dissipation and thermal radiation increase the rate of entropy generation. A comparison of skin friction coefficient with previous studies demonstrates a strong agreement.

Regression analysis of Cattaneo–Christov heat and thermal radiation on 3D Darcy flow of Non-Newtonian fluids induced by stretchable sheet

This study explores the influence of thermal radiation and heat source on magnetized flow micropolar nanofluid through a Stretchable Sheet in the presence of mobile microbes. The presence of microorganisms adds a biological dimension to the problem, affecting fluid dynamics and heat transfer, which are central to this investigation. To motivate the problem, the flow is induced by a Darcy porous exponentially stretching sheet with generalized boundary conditions. A regression analysis is conducted to analyze the interplay of various parameters on the flow and heat transfer characteristics. Additionally, similarity transformations are implemented to transform the set of partial differential equations (PDEs) into a set of ordinary differential equations (ODEs). The resulting equations are solved numerically using the shooting approach via the bvp4c platform in Matlab. The regression model quantifies the impact of each parameter and their interactions on the flow field, temperature distribution, and Darcy effects. Furthermore, the impact of involved parameters on flow, energy, volumetric concentration, density of microbes, and micro-rotations distribution are analyzed and discussed through graphs, literature, and tables. The findings of this research are crucial for various engineering, industrial, and pharmaceutical applications, including biofilm formation, geothermal energy extraction, and wastewater treatment processes.

Comparative characterization of heat transfer and entropy generation of micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade binary nanofluids in PTSCs settings

AbstractIn this paper, we delve into the behavior of binary micropolar nanofluids, specifically micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade, within the parabolic trough solar collector (PTSC) configurations. The primary objective is to enhance the collective efficiency of this device by means of a comprehensive comparison amongst the three aforementioned nanofluids. The governing equations, including continuity, linear momentum, angular momentum, and energy equations, were systematically formulated. Subsequently, the introduction of suitable similarity variables facilitated the transformation of the intricate partial differential equations into manageable ordinary differential equations. These resultant equations were then tackled utilizing the shooting method via the bvp4c numerical package in MATLAB. The study critically examines the influence of diverse parameters that dictate the flow dynamics of the nanofluids. This encompasses nanofluid velocity, angular velocity, temperature distribution, entropy generation, skin friction coefficient, and local Nusselt number. Remarkably, the research uncovers that the maximum temperature levels experienced enhancements of 12.1134%, 12.0616%, and 11.0645% for the micropolar‐Jeffrey, micropolar‐Oldroyd‐B, and micropolar‐Second grade nanofluids, respectively. These results imply that the introduction of these binary micropolar nanofluids leads to notable thermal enhancements in the PTSCs settings.

An in‐depth comparative analysis of entropy generation and heat transfer in micropolar‐Williamson, micropolar‐Maxwell, and micropolar‐Casson binary nanofluids within PTSCs

AbstractSolar energy holds promise as a sustainable and environmentally friendly source of power. In this study, we focus on improving the thermal efficiency of parabolic trough solar collectors (PTSCs) by investigating the performance of three different binary micropolar nanofluids – micropolar‐Casson, micropolar‐Maxwell, and micropolar‐Williamson – when used as heat transfer fluids within these collectors, with engine oil as the base fluid. The problem studied revolves around enhancing the heat transfer characteristics within PTSCs, crucial for maximizing energy conversion efficiency in solar power generation. By exploring the behavior of these nanofluids under various flow conditions, we aim to optimize the design and operation of PTSC systems for improved performance and sustainability. The importance of this research lies in its potential to significantly enhance the efficiency of solar energy harvesting, thereby contributing to the transition toward cleaner energy sources and reducing dependence on fossil fuels. Additionally, the findings have implications for diverse applications, including solar aviation, solar‐powered maritime vessels, solar thermal power plants, industrial process heating, and solar‐driven water pumping mechanisms, where improved heat transfer efficiency is paramount for enhancing overall system performance and reducing operational costs. Furthermore, the investigation delves into the influence of various factors governing the flow of these binary micropolar nanofluids within PTSC setups, including aspects such as velocity, thermal characteristics, entropy generation, skin friction, drag force, and local Nusselt number. The results notably reveal substantial enhancements in thermal efficiency, with maximal relative enhancements quantified as 22.1768%, 19.3662%, and 17.7349% for micropolar‐Casson, micropolar‐Maxwell, and micropolar‐Williamson nanofluids, respectively.

Thermal stability and slip effects in micropolar nanofluid flow over a shrinking surface: A numerical study via Keller box scheme with block-elimination method

Thermal stability and slip effects in micropolar nanofluid flow over a shrinking surface: A numerical study via Keller box scheme with block-elimination method

Heat and mass transport micropolar Maxwell and Williamson nanofluids flow past a perpendicular cylinder using combined convective flow

The current study aims to investigate the heat and mass transport characteristics of micropolar Maxwell and Williamson nanofluids flowing past a perpendicular cylinder under the influence of combined convective flow using the Buongiorno nanofluid model. The objective is to analyze the axisymmetric flow of these nanofluids around an orthogonal cylinder, highlighting the effects of various physical parameters on temperature profiles and velocity distributions. Maple 23 software was employed to solve the coupled nonlinear differential equations derived from appropriate similarity transformations. The numerical results are presented in tabular and graphical form to show the impacts of key parameters on the selected micropolar nanofluids. The significant outcomes show that the skin friction coefficient, as well as the Nusselt and Sherwood numbers, increase along the axial direction, indicating enhanced heat and mass transfer capabilities. Additionally, the study emphasizes the roles of micro polarity, relaxation time, and viscoelastic properties in modulating these transfer processes. These findings have significant implications for applications in biomechanics, polymer manufacturing, aerosol deposition, and thermal treatment processes, offering valuable insights for future research and industrial practices.

Behaviour of effective heat transfer rate in radiating micropolar nanofluid over an expanding sheet with slip effects

The enhancement in the heat transfer rate is one of the vital aspects nowadays for the main objective of various industries to get better quality as well as the longevity of the product. Not only in industries but also in various areas such as in drug delivery, peristaltic pumping process, etc. it is found that this will be benefited by the utility of the various nanofluids that gives rise to enhanced thermal conductivity. Therefore, the present investigation leads to analyse the performance of effective heat transfer rate considering the flow of radiating micropolar nanofluid through a permeable expanding sheet embedding within a permeable medium. Precisely, the consideration of slip boundary conditions of both velocity and thermal profile enhances the flow phenomena. The main focus of the study is the consideration of Gherasim model viscosity and Hamilton-Crosser model which energies the thermal properties. Shooting based “Runge-Kutta fourth-order” technique is useful for the solution of governing equation followed by the transformation of these equations into dimensional form to the non-dimensional for with the help of suitable similarity rules. Further, a robust statistical approach i.e. “response surface methodology” is adopted to get optimized heat transfer rate for various factors in two different conditions such as injection and suction. However, the validation is presented through hypothetical test comparing the variances. Moreover, the important outcomes are: Nanoparticle concentration encourages the flow properties along with the heat transport phenomena. The thermal energy due to the enhanced thermal radiation accelerates the heat transmission rate for both the case of suction/injection.

Linear stability analysis of micropolar nanofluid flow across the accelerated surface with inclined magnetic field

PurposeThe purpose of this paper is to study the two-dimensional micropolar fluid flow with conjugate heat transfer and mass transpiration. The considered nanofluid has graphene nanoparticles.Design/methodology/approachGoverning nonlinear partial differential equations are converted to nonlinear ordinary differential equations by similarity transformation. Then, to analyze the flow, the authors derive the dual solutions to the flow problem. Biot number and radiation effect are included in the energy equation. The momentum equation was solved by using boundary conditions, and the temperature equation solved by using hypergeometric series solutions. Nusselt numbers and skin friction coefficients are calculated as functions of the Reynolds number. Further, the problem is governed by other parameters, namely, the magnetic parameter, radiation parameter, Prandtl number and mass transpiration. Graphene nanofluids have shown promising thermal conductivity enhancements due to the high thermal conductivity of graphene and have a wide range of applications affecting the thermal boundary layer and serve as coolants and thermal management systems in electronics or as heat transfer fluids in various industrial processes.FindingsResults show that increasing the magnetic field decreases the momentum and increases thermal radiation. The heat source/sink parameter increases the thermal boundary layer. Increasing the volume fraction decreases the velocity profile and increases the temperature. Increasing the Eringen parameter increases the momentum of the fluid flow. Applications are found in the extrusion of polymer sheets, films and sheets, the manufacturing of plastic wires, the fabrication of fibers and the growth of crystals, among others. Heat sources/sinks are commonly used in electronic devices to transfer the heat generated by high-power semiconductor devices such as power transistors and optoelectronics such as lasers and light-emitting diodes to a fluid medium, thermal radiation on the fluid flow used in spectroscopy to study the properties of materials and also used in thermal imaging to capture and display the infrared radiation emitted by objects.Originality/valueMicropolar fluid flow across stretching/shrinking surfaces is examined. Biot number and radiation effects are included in the energy equation. An increase in the volume fraction decreases the momentum boundary layer thickness. Nusselt numbers and skin friction coefficients are presented versus Reynolds numbers. A dual solution is obtained for a shrinking surface.

Bio-Convective Flow of Micropolar Nanofluids over an Inclined Permeable Stretching Surface with Radiative Activation Energy

The focal concern of this study is to examine the behaviour of bio-convective flow featuring micropolar nanofluids over an inclined permeable stretching surface while considering the influence of radiative activation energy. This investigation addresses the complex interplay of factors such as biological activity, convective heat and mass transfer, unique attributes of micropolar fluids, the dynamics of nanofluids, and radiative effects. This analysis employed Buongiorno’s model, considering thermal radiation and activation energy on the bioconvective flow of micropolar nanofluids over an inclined stretching surface. Some suitable similarity variables were used to obtain a set of non-linear differential equations from the initial partial differential equations which were then solved numerically using the Runge-Kutta Fehberg method along with shooting technique. The effects of some physical parameters were examined on the velocity, temperature, concentration, and microorganism density profiles of the flow. The result revealed that each increase in the heat source/sink, thermal radiation, thermophoresis, and Brownian motion lead to a corresponding increase in the thermal boundary layer; activation energy increased the concentration while Peclet number and bioconvective Lewis number declined the microorganism density profile. Insights gleaned from this study can find applications in biomedical fields. Understanding the behavior of bio-convective nanofluids has implications for controlled heat transfer in medical applications like hyperthermia treatments or targeted drug delivery, thereby impacting patient care.

Numerical treatment of MHD micropolar nanofluid flow with activation energy, thermal radiation, and Hall current past a porous stretching sheet

ABSTRACT This communication investigates the heat and mass transfer properties of MHD micropolar nanofluid fluid flow behaviour with activation energy, thermal radiation, and Hall current past a linear stretching sheet. The governing non-linear partial differential equations of the flow are transformed into non-linear ordinary differential equations using similarity transformation variables and solved using Runge Kutta 4th order in conjunction with the shooting methodology. The shooting approach in MAPLE is then employed to solve the associated system of ordinary differential equations. The impact of pertinent parameters is revealed and discussed on velocity, temperature, and concentration. Increasing micropolar parameters increases tangential velocity profiles while decreasing the transfer velocity profiles. The comparison table for local skin friction coefficient, Nusselt number, and Sherwood number are represented with the effects of pertinent non-dimensional variables. The model has undergone thorough validation using existing data and has shown outstanding performance. It is revealed in the study that an increase in the micropolar term increases the tangential velocity for an enhanced engineering working fluid. Also, a rise in the Hall current term boosts the heat transfer to strengthen thermal science fluids performance.

A Numerical Simulation of the Magneto-Micropolar Nanofluid Flow Configured by the Stimulus Energies and Chemical Interaction

Inspired by the numerous applications of non-Newtonian nanomaterials in science and industries, the two-dimensional convective hydromagnetic movement in a micropolar nanofluid within an expanding permeable surface with the existence of binary chemical reaction and convective boundary constraints is examined in this study. Thermal radiation, energy generation, and activation energy interactions are employed to handle the nanofluid flow. The underlying equations are transformed via the similarity transitions into an array of non-linear ODE. The BVP4C MATLAB package is applied to solve the system of equations numerically. The necessary outcomes of the micropolar fluid velocity, micro-rotation, temperature, concentration, friction factor, mass transfer, and heat transfer rates are shown graphically and thoroughly analyzed quantitatively. The micropolar nanofluid’s mobility is reduced by the heating and solutal Grashof numbers. It is noted that the magnetic coefficient decreases velocity, it has the opposite impact on the degree of temperature. The plotted outcomes also show that the temperature increases as the increase in stimulation radiation variable. Meanwhile, the thermal field exhibits strengthen as the intensity of Biot number and Eckert number responses enhances. The growth of the activation energy leads to a noticeable enrichment in the concentration profile.

Activation energy and angular momentum in electromagnetic radiation micropolar nanofluids: Focus on microbial eukaryotic species

Microbial eukaryotic species play a crucial role in biomedical research, aiding in the study of bacterial impurities, microorganism pathogenesis, and development of tactics to combat antimicrobial struggle. These species represent a complex and diverse aspect of bacteriological life, influencing ecosystems, human health, and technological progress. This study aims to create a comprehensive computational model to analyze the magnetohydrodynamics of a non-Newtonian micropolar nanofluid over an exponentially stretchable surface. It incorporates the Buongiorno model, which considers thermophoretic diffusion and Brownian motion effects to study the thermal behavior of micropolar nanofluids. It is also investigated how thermal radiation affects the current model. The classical Navier's stokes equations of motions of the current model are transform into a system of ordinary differential equation by employing similarity approach. The classical Navier-Stokes equations of motion are transformed into ordinary differential equations using similarity transformations, and MATLAB is used to solve them numerically. Here we considered three different cases, (i)-injection fw>0, (ii)-impermeable wall fw=0, (iii)-suction fw<0 which are illustrated visually. The consequence of various flow parameters effects on velocity, temperature, concentration, motile microorganism, and angular profiles are illustrated graphically. The high concordance between the model's results and the available data validates its originality. Present results indicate that while a larger porosity and Hartman number decrease velocity, increasing the mass and thermal convective factors raises the velocity profile. Raising the thermophoretic and magnetic parameters causes the temperature profile to climb; however, raising the temperature exponent and Prandtl number causes it to fall. The behavior of micropolar nanofluids is better understood thanks to this research, which could have applications in a variety of industries including manufacturing, energy, electronics, and healthcare. The novelty of the current model is verified using data that has already been published, and a great agreement is observed. When the values of the parameter K lies between the ranges 0.2<K< 0.3, and 0.3<K< 0.4, percentage increment noted in heat transfer enhancement is about 2.3 % and 6.3 % Until now, no such investigation has been performed to examine the implications of three-dimensional bio-convection micropolar based Casson fluid flow under the activation energy and suction/injection. From the outcomes, it was established that nanofluids are more fruitful for heat transfer enhancement.

Heat and mass transfer of Williamson and Maxwell micropolar nanofluid over a wedge with magnetic field and activation energy effects

The numerical investigation conducted in this study focuses on analyzing the behavior of magneto-micropolar flow, particularly concerning the transportation of magneto-Williamson and Maxwell micropolar nanofluids past a non-isothermal wedge. The governing partial equations describing the flow dynamics transform a system of ordinary differential equations through similarity analysis. These transformed equations are subsequently solved utilizing MAPLE 23. This study employs an array of graphical depictions to illustrate how various parameters affect the spatial distribution of critical variables, thereby highlighting their tangible effects. The numerical findings are validated by comparing the computed values of skin friction with those available in published sources, revealing a favorable agreement. Moreover, the investigation reveals notable findings: heat transfer rates are higher for Williamson micropolar nanofluids than Maxwell micropolar nanofluids. Additionally, the Sherwood number, indicative of mass transfer, positively correlates with the Schmidt number and Brownian motion parameter while being inversely affected by the thermophoresis and energy activation parameters. The specific novelty of this work lies in its comprehensive parametric analysis of magneto-Williamson and Maxwell micropolar nanofluids under non-isothermal conditions, employing similarity transformations and advanced numerical methods to uncover new insights into the heat and mass transfer behaviors in these complex fluid systems.

Thermal optimization of buoyancy driven radiative engine-oil based viscous hybrid nanofluid flow observing the micro-rotations in an inclined permeable enclosure

Thermal enhancement of engine oil plays an important role in a variety of industrial applications including heat exchangers, automotive cooling systems, renewable energy systems, biomedical devices, and advanced manufacturing processes. Considering the high demand in industry, present investigation explores thermal optimization of engine oil contained in a porous inclined cavity involving dispersion of hybrid nanoparticles along with inclusion of micropolar fluid flow phenomena. Numerical analysis is performed on the micropolar nanofluid containing iron oxide and molybdenum disulfide while considering the effect of thermal radiation, buoyancy force, viscous dissipation, magnetic field’s strength, porosity, and vortex viscosity. Numerical solutions of the dimensionless governing equations are provided through utilization of FVM. The coupling of velocity and pressure terms was achieved through implementation of SIMPLE algorithm. The results are illustrated through streamlines, contours, velocity, temperature profiles and heat flux. The outcomes revealed that an augment in Hartmann number and thermal radiation parameter results in higher heat flux rate. The incrementation in Hartmann number disrupted the flow resulting a reduction in the size of major vortices and similar trend is noted in case of temperature profile for the said parameters. The outcomes complement the continuing efforts to improve the thermal management of various applications and offer insightful information for optimizing engine oil compositions.

Numerical heat transfer analysis of bio convective flow of non-Newtonian nanofluid with Darcy-Forchheimer effect over a curved stretching surface

The main aim of this study is to investigate the behavior of bio-convective flow of 2nd grade micropolar nanofluid with Darcy-Forchheimer law over a curved porous stretching surface. The fluid flow analysis includes novel aspects such as the nonuniform heat source/sink, Joule heating, magnetic field, chemical reaction, and thermal radiation. Furthermore, the boundary of the stretching surface is acquired the stratification conditions. A suitable conversion method is employed to transform the flow model into a collection of ordinary differential equations, characterized by their nonlinearity. The bvp4c technique on the MATLAB is utilized to acquire numerical solutions for this set of nonlinear equations. The characteristics of various influential parameters on the velocity, temperature, concentration, and microorganism density profiles are observed and discussed. In the present problem, it is observed that by the growth of micropolar parameter enhances the angular fluid velocity. Moreover, larger values of the magnetic parameter, Darcy number, and porosity parameter result in a decrease in the fluid’s linear velocity. The temperature profile exhibits a decreasing pattern with the elevation thermal stratification parameter, while the opposite trend shows by the increment of the radiation parameter and Eckert number. Additionally, the concentration of nanoparticles decreases as the Schmidt number and Brownian motion parameter increases.