Brownian Motion Effects Research Articles

Magnetohydrodynamic Mixed Convection Heat and Mass Transfer of Nanofluid Flow Over a Stretching Wedge-Shaped Surface with the Effect of Thermophoresis and Brownian Motion

The present study has been investigated to the consequence of the magnetic parameter, Grashof number, modified Grashof number, Prandtl number, thermal radiation parameter, Brownian motion parameter, thermophoresis parameter, heat generation parameter, Schmidt number, Biot number, stretching parameter, Lewis number, and chemical reaction parameter, respectively, over a stretching wedge of the magnetohydrodynamic (MHD) BL nanofluid flow. The main goal of this paper is to numerically investigate the nature of the MHD BL nanofluid flow along a stretching wedge-shaped surface with radiation, heat source, and chemical reaction parameters. The fundamental equations has been transformed into ordinary differential equations (ODEs) by the usual transformation. The numerical solutions are found by employing Runge-Kutta fourth-order method by exploiting symbolic software MATLAB via the shooting method. The novelty of the current study is implicated in the area of fluid dynamics to solve nonlinear differential equations numerically and is an important contribution to the field of nanofluids flow. Numerical solutions reveal that the concerned physical parameters lead to progress in the skin friction factor, rate of change of heat transfer as well as the rate of change of concentration. Brownian motion and thermophoresis parameters play a crucial role in the variation of temperature and concentration profiles and also in the development of thermal and concentration boundary layers.

Dual Solutions and Stability Analysis for Buongiorno Model of Magnetohydrodynamics Nanofluid Flow Past a Heated Shrinking Slippery Surface

This study investigates the combined effects of magnetic field, Joule heating, viscous dissipation, thermophoresis, and Brownian motion towards a convectively heated shrinking and slippery surface on a stagnation point flow of nanofluid is theoretically examined. The modified Buongiorno model for nanofluid flow is employed and numerically solved using a shooting technique together with the Runge-Kutta-Fehlberg integration scheme. It is found that dual solutions appear in certain range of shrinking surface parameter. The temporal stability analysis of the dual solutions to small disturbances was performed and the upper solution branch is found to be a stable and physically realistic solution to the problem. Appropriate results showing the influence of magnetic field, Surface slipperiness, Eckert number, Biot number, Brownian motion, and thermophoresis parameters on the nanofluid temperature, velocity, nanoparticles concentration, Nusselt number, skin friction, and Sherwood number are quantitatively discussed, and depicted graphically and in tables.

Numerical Solutions of Casson-Nano Fluid Flow Past an Isothermal Permeable Stretching Sheet: MHD, Thermal Radiation and Transpiration Effects

The Runge-Kutta Shooting Technique may be used to discover numerical solutions by the absence of magnetic field, thermal radiation, then transpiration consequence for viscous, incompressible, electrically conducting with combination of Casson and Nano-fluids that approach an isothermal permeable non-linearly stretched sheet. The governing equations for this fluid flow were transformed keen on non-linear ODEs using the similarity quantities. Visualizations of velocities, temperatures, and concentrations illustrate the mathematics behind the issue. According to tabular data, these flow regulating factors affect the coefficient of friction for skin-friction, heat transfer, and mass flow coefficients. Program code validation literature has been compared to the new numerical findings. It has been shown that flow characteristics are greatly affected by the amount of air that is exhaled. The study’s applications include industrial Nano-technological manufacturing processes. In this current work, the speed profiles are diminishing growing values of Casson fluid limitation as well as decreases by growing values of Magnetic field & Suction/Injection parameters. With increasing effects Brownian motion and Thermophoresis temperature profiles are increase. As the values of Thermal radiation of limitation enhances, the temperature profiles are also increases. The concentration profiles are increasing with increasing values of Thermophoresis parameter and reverse effect observed in case of Brownian motion effect. Also, concentration profiles decreases with increasing values of Lewis number.

Melting Heat Transfer on Magnetohydrodynamics-Nanofluid Boundary Layer Flow Past a Stretching Sheet: Thermal Radiation and Viscous Dissipation Effects

The effects of melting heat transfer, thermal radiation, and porous medium on steady, 2-D, viscous, incompressible, magneto hydrodynamic nano-fluid flow concluded a linearly extending sheet in the occurrence of viscous dissipation, as well as first and subsequent order slip effects, were always considered in this numerical research. In this research, appropriate similarity variables were employed to turn the controlling nonlinear partial differentiated equations hooked on a system of linked nonlinear ordinary differential comparisons that are mathematically explained using the Runge-Kutta approach with a firing scheme. The consequence of several pertinent limitations on rapidity profiles, temperature profiles, and attentiveness profiles is graphically explored also thoroughly interpreted. In this work, images and tables were utilized to represent various progressive values of non-dimensionalized parameters, while numerical data was employed to examine variations in skin-friction, heat, and mass transmission charges. The present study of my observation compared with previous studies in a limiting case. A reliable agreement between the numeric values is achieved here. The velocity profiles in this issue decrease as the values of the Suction/Injection fluid parameter as well as the Magnetic field limitation growth. Temperature profiles rise as the impacts of thermophoresis and Brownian motion become stronger. When the value of the Dufour number rises, so do the temperature profiles. Thermophoresis parameter expansions results in enhanced nanoparticle volume concentration distributions, whereas Brownian motion effects produces the opposite effects. As the Soret number parameter increases, so do the concentration profiles. This melting heat transfer study work includes numerous industrial applications, including casting, welding, and magma solidification, permafrost melting and ground thawing, and so on.

Numerical computation of Brownian motion and thermophoresis effects on rotational micropolar nanomaterials with activation energy

The current article investigates the numerical study of the micropolar nanofluid flow through a 3D rotating surface. This communication may manipulate for the aim such as the delivery of the drug, cooling of electronic chips, nanoscience and the fields of nanotechnology. The impact of heat source/sink is employed. Brownian motion and thermophoresis aspects are discussed. The rotating sheet with the impacts of Darcy-Forchheimer law is also scrutinized. Furthermore, the influence of activation energy is analyzed in the current article. The numerical analysis is simplified with the help of befitted resemblance transformations. The succor of the shooting algorithm with built-in solver bvp4c MATLAB software is used for the numerical solution of nonlinear transformed equations. The consequences of different physical factors on the physical engineering quantities and the subjective fields were examined and presented. According to outcomes, it can be analyzed that the flow profile declined with the rotational parameter. It is observed that angular velocity diminishes via a larger porosity parameter. Furthermore, the temperature gradient is declined via a larger magnitude of the Prandtl number. The heat transfer is enhanced in the occurrence of Brownian motion. The activations energy parameter causes an increment in the volumetric concentration field. Moreover, the local Nusselt number is reduced via a greater estimation of the porosity parameter.

Impact of Joule heating on magnetohydrodynamic dissipative flow above a slendering surface with thermophoresis and Brownian movement with slip/no-slip conditions

ABSTRACT Purpose Hybrid nanofluids meet the necessities of several technological and production industries. Owing to these ample applications, a numerical investigation is accomplished to examine the thermal transmission feature of magneto-hybrid nanofluid flow due to an extending surface of varied thickness with multiple slip effects. Design/methodology The arising system of Partial Differential equations (PDEs) are exercised by adopting suitable similarities to attain the non-dimensional Ordinary Differential equations (ODEs) and the solutions are obtained by implementing bvp5c built in MATLAB package. The energy equation is loaded with Brownian motion, thermophoresis and Joule heating effects. The implication of pertinent constraints upon the flow features is discussed graphically. Findings The outcomes imply that the energy transmission rate is considerably high in no-slip case as equated with the slip case. Further, the power-law index parameter effectively uplifts the thermal and concentration gradients in both the situations. Originality The prime motive of this research is to present the relative analysis of heat transmission of hybrid nanoliquid in two different situations, namely slip and no-slip cases.

Numerical study on magnetohydrodynamics micropolar Carreau nanofluid with Brownian motion and thermophoresis effect

ABSTRACT The current work explores the investigation of the influence of nonlinear thermal radiation on unsteady, magnetohydrodynamics boundary layer flow of micropolar Carreau nanofluid past a stretching sheet. Viscous dissipation, internal heating, Brownian motion, heat source/sink, thermophoresis, chemical reaction, and Joule heating effects are considered in the study. To analyze the model, the governing partial differential equations are rephrased and written in the non-dimensional form with the relevant dimensionless quantities. To obtain the solutions, the nonlinear non-dimensional governing equations are numerically solved using finite difference approximation. The impact of every significant flow parameter on fluid motion, micro-rotation, temperature, concentration, surface drag, heat, and mass transfer rates are presented through plotted graphs and tables. It is noted from the study that the fluid flow and angular motion increase, whereas the temperature declines with higher values of the micropolar constant. Further, it is noticed that thermal distribution is a rising function of radiation parameter, and due to the nonlinear thermal radiation effect, there is an increase of 4.903% in temperature distribution when compared to linear thermal radiation. To support the validity of the solutions, a comparison was made with notable results from the existing literature for the specific case of this study.

Impacts of multiple slip on magnetohydrodynamic Williamson and Maxwell nanofluid over a stretching sheet saturated in a porous medium

This study addresses the magnetohydrodynamic boundary layer with multiple slip conditions on Williamson and Maxwell nanofluid across a stretching sheet saturated in a porous medium. Due to the existence of nanoparticles, Brownian motion and thermophoresis effects are assumed. Here, we considered the impact of thermal radiation, viscous dissipation, Ohmic heating, and chemical reaction. The governing Partial Differential Equations (PDEs) are nondimensionalized using suitable similarity conversions and transmuted into nonlinear Ordinary Differential Equations (ODEs). Solutions are acquired numerically using the bvp4c solver in MATLAB. Moreover, the relevant physical parameters like magnetic, permeability, Brownian motion, Prandtl and Eckert number, radiation, thermophoresis, and chemical reaction on velocity, temperature, and concentration fields are depicted graphically. We perceived that augments in magnetic and permeability parameters cause a downfall in the velocity profile, while the opposite trend is notable for the remaining profiles. Velocity declines when escalating the Williamson and Maxwell parameter values. Results show that increasing velocity, thermal, and concentration slip parameters reduce the relevant profiles. Skin friction increases for increasing values of the Williamson, Maxwell, and suction parameters, whereas other parameters exhibit the opposite trend. A dual solution is performed for the velocity and temperature profiles with and without suction. Our current solution has been compared with existing literature and is determined to be in perfect accord.

Mathematical modelling of heat and solutal rate with cross‐diffusion effect on the flow of nanofluid past a curved surface under the impact of thermal radiation and heat source: Sensitivity analysis

AbstractThis study analyses the effect of Brownian motion and thermophoresis on the flow of nanofluid along an impermeable curved surface. The Darcy‐Forchheimer drag vis‐à‐vis the radiating heat and the heat source enriches the flow phenomena. This drag force has several applications such as in (i) biomedical engineering for the flow of blood through curved arteries and veins, (ii) civil engineering for the flow of water through porous materials such as soil or rock, etc. The convective heat and solutal transport properties embedded in boundary conditions develop the heat transport phenomena. The dimensional governing equations are transformed into non‐dimensional form by using suitable substitution of transformed variables and stream function. Further, numerical practice is adopted to handle the set of nonlinear differential equations. The simulation of the optimized heat and solutal transfer rate for various factors is carried out using the ‘central composite design’ (CCD) associated with the ‘response surface methodology’ (RSM). The regression analysis and residual error are computed through the statistical approach of analysis of variance and finally, the sensitivity analysis is proposed for the various factors. However, the enhanced properties and flow behaviour for the diversified values of the physical parameters are presented and described briefly via the corroboration of the present methodology with the published work in particular cases. The notable outcomes are the axial velocity profile enriches for the increasing curvature constraints and the regression analysis is presented for the optimizing heat transfer rate using response surface methodology.

The effect of Brownian motion and noise strength on solutions of stochastic Bogoyavlenskii model alongside conformable fractional derivative

Fractional order models involving nonlinearity are remarkable for having substantial application in real-world. The present determination is due to obtain applicable wave solutions of fractional order stochastic Bogoyavlenskii equation (SBE) in the viewpoint of stratonovich regarding multiplicative noise. Enhanced rational (G′/G)-expansion and improved auxiliary equation approaches are imposed to the suggested model which accumulate diverse wave solutions in appropriate form. The investigators might depict sophisticated tangible phenomena in a wide range with the assistance of the found well-furnished wave solutions as the governing equation makes understanding about the plasma physics, the wave of propulsion fluid-flow, and the dynamic characteristics of shallow-water waves. Various obtained solutions are figured out to portray prominent physical characteristics of nonlinear wave outlines. Different types of solitons are organized graphically in 3D shapes such as periodic, anti-periodic, compacton, anti-compacton, bell, anti-bell, peakon, kink, anti-kink, cuspon etc. Diverse 2D plots are comprised to make noticeable the wave velocity while contour plots signify the association among the concerned variables. The graphical representations are brought out together with the effects of noise strength and Brownian motion. The observation of the current whole work might captivate the researchers for future related work by employing the recommended approaches which are competent, pioneering, and concise.

Multiple slips and double stratification in MHD flow of hybrid nanofluid past a permeable sheet: triple solutions and stability analysis

Hybrid nanofluid flow past a stretching/shrinking sheet has various applications in industrial and engineering processes, e.g. in glass blowing, the extrusion of polymer sheets, and paper production. Motivated by these numerous uses of hybrid nanofluid in diverse geometries and conditions, the present study analyzes the solutions for MHD flow of Ag-CuO/water hybrid nanofluid past a shrinking sheet. The governing equations and boundary conditions are formulated together with the effects of Brownian motion, double stratification, porous medium, suction, slips, and thermophoresis. Then, similarity transformations are employed to form non-linear ordinary differential equations and boundary conditions for numerical computation in Matlab using the bvp4c solver. A significant finding of triple solutions in the shrinking sheet case prompted a stability analysis to be carried out, and the results show that only the first solution is stable. The effects of controlling parameters on the physical quantities of interest, velocity, temperature, and concentration profiles are analyzed and discussed. The heat and mass transfer rates are noted to improve, with an average of 7.91% and 258.36%, by increasing the Darcy number related to the permeability of the porous medium. Meanwhile, augmenting the nanoparticle volume fraction of Ag from 0.03 to 0.05 enhances the skin friction, heat transfer, and mass transfer rates by 9.4%, 7.36%, and 150.31%, respectively. However, the heat and mass transfer performances of the hybrid nanofluid are inhibited by the double stratification parameters.

Fractional order interdependent nonlinear chaotic spatiotemporal calcium and Aβ dynamics in a neuron cell

The formation of β-amyloid (Aβ) and its accumulation depend on the calcium ([Ca2+]) signaling in neurons. The individual and independent dynamics of calcium and β-amyloid give very limited information about different cellular mechanisms. Some researchers have explored the interdependent system dynamics of integer-order calcium and β-amyloid, which provides some more crucial information on different regulatory and dysregulatory processes in neurons. However, these integer-order systems are not capable of generating the information on the superdiffusion, cell memory and Brownian motion effects in neuron cells. A nonlinear mathematical model has been framed to explore the fractional-order interdependent chaotic spatiotemporal [Ca2+] and Aβ dynamics in neurons. The proposed model integrates the two-way feedback mechanism between [Ca2+] and Aβ dynamics in neurons. The Crank-Nicolson scheme with the Grunwald approximation is employed for space fractional derivatives and the L1 formula is employed for time fractional derivatives. The Gauss-Seidel iterations are utilized to solve the resultant system of nonlinear algebraic equations. The effects of cell memory, Brownian motion and superdiffusion phenomena with different crucial mechanisms like buffer, source influx, ryanodine receptor, etc on the spatiotemporal interdependent [Ca2+] and Aβ dynamics have been explored in neurons. The numerical findings give novel insights on the regulatory and dysregulatory effects of cell memory, Brownian motion and superdiffusion on the system dynamics of [Ca2+] and Aβ in neuron cells and the conditions that may cause the different neurodegenerative illnesses like Alzheimer’s disease.

Impact of melting heat transfer and outer-velocity of casson nanofluid over a stretching sheet

A study has been done to analyze the combined effect of melting process with outer velocity in a casson Nanofluid over a stretching Sheet. The effect of Brownian motion and thermophoresis parameter are also taken into consideration in our study. The coupled non– linear partial differential Equations are mould into ordinary differential equation with the help of similarity variables. The mould differential equations are numerically solved by RKF method with shooting techniques in MATLAB. The effect of prominent nanofluid parameters on velocity, temperature and concentration are studied and presented graphically and also skin friction coefficient, nusselt number and sherwood number has been observed on various nanofluid parameters are presented through tables. This research will be crucial for creating cooling devices and heat sinks of various shapes that will improve the heat transfer capabilities of Casson nanofluids, expanding their industrial potential. Casson nanofluid parameter rises, the nanofluid velocity rises, while the thickness of boundary layer reduces.

NUMERICAL study of MAGNETO convective Buongiorno nanofluid flow in a rectangular enclosure under oblique magnetic field with heat generation/absorption and complex wall conditions

A mathematical model is presented to analyze the magnetohydrodynamic (MHD) convective flow in a rectangular enclosure. Earlier studies on the Tiwai-Das volume fraction nanofluid model did not consider the Buongiorno nanofluid model. This is the focus of the present analysis which examines the laminar mixed convection magnetohydrodynamic flow of a nanofluid in a differentially heated rectangular enclosure with complex boundary conditions under an inclined magnetic field. Buongiorno's two-component nanofluid model is employed, which incorporates the effects of Brownian motion and thermophoretic diffusion of nanoparticles. Magnetic nanofluids have considerable potential for enhancing transport processes in energy systems such as hybrid fuel cells. The study is essential with heat generation/absorption effects. Additionally, the work is highlighted by the general case of an oblique (inclined) magnetic field. The conservation equations for mass, primary and secondary momentum, energy, and nanoparticle concentration with wall boundary conditions are dimensionless using appropriate scaling transformations. A finite-difference computational scheme known as the Harlow-Welch Marker and Cell (MAC) method is employed to solve the dimensionless nonlinear coupled boundary value problem. A mesh independence study is included. Graphical plots are presented for the impact of key control parameters on streamline contours, isotherm contours, iso-concentration (nanoparticle mass) contours, and local Nusselt number. With heat sink (absorption), the Nusselt number is enhanced in magnitude whereas it is suppressed with heat generation since there is a heat reduction transmitted to the boundary. The configurations of streamlines, isotherms, and iso-concentrations are mostly invariant to magnetic field direction changes. The obtained results show interesting behaviors of the flow and thermal fields, which mainly involve the effect of Brownian motion and thermophoresis parameters, as well as unsteady regimes, depending on specific values of the Schmidt number, Richardson number, and Prandtl numbers. Increasing the Schmidt number induces a contraction in the central cooler zone in the enclosure and also reduces the iso-concentration magnitudes in the central region across the enclosure. The core region of the enclosure heats up as the thermophoresis and Brownian motion parameters rise, pushing the previously cooler top and bottom wall zones further away from the center. There is also a decrease in iso-concentration magnitudes in particular at the upper and lower boundaries at higher values of Brownian motion and thermophoresis parameters. At decreasing buoyancy ratios, the left vortex cell first decelerates while the right vortex cell accelerates. However, when the buoyancy ratio increases, the left vortex cell streamlines magnitudes increase with a contraction in vortex size, while the right cell develops. A Very minor alteration is observed in the isotherm and iso-concentration contours with an increasing buoyancy ratio. When the Richardson number increases, the vortex cell structures shift from a strong circulation cell on the left to a weaker cell on the right, resulting in reverse distribution. With the rising Richardson number, significant cooling is also caused in the core zone, as well as a drop in iso-concentrations, with the original dual low-concentration upper and lower zones merging into a single center zone. The original symmetric left and right vortex cells are gradually twisted diagonally towards the right wall as the magnetic field increases, yet the stronger right cell and the weaker left cell are maintained.

Effects of thermophoresis and brownian motion on the pulsating nano-fluid in a curved diseased arterial segment

In this article, we have examined the impacts of curvature on the time dependent non-Newtonian flow of the nano-fluid. In this numerical study, a mathematical framework is created to analyse the impacts of blood shear thinning/thickening on the rheology of the nano-fluid within the curved channel, which is not yet explored. The pulsating flow of a nano-fluid (blood) through a curved artery with stenosis and post-stenotic dilatation in its interior is analyzed numerically to determine the impacts of Thermophoresis and Brownian motion. The basic suggested physical system mathematically incorporates the 2-dimensional curvilinear coordinate system. The Herschel-Bulkley model successfully captures the fluid’s rheology. By applying the mild stenosis premise, we are able to describe and simplify the highly coupled momentum, energy, and mass concentration. The non-dimensionalized governing equations associated with the boundary condition can be discretized and solved by employing explicit finite differences methods. Graphs and discussions of the effects of changing pertinent geometric and rheological factors on key flow characteristics, such as temperature, velocity, and mass concentration, are provided. Even though the curvature of the artery only marginally modifies the blood’s temperature and mass concentration, the curved channel’s radius is observed to significantly impact blood velocity. Furthermore, as the Brownian motion of the nano-fluid increases, the temperature of the fluid decreases, while the thermophoresis measure exhibits the contrary behavior.

Computational analysis of MHD driven bioconvective flow of hybrid Casson nanofluid past a permeable exponential stretching sheet with thermophoresis and Brownian motion effects

This study examines the flow of Casson hybrid nanofluid upon an exponentially elongating sheet with impact of gyrotactic microorganisms. The influence of mixed convection has been used in momentum equation. A magnetic field has employed to flow system in normal direction to flow streams and its impact has been taken mathematically in momentum and energy equations. There are enormous applications for this issue, notably in the pharmaceutical industry and purification of cultures. The hybridization process is done by considering TC4(Ti-6AI-4 V) and NiCr(80%+20%) nanoparticles with engine oil as pure fluid. A hybrid volume fraction model and the Buongiorno model have been employed. Through similarity substitutions the system of modeled equations is converted to dimension-free form. Heat source and thermal radiation have also been employed to the problem with its mathematical effect has been depicted in energy equation. Chemical reaction has been used in flow model with its mathematical expression in concentration equation. Solution of the subsequent set has been determined by using homotopy analysis method. The reason that we have conducted this study is to investigate the Casson hybrid nanofluid flow past an exponentially extending surface under the effects of applied external forces. After in-depth insight of the work it has concluded that the fluid motion has declined with upsurge in magnetic, mixed convection, buoyancy ratio, Casson and porosity factors. Temperature distribution has been amplified with growth in Eckert number, Brownian motion, magnetic, thermophoresis, heat source, and radiation factors. Concentration characteristics have declined with upsurge in Brownian motion factor and Schmidt number while thermophoresis factor has supported the concentration profiles. Density number of microorganisms has weakened with higher values of Peclet, and bio-convection Schmidt numbers as well as with growth in bioconvection difference parameter. The impact of various factors has deliberated numerically for various quantities of engineering interest in tabular form. Validation under special case has been conducted with preceding works and has established a fine agreement.

Investigation of radiative MHD Carreau nanofluid over an inclined stretching cylinder with activating energy, Wu’s slip, and convective heating

The influence of radiation, convective heating, second-order velocity slip condition, and activating energy on the magnetohydrodynamic (MHD) Carreau nanofluid and heat/mass transfer are depicted in this study. A mathematical model of the Carreau nanofluid is carried out with the effects of thermophoresis and Brownian motion. The governing equations are transformed into a system of nonlinear coupled differential equations. Solutions of the transformed equations are derived by the Matlab BVP4c solver. Efficiency of the solver is verified by the comparison with the previous literature. Moreover, the impacts of the dimensionless velocity, temperature, and nanoparticle concentration profile are elucidated graphically.

The Motion and Deposition of Small Particles in the Human Lung Acinus, Part B: Weibel’s Model of Bifurcating Airways

Weibel’s model A for the human lung is applied in which the lung comprises a binary bifurcating tree of 23 generations of airways. It assumes that each airway bifurcates into two airways their sizes defined by the generation number. The goal of this analysis is to predict deposition efficiencies of various size particles which reach the human acinus vis-a-vis generation number, a result that can be used in designing inhaled therapeutical particles or preventing dangerous substances like Covid 19 of reaching the blood stream. The simulations account for particle convection, the effects of gravity and Brownian motion. Applying ANSYS Fluent, a commercial program which includes a two-phase model for finite volumes, it is found that particle diameters within the range (0.4 ¸ 1.0 mm) and densities as low as 500 kg/m3 reach deep into the human lung acinus and are likely to reach the blood stream. Particles of higher densities and diameters outside the foregoing range deposit at lower branches of the acinar tree, the smaller particles due to dominant diffusion and the bigger due to gravity.

On the thixotropy of mature fine tailings

The rheological behavior of mature fine tailings (MFTs) is investigated using transient and steady shear flow fields. The structure breakdown of intact MFT samples is examined by a startup flow experiment at various shear rates. The yield stress of MFTs is estimated by the steady shear stress values at low shear rates. Oscillatory shear (strain amplitude sweep) is also used to verify the obtained yield stress value. MFT samples exhibit thixotropy and a positive hysteresis loop at short shearing time intervals in increasing and decreasing stepwise shear rate tests. The observed hysteresis loops and thixotropy disappear by increasing the shearing time intervals, as the system reaches its equilibrium steady-state structure. The time-dependent rheological behavior of MFTs is quantified by a structural kinetics model through the dimensionless structure parameter, λ. [Toorman, “Modelling the thixotropic behaviour of dense cohesive sediment suspensions,” Rheol. Acta 36, 56–65 (1997).] The kinetic parameters are estimated based on steady-state stresses, elucidating the relative effects of shear rate and Brownian motion on buildup and breakdown of the structure. The flow behavior of MFTs predicted by the structural kinetics model is in agreement with the experimental data.

An electroosmotic peristaltic flow of graphene-lubrication oil nanofluid through a symmetric channel

The purpose of this manuscript is to analyze the electroosmotic peristaltic motion of graphene-lubrication oil nanofluid. Rheological characteristics of such fluids are predicted by using the Carreau’s model. Effects of magnetic field, electric field, viscous dissipation, Joule heating, Brownian motion and thermophoresis are also reckoned. Debye-Hückel linearization and lubrication approach are employed in mathematical modeling. Obtained non-linear system of equations are analytically solved by using the builtin command NdSolve and parametric study is carried out to visualize the variation in temperature, velocity, heat transfer rate, concentration profiles, pressure gradient and pressure rise per wavelength. Results unveil that strong electroosmotic parameter enhances both velocity and temperature. Temperature and velocity decline on the enlargement of the Helmholtz-Smoluchowski velocity. Variation in electroosmotic parameter decreases and Helmholtz-Smoluchowski velocity increases mass transfer rate. Pumping region can also be maintained by thickening and thinning the Electric Double Layer (EDL). Present study has useful applications in industries, defect sensor, energy saving, domestic air conditioning, cooling power electronic components and heat extraction and heat transportation.