Thermophoresis and Brownian motion effects on boundary layer flow of nanofluid in presence of thermal stratification due to solar energy

The problem of laminar fluid flow, which results from the stretching of a vertical surface with variable stream conditions in a nanofluid due to solar energy, is in- vestigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of thermal stratification. The sym- metry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations, namely, the scaling group of transfor- mations. An exact solution is obtained for the translation symmetrys, and the numerical solutions are obtained for the scaling symmetry. This solution depends on the Lewis number, the Brownian motion parameter, the thermal stratification parameter, and the thermophoretic parameter. The conclusion is drawn that the flow field, the temperature, and the nanoparticle volume fraction profiles are significantly influenced by these param- eters. Nanofluids have been shown to increase the thermal conductivity and convective heat transfer performance of base liquids. Nanoparticles in the base fluids also offer the potential in improving the radiative properties of the liquids, leading to an increase in the efficiency of direct absorption solar collectors.

Thermophoresis effects on gas-particle phases flow behaviors in entrained flow coal gasifier using Eulerian model

A numerical model based on the Eulerian–Eulerian two-fluid approach is used to simulate the gasification of coal char inside an entrained flow gasifier. In this model, effects of thermophoresis of coal char particles are thoroughly investigated. The thermophoresis is due to the gas temperature gradient caused by absorpted heat of coal char gasification. This work, firstly, calculates the gas temperature gradient and thermophoretic force at1100 °C,1200 °C,1300 °C and 1400 °C wall temperatures. Then, the changes of particle volume fraction and velocity in the gasifier are studied in the simulation with thermophoresis or not. The results indicate that considering the particle thermophoresis has some effects on the calculation of particle volume fraction in the gasifier, especially at wall temperature of 1400 °C, and the maximum particle volume fraction variance ratio reaches up to 1.38% on wall surface of the gasifier. These effects are mainly caused by large gas temperature gradient along the radial direction of the gasifier. For the particle velocity, the changes are small but can be observable along radial direction of the gasifier, which has good agreement with the distributions of radial gas temperature gradient and thermophoretic force. These changes above may have certain effects on gasification reaction rates in this Eulerian model. So the change of gasification reaction rates in the simulation with thermophoresis or not is studied finally.

Effects of Thermophoresis on Unsteady MHD Free Convective Heat and Mass Transfer along an Inclined Porous Plate with Heat Generation in Presence of Magnetic Field

An analysis of Thermophoresis effect on unsteady magneto-hydrodynamic free convection flow over an inclined porous plate with time dependent suction in presence of magnetic field with heat generation has been considered by employing Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. Resulting non-dimensional velocity, temperature and concentration profiles are then presented graphically for different values of the parameters entering into the problem. Finally, the effects of the pertinent parameters on the skin-friction coefficient, the rate of heat transfer (Nusselt number) and wall deposition flux (Stanton number), which are of physical interest, are exhibited in tabular form.

Dynamics of Unsteady MHD Convective Flow with Thermophoresis of Particles and Variable Thermo-Physical Properties past a Vertical Surface Moving through Binary Mixture

The dynamics of unsteady magnetohydrodynamic convective fluid flow with radiation and thermophoresis of particles past a vertical porous plate moving through a binary mixture in an optically thin environment is investigated. The approximate form of the radiative heat flux is considered as the fourth power of temperature. Chemical reaction that occurs as the chemically reacting fluid flow through binary mixture is accounted for in energy and species concentration equations. Exponential space dependent heat source is introduced to generate additional heat energy across the fluid domain. The corresponding influence of heat energy is properly accounted for. It is assumed that viscosity and thermal conductivity vary as a linear function of temperature. The governing boundary layer equations are converted to nonlinear ordinary differential equations using similarity variables. A novel method of obtaining root finding starting with three guesses in shooting techniques is presented. The corresponding nonlinear coupled ordinary differential equations is solved numerically by shooting technique along with quadratic interpolation scheme. Graphical results of the dimensionless velocity, temperature and concentration distributions are shown for certain pertinent parameters controlling the fluid flow. The quadratic interpolation method is found to produce better estimated values of , which satisfy the degree of accuracy and proportional to the physical quantities.

Influence of Magnetic Field, Viscous Dissipation and Thermophoresis on Darcy-Forcheimer Mixed Convection Flow in Fluid Saturated Porous Media

This paper presents an application of the spectral homotopy analysis method (SHAM) to solve a problem of darcy-forcheimer mixed convection flow in a porous medium in the presence of magnetic field, viscous dissipation and thermopherisis. A mathematical model governed the flow is analyzed in order to study the effects of chemical reaction, magnetic field, viscous dissipation and thermophoresis on mixed convection boundary layer flow of an incompressible, electrically conducting fluid past a heated vertical permeable flat plate embedded in a uniform porous medium. The similarity variable is used to transform the governing equations into a boundary valued problem of coupled ordinary differential equations which are then solved using spectral homotopy Analysis Method. The spatial domains are discretized using Chebyshev-Gauss-Lobatto points and numerical computations are carried out for the non-dimensional physical parameters. A parametric study of selected parameters is conducted and the results for the velocity, temperature and concentration are illustrated graphically and physical aspects of the problem are discussed.

Active thermophoresis and diffusiophoresis

Thermophoresis and diffusiophoresis respectively refer to the directed drift of suspended particles in solutions with external thermal and chemical gradients, which have been widely used in the manipulation of mesoscopic particles. We here study a phoretic-like motion of a passive colloidal particle immersed in inhomogeneous active baths, where the thermal and chemical gradients are replaced separately by activity and concentration gradients of the active particles. By performing simulations, we show that the passive colloidal particle experiences phoretic-like forces that originate from its interactions with the inhomogeneous active fluid, and thus drifts along the gradient field, leading to an accumulation. The results are similar to the traditional phoretic effects occurring in passive colloidal suspensions, implying that the concepts of thermophoresis and diffusiophoresis could be generalized into active baths.

Lie group analysis for the effect of temperature-dependent fluid viscosity and thermophoresis particle deposition on free convective heat and mass transfer under variable stream conditions

This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equa- tions. The system remains invariant due to some relations among the transformation parameters. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.

Thermophoresis of Carboxylic Nanotubes in Gaseous Atmosphere

The present paper deals with motion of carbon nanotubes in a temperature gradient field. A determined-static theory of nanosized particles’ thermophores is developed. Analytical expressions for thermophoretic velocity and force of ultramicroheterogeneous particles in a gaseous atmosphere under near-normal conditions are provided. The calculations performed according to the suggested theory, as applied to closed carbon nanotubes, found the value of dimensionless velocity of thermophoresis. In accordance with the proposed hypothesis, Waldman’s limit is achieved, which is expressed in constancy of thermophoretic velocity within the interval of the Knudsen parameter change from 10 to 100. In addition, it is found out that under conditions defined below, velocity of thermophoresis is independent of the length of a carboxylic nanotube. A good agreement with experiments is reached, which makes it possible to assume correspondence of the theory to the physical truth.

Effects of thermophoresis particle deposition and of the thermal conductivity in a porous plate with dissipative heat and mass transfer

Network simulation method（NSM） is used to solve the laminar heat and mass transfer of an electricallyconducting,heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule heating problem. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations,in a single independent variable,畏. The resulting coupled,nonlinear equations are solved under appropriate transformed boundary conditions. Computations are performed for a wide range of the governing flow parameters,viz Prandtl number,thermophoretic coeffcient（a function of Knudsen number）,thermal conductivity parameter,wall transpiration parameter and Schmidt number. The numerical details are discussed with relevant applications. The present problem finds applications in optical fiber fabrication,aerosol filter precipitators,particle deposition on hydronautical blades,semiconductor wafer design,thermo-electronics and problems including nuclear reactor safety.

Effects of Hydromagnetic and Thermophoresis of Unsteady Forced Convection Boundary Layer Flow over Flat Plates

In this paper, we analyze unsteady two dimensional hydromagnetic forced convection boundary layer flow of a viscous incompressible fluid along flat plates with thermophoresis. The potential flow velocity has been taken as a function of the distance x and time t. The governing partial differential equations are transformed to ordinary differential equation by applying local similarity transformation. The resulting similarity equations are then solved numerically for unsteady case, applying Nachtsheim-Swigert shooting iteration technique with six order Runge-Kutta method. The variations in fluid velocity, fluid temperature and species concentration are displayed graphically and discussed for different material parameters entering into the analysis. The effects of the pertinent parameters on the skin-friction coefficient, wall heat transfer coefficient and wall deposition flux rate are also displayed in tabulated form and discussed them from the physical point of view. An analysis of the obtained results shows that the flow field is influenced appreciably by the magnetic field parameter and the thermophoresis particle deposition.

Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: a Galerkin approach

This article concerns the analysis of an unsteady stagnation point flow of Eyring–Powell nanofluid over a stretching sheet.The influence of thermophoresis and Brownian motion is also considered in transport equations.The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations.The numerical experiments are performed using the Galerkin scheme.A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme(RK-4)is available to show the credibility of the Galerkin method.The numerical exploration is carried out for various governing parameters,namely,Brownian motion,steadiness,thermophoresis,stretching ratio,velocity slip,concentration slip,thermal slip,and fluid parameters,and Hartmann,Prandtl and Schmidt numbers.The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing,but the behavior is reversed for assisting cases.The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases(assisting and opposing).The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter.All the outcomes and the behavior of emerging parameters are illustrated graphically.The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method.It is concluded that said method could be extended to other problems of a complex nature.

Effectiveness of radiative heat flux in MHD flow of Jeffrey-nanofluid subject to Brownian and thermophoresis diffusions

Our interest here in this investigation is to explore the thermophoresis and Brownian motion characteristics in flow induced by stretched surface.Electrically conducted Jeffrey material formulates the flow equation.Linear forms of stretching and free stream velocities are imposed.Nonlinear radiation and convective heating processes describe the phenomenon of heat transfer.Passive controls of nanoparticles are considered on the boundary.The compatible transformations produce the strong nonlinear differential systems.The problems are computed analytically utilizing HAM.Converge nee domain is detennined and major results are concluded for different parameters involved.Heat transfer rate and drag force are also explained for various physical variables.Our analysis reveals that heat transfer rate augments via larger radiation parameter and Biot number.Moreover larger Brownian motion and thermophoresis parameters have opposite characteristics on concentration field.

Thermophoresis of nanoparticles hotter/colder than the surrounding dilute gases

Aerosol particles suspended in a diluted gas with non-uniform temperature distribution are expected to experience a thermophoretic force.In theoretical treatment of thermophoresis,it is usually assumed that the particle temperature is equal to the surrounding gas temperature.However,this might not always be the case.In some particular applications,the particle temperature can significantly differ from the gas temperature.In the present paper,we theoretically investigate the effect of the particle tempera-ture on the thermophoresis of nanoparticles in the free molecule regime.Theoretical formulas for the thermophoretic force and thermophoretic velocity are obtained based on the gas kinetic theory.As exam-ples,a spherical Ag nanoparticle suspended in a dilute He gas is considered,and the Rudyak-Krasnolutski potential is employed to model the gas-particle interaction.It is found that the influence of the particle temperature on the thermophoresis of nanoparticles can be significant.With increasing particle size,the error due to the equal gas-particle temperature assumption can be neglected.

Effects of thermophoresis on Brownian coagulation of spherical particles over the entire particle size regime

In many energy and combustion applications.particles experience large temperature gradients,which can affect the coagulation process due to thermophoresis.This study presents a rigorous theory of thermophoretically modified Brownian coagulation in the entire particle size regime.The theoretical derivations are based on the kinetictheory forthe free-molecular regime and the harmonic mean method for the transition regime.The coagulation kernels in different size regimes can be expressed as the basic Brownian coagulation kernel times an enhancement factor,The enhancement factor represents the coagulationrate enhancement induced by thermophoresis and is a function of specific dimensionless numbers.Based on the enhancement factor,the thermophoretic enhancement effects on particle coagulation are further analyzed under a wide range of gas and particle conditions.The results show that thermophoretic enhancement effects are ignorable in the free-molecular regime,but need to be considered in the continuum regime and the transition regime.In addition,the enhancement effects increase significantly with increase of gas temperature and temperature gradient while decrease with increase of gas pressure.The present study can improve understanding ofthermophoretic effects on Brownian coagulation in the entire size regime and provide a useful tool to calculate the coagulation rates in presence of thermophoresis.

Biomathematical study of time-dependent flow of a Carreau nanofluid through inclined catheterized arteries with overlapping stenosis

This work is concerned with the analysis of blood flow through inclined catheterized arteries having a balloon(angioplasty) with time-variant overlapping stenosis. The nature of blood in small arteries is analyzed mathematically by considering it as a Carreau nanofluid. The highly nonlinear momentum equations of nanofluid model are simplified by considering the mild stenosis case. The formulated problem is solved by a homotopy perturbation expansion in terms of a variant of the Weissenberg number to obtain explicit forms for the axial velocity, the stream function, the pressure gradient, the resistance impedance and the wall shear stress distribution. These solutions depend on the Brownian motion number, thermophoresis number, local temperature Grashof number G_r and local nanoparticle Grash of number B_r. The results were also studied for various values of the physical parameters, such as the Weissenberg number W_i, the power law index n, the taper angle φ, the maximum height of stenosis δ~*, the angle of inclination α, the maximum height of balloon σ~*, the axial displacement of the balloon z_d~*,the flow rate F and the Froud number Fr. The obtained results show that the transmission of axial velocity curves through a Newtonian fluid(Wi=0, n=1, Gr=0, Br=0, Nt=0, Nb≠0) is substantially lower than that through a Carreau nanofluid near the wall of balloon while the inverse occurs in the region between the balloon and stenosis. The streamlines have a clearly distinguished shifting toward the stenotic region and this shifting appears near the wall of the balloon, while it has almost disappeared near the stenotic wall and the trapping bolus in the case of horizontal arteries and Newtonian fluid(Wi=0, n=1, Gr=0, Br=0, Nt=0, Nb≠0) does not appear but for the case of Carreau nanofluid bolus appears.

The expression and binding properties of the rice WRKY68 protein in the Xa21-mediated resistance response to Xanthomonas oryzae pv. Oryzae

Plant WRKY transcription factors are involved in various physiological processes, including biotic and abiotic stress responses, as well as developmental processes. In this study, the expression patterns of the WRKY68 protein during interactions between rice 4021 containing the bacterial blight resistance gene Xa21 and Xanthomonas oryzae pv. oryzae（Xoo） were investigated. A possible modified form of the WRKY68 protein appeared in the Xa21-mediated disease resistance response, and its expression levels were similar in compatible and incompatible responses, but differed significantly from that of the mock control treatment, suggesting that WRKY68 may be involved in the bacterial blight response in rice. To further understand WRKY68＇s roles in the resistance signaling pathway, WRKY68 recombinant protein was expressed in Escherichia coli and a microscale thermophoresis analysis was performed to investigate the interactions between WRKY68 and cis-elements in crucial pathogenesis-related（PR） genes. The results showed that the WRKY68 protein binds to W-boxes in the PR1 b promoter region, with an apparent dissociation constant of 25 nmol L–1, while the binding between WRKY68 and PR10 a was W-box independent. The results suggested that a possible modified form of the WRKY68 protein was induced during the interaction between rice and Xoo, which then regulated the activity of the downstream PR genes by binding with the W-boxes in the PR1 b gene＇s promoter region. Moreover, the constitutive transcription of the WRKY68 gene in dozens of rice tissues and the expression of the WRKY68 protein in leaves during all growth stages suggests that WRKY68 plays important roles in rice during normal growth processes.

Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium

The present article explores the entropy generation of radiating viscoelastic second grade nanofluid in a porous channel confined between two parallel plates. The boundaries of the plates are maintained at distinct temperatures and concentrations while the fluid is being sucked and injected periodically through upper and lower plates. The buoyancy forces, thermophoresis and Brownian motion are also considered due to the temperature and concentration differences across the channel. The system of governing partial differential equations has been transferred into a system of ordinary differential equations(ODEs) by appropriate similarity relations, and a shooting method with the fourth-order Runge-Kutta scheme is used for the solutions. The results are analyzed in detail for dimensionless velocity components. The temperature, concentration distributions, the entropy generation number, and the Bejan number corresponding to various fluid and geometric parameters are shown graphically. The skin friction, heat and mass transfer rates are presented in the form of tables. It is noticed that the temperature profile of the fluid is enhanced with the Brownian motion, whereas the concentration profile of the fluid is decreased with the thermophoresis parameter, and the entropy and Bejan numbers exhibit the opposite trend for the suction and injection ratio.

Numerical solutions to heat transfer of nanofluid flow over stretching sheet subjected to variations of nanoparticle volume fraction and wall temperature

The numerical analysis of heat transfer of laminar nanofluid flow over a fiat stretching sheet is presented. Two sets of boundary conditions （BCs） axe analyzed, i.e., a constant （Case 1） and a linear streamwise variation of nanopaxticle volume fraction and wall temperature （Case 2）. The governing equations and BCs axe reduced to a set of nonlinear ordinary differential equations （ODEs） and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.

A Review of Termo- and Diffusio-Phoresis in the Atmospheric Aerosol Scavenging Process. Part 1: Drop Scavenging

The role of phoretic forces in providing in-cloud and below-cloud scavenging due to falling drop is reviewed by considering published papers dealing with theoretical models, laboratory and field measurements. Theoretical analyses agree that Brownian diffusion appears to dominate drop scavenging of aerosol with radius less than 0.1 μm, and inertial impaction dominates scavenging of aerosol with radius higher than 1 μm. Thus, there is a minimum collection efficiency for particles in the approximate range 0.1 μm - 1 μm, where phoretic forces are felt. Generally speaking, published papers report not uniform evaluations of the contribution of thermo- and diffusiophoretic forces. This disagreement is partially due to the different laboratory and field conditions, and different theoretical approaches.

A comparative analysis of unsteady and steady Buongiorno’s Williamson nanoliquid flow over a wedge with slip effects

Comparison between unsteady and steady MHD Buongiorno’s model Williamson nanoliquid flow through a wedge with slip effects,chemical reaction and radiation is made in this analysis.Thermophoresis and Brownian motion are also considered in this study.Appropriate similarity variables are presented to transmute the governing PDEs into the set of non-linear ODEs.The most widely authenticated finite element method is implemented to analyze these set of ODEs numerically.The behavior of concentration,temperature and velocity sketches for varied values of relevant parameters is numerically calculated and the outcomes are plotted through graphs.The numerical values of dimensionless rates of mass transfer,heat and velocity are also evaluated and depicted through tables.It is noted that with upsurging values of angle of wedge parameter,the distributions of temperature of the liquid intensify in both steady and unsteady cases.