Thermophoresis Particle Deposition Research Articles

Combined effects of electrophoresis and thermophoresis in Darcy Forchheimer flow of trihybrid nanofluid over a Riga plate: Yamada-Ota and Xue models

The physical phenomena of Darcy-Forchheimer flow of trihybrid nanofluid over a Riga plate with the influence of electrophoresis and thermophoresis on the particle deposition and non-uniform heat generation in a porous medium is discussed in this article. In a Marangoni convective flow, this study examined the impact of electrophoresis and thermophoresis on the rate at which aerosol particles deposited across a Riga plate. One of the most basic processes for moving tiny particles across a temperature gradient is known as thermophoresis particle deposition, and it is significant to both aero-solution and electrical engineering. Trihybrid nanofluid containing Cobalt iron oxide (COFe2O4), Manganese Zinc iron oxide (MnZnFeO4) and Molybdenum disulfides (MOS2) nanoparticles, and based fluid water is used. For the case of trihybrid nanoparticles, the Xue and Yamada-Ota nanofluid models have been expanded. The objective of this envisaged model is to compare the performance of two renowned ternary hybrid nanofluid models namely Xue and Yamada–Ota. The required similarity transformations are used to translate the set of governing equations into a collection of ODEs. The homotopy analysis method (HAM) is used to analytically solve these simplified equations. For the embedded non-dimensional parameters, the graphic exploration of the velocity, concentration and thermal fields is made. The study's primary outcomes are that as the Marangoni convection parameter is increased, the velocity profile is improved and the temperature and concentration distributions are lowered. The concentration profile decreases with increasing electrophoretic parameter, however the opposite behavior is seen with increasing electrophoretic parameter.

Analyzing the impact of thermophoresis particle deposition and magnetohydrodynamic cross‐flow of Williamson hybrid nanofluids across a permeable deformable surface

AbstractThe need to examine the thermal transport of hybrid nanofluids has arisen from the need for improved heat transfer to control the rising heat density of small‐scale and many other technical procedures. Hybrid nanofluids are made up of two different kinds of nanoparticles suspended in the primary fluid. This improves the ability of regular fluids to transport heat and makes them better heat exponents than nanofluids. In this study, we evaluate the cross‐flow and heat transport characteristics of Williamson hybrid nanofluid across an extendable surface. The impacts of thermal radiation, non‐uniform heat sources, and magnetic effects are provoked in this study. The set of partial different equations is obtained as a result of the theoretical formulation. The similarity variables are hired to get the ordinary differential equations. The bvp4c solver is availed to compute the numerical dual solutions for different physical parameters. The results indicate that the friction factor is enhanced due to the presence of magnetic, suction, and Williamson parameters. Whereas, the heat transfer rate decreases due to Williamson and magnetic parameters, whilst the opposite impact is seen due to suction. Moreover, the Williamson parameter reduces the Sherwood number, whereas the suction uplifts the Sherwood number.

MHD Williamson fluid flow on an extending sheet with thermophoresis and chemical reaction

This research investigates the steady, two-dimensional, incompressible flow of a pseudoplastic Williamson fluid subjected to a linearly stretched sheet. The study incorporates the effects of magnetic fields, chemical reactions, and thermophoresis on fluid behavior. By applying boundary layer techniques and similarity transformations, the governing equations are simplified for numerical analysis. The MATLbvp4c solver is employed to solve the reduced equations. The obtained results are visually represented and thoroughly discussed to comprehend the model's physical characteristics. The investigation highlights the magnetic field's influence, chemical reaction, and impact of thermophoresis particle deposition on the flow behavior of Williamson fluid over the extended sheet. Findings: Moreover, significant roles are found for chemical reactions and thermophoresis parameters in determining the fluid concentration near the boundary layer. It is observed that an increase in the chemical reactions and thermophoresis parameters results in a reduced thickness of the fluid concentration near the boundary layer. Notably, an increase in Schmidt value also diminished the thickness of the fluid concentration close to the boundary layer. MHD parameter significantly influences the fluid's velocity and temperature near the surface. It has been noted that an increase in the MHD parameter decreases the fluid?s velocity and increases the temperature near the surface. The impact of skin friction coefficient and Nusselt number and the impact of mass transfer coefficient on Williamson fluid will be discussed. The findings acquired are examined in relation to existing research and the correlation is provide as table.

Numerically analysis of Marangoni convective flow of hybrid nanofluid over an infinite disk with thermophoresis particle deposition

This study discusses the flow of hybrid nanofluid over an infinite disk in a Darcy–Forchheimer permeable medium with variable thermal conductivity and viscosity. The objective of the current theoretical investigation is to identify the thermal energy characteristics of the nanomaterial flow resulting from thermo-solutal Marangoni convection on a disc surface. By including the impacts of activation energy, heat source, thermophoretic particle deposition and microorganisms the proposed mathematical model becomes more novel. The Cattaneo-Christov mass and heat flux law is taken into account when examining the features of mass and heat transmission rather than the traditional Fourier and Fick heat and mass flux law. MoS2 and Ag nanoparticles are dispersed in the base fluid water to synthesize the hybrid nanofluid. PDEs are transformed to ODEs by using similarity transformations. The RKF-45th order shooting method is used to solve the equations. With the use of appropriate graphs, the effects of a number of non-dimensional parameters on velocity, concentration, microorganism, and temperature fields are addressed. The local Nusselt number, density of motile microorganisms and Sherwood number are calculated numerically and graphically to derive correlations in terms of the relevant key parameters. The findings show that as we increase the Marangoni convection parameter, skin friction, local density of motile microorganisms, Sherwood number, velocity, temperature and microorganisms profiles increase, whereas Nusselt number and concentration profile exhibit an opposite behavior. The fluid velocity is reduced as a result of enhancing the Forchheimer parameter and Darcy parameter.

Swirling Flow of Chemically Reactive Viscoelastic Oldroyd-B Fluid through Porous Medium with a Convected Boundary Condition Featuring the Thermophoresis Particle Deposition and Soret–Dufour Effects

In this study, an analysis of the rotating flow of viscoelastic Oldroyd-B fluid along with porous medium featuring the Soret–Dufour effects is explored. The heat transport mechanism is discussed with the involvement of thermal radiation and heat source/sink. Additionally, the thermophoresis of particle deposition and chemical reaction are taken into the concentration equation in order to investigate the mass transportation in the liquid. To formulate the non-linear ordinary differential equations, the von Karman similarity approach is used in the system of partial differential equations and then integrated numerically by the bvp midrich scheme in Maple programming. Results are provided by graphical framework and tabular form. A quick parametric survey is carried out concerning flow field, thermal, and solutal distributions through graph representation. The curves show that increasing the values of the retardation time parameter decreases the radial velocity while increasing the angular velocity. Additionally, when the relaxation time parameter becomes powerful, the magnitude of the velocity curves decreases considerably in the radial and axial directions. The presence of a radiation parameter indicates that the fluid will absorb a greater amount of heat, which is equivalent to a higher temperature. Further, an increase in the stretching parameter leads to a reduction in the temperature components.

Flow of Maxwell Fluid with Heat Transfer through Porous Medium with Thermophoresis Particle Deposition and Soret–Dufour Effects: Numerical Solution

In this paper, we study the magnetohydrodynamics of Darcy flow in a non-Newtonian liquid. The influence of thermophoresis on particle deposition is examined in the Darcy flow of a Maxwell nanofluid. In our model, the temperature distribution is generated by the Fourier law of heat conduction with nonlinear thermal radiation and heat sink/source. We also examine the Soret–Dufour effects in the mass concentration equations. The Brownian and thermophoretic diffusions are assumed to be generated by nanoparticle dispersion in the fluid. The similarity method is used to transform the partial differential equations into nonlinear ordinary differential equations. The transformed flow equations were solved numerically using the BVP Midrich scheme. The results of the computation are displayed graphically and in tabular form. The results obtained show that increasing the Deborah number leads to a decline in radial and angular motion and a decrease in the magnitude of axial flow. As expected, the strength of the heat source and the values of the thermal radiation parameters determine the temperature of the liquid. We also found that as the Soret number rises (or the Dufour number falls), so does the mass transfer rate.

Thermophoresis deposition of hybrid ferrite nanoparticles on micropolar flow through a shrinking sheet with non-uniform heat source/sink and nonlinear radiation

Nowadays, the researchers have voiced their enthusiasm and interest in hybrid nanofluids due to their practical uses in engineering and industrial applications. Thus, our goal is to investigate the micropolar fluid flow towards a shrinking sheet containing hybrid ferrite nanoparticles with the substantial influence of thermophoresis particle deposition. Moreover, the impact of nonlinear radiation and non-uniform heat source/sink are also considered. The partial differential equations are converted to the similarity equations of a particular form through the similarity variables. Numerical outcomes are computed by applying the built-in program bvp4c in MATLAB. Multiple solutions are developed for a certain range of the suction parameter. The mass and heat transfer, as well as the friction and couple shear stress factors upsurge owing to the rise of the hybrid nanoparticles. The imposition of nonlinear radiation and non-uniform heat source/sink reduces the heat transfer, significantly. Meanwhile, thermophoresis particle deposition lowers the mass transfer. Lastly, the first solution is shown as a reliable and stable solution.

Inspection of hybrid nanoparticles flow across a nonlinear/linear stretching surface when heat sink/source and thermophoresis particle deposition impacts are significant

The aim of this paper is to highlight the impact of thermophoretic particle deposition (TPD) and heat source/sink on the steady two-dimensional laminar motion of Casson hybrid-type nanoliquid through a nonlinear stretched surface. Ordinary differential equations (ODEs) are created by taking a collection of partial differential equations (PDEs) and simplifying them using an appropriate similarity component. The reduced ODEs are then evaluated using the shooting method and Runge–Kutta–Fehlberg’s fourth and fifth orders. Finally, tables and graphs are used to display the numerical data. It is seen that the fluid velocity step-downs when the porous parametric quantity and solid nanoparticle values increase. Heat distribution is enhanced with an enhancement in the heat source/sink constraint. Concentration goes down with an enhancement in thermophoretic constraint. The use of nanoparticles improves heat dispersion but reduces concentration in the linear case while increasing axial velocity in the nonlinear scenario.

Analytic simulation of thermophoretic second grade fluid flow past a vertical surface with variable fluid characteristics and convective heating

The study considers the effect of thermophoresis particle deposition on the flow properties of second grade fluid with variable viscosity, variable thermal conductivity and variable concentration diffusivity subjected to a convective boundary condition. To further describe the transport phenomenon, the special case of assisting and opposing flows is explored. Using similarity transformations, the governing equations of the fluid model are transformed and parameterized into a system of nonlinear ordinary differential equations. The approximate analytic solution of a dimensionless system is obtained through the Optimal Homotopy Analysis Method (OHAM). It is observed that velocity and temperature distributions are decreasing functions of the second grade parameter for both assisting and opposing flows. When the thermophoretic parameter is increased, the concentration distributions at the first and fourth orders of chemical reaction decrease. For both opposing and assisting flows, velocity distributions are enhanced due to larger temperature-dependent viscous parameters.

Thermophoresis particle deposition of CoFe2O4-TiO2 hybrid nanoparticles on micropolar flow through a moving flat plate with viscous dissipation effects

PurposeThis study aims to investigate the micropolar fluid flow through a moving flat plate containing CoFe2O4-TiO2 hybrid nanoparticles with the substantial influence of thermophoresis particle deposition and viscous dissipation.Design/methodology/approachThe partial differential equations are converted to the similarity equations of a particular form through the similarity variables. Numerical outcomes are computed by applying the built-in program bvp4c in MATLAB. The process of flow, heat and mass transfers phenomena are examined for several physical aspects such as the hybrid nanoparticles, micropolar parameter, the thermophoresis particle deposition and the viscous dissipation.FindingsThe friction factor, heat and mass transfer rates are higher with an increment of 1.4%, 2.2% and 1.4%, respectively, in the presence of the hybrid nanoparticles (with 2% volume fraction). However, they are declined because of the rise of the micropolar parameter. The imposition of viscous dissipation reduces the heat transfer rate, significantly. Meanwhile, thermophoresis particle deposition boosts the mass transfer. Multiple solutions are developed for a certain range of physical parameters. Lastly, the first solution is shown to be stable and reliable physically.Originality/valueAs far as the authors have concerned, no work on thermophoresis particle deposition of hybrid nanoparticles on micropolar flow through a moving flat plate with viscous dissipation effect has been reported in the literature. Most importantly, this current study reported the stability analysis of the non-unique solutions and, therefore, fills the gap of the study and contributes to new outcomes in this particular problem.

A study of dual stratification on stagnation point Walters' B nanofluid flow via radiative Riga plate: a statistical approach

Features of double stratification on stagnation point flow of Walter's B nanoliquid driven through Riga surface are examined in the current study. Via solutal stratification, radiation and thermal effects, heat and mass phenomena are evaluated. The novelty of the proposed investigation is focused on the important effect of melting phenomenon and EMHD Lorentz force along with stratification and heat generation over the rheology of the liquid flow. The influence of Brownian and thermophoresis particle deposition is included in transport equations involved in the analysis. Transformation is incorporated by the basic laws of mass, energy and linear momentum to acquire nonlinear differential system of equations. Utilizing Optimal Homotopy Analysis Method through BVPh2.0.0, optimum value of convergence control factors is estimated. Graphical findings for the dimensionless temperature, velocity and concentration for different pertinent parameters are explained. Numerical values of physical interest like skin friction coefficient, local Sherwood number and local Nusselt number are computed and visualized graphically. The heat generation and advanced modified Hartmann number improve the speed of flow. It is also observed that weaker thermal stratification upraises the rate of heat transport, and mass transport rate lessens for stronger mass stratification. In addition, contour graphs of velocity for ratio parameter A describe the accurate perception of flow. The intensity of temperature and concentration field is low owing to double stratification, whereas the stronger radiation corresponds the significantly rise in temperature. Reliability of outcomes assured by means of probable error analysis.

Thermophoresis particle deposition analysis for nonlinear thermally developed flow of Magneto-Walter’s B nanofluid with buoyancy forces

In this study, we have discussed thermophoresis particle deposition effects under the action of both pressure and buoyant forces flow of magneto-Walter’s B nanofluid induced by a stretched surface. The Buongiorno nanofluid model is employed to analyze the dynamic impact of thermophoretic dispersion and Brownian motion. The effects of chemical reaction, Joule heating and non-linear radiation relations are also incorporated. The analysis has been performed in view of solutal and heat convective boundary constraints. The analytical technique namely homotopy analysis scheme followed to solve the resulting non-linear governing equations. The behavior of velocity, temperature and concentration profiles are observed graphically. The physical consequences for all physical parameters are justified. It is noted that heat thermal Biot number, thermophoretic constant and viscoelastic parameter increases the nanofluid temperature and concentration. A decaying concentration profile is noted for Schmidt number.

Oldroyd-B fluid flow over a rotating disk subject to Soret–Dufour effects and thermophoresis particle deposition

In this study, an investigation of magnetohydrodynamics flow of Oldroyd-B fluid by a rotating disk with the influence of thermophoresis on the deposition of particles is discussed. Additionally, the Soret–Dufour effects are taken into consideration. The von Karman transformation is used and the numerical results are obtained through BVP Midrich technique in Maple. The results are given through graphical structure and tabular form. The solutions of the governing equations are obtained and presented graphically in the form of velocity fields, temperature and concentration distributions. The results of local Stanton number (or inward axial thermophoretic deposition velocity) are presented through table. Results reveal that axial thermophoretic velocity enhances with the enlargement of relative temperature difference parameter and thermophoretic coefficient.

The Effectiveness of Variable Properties on Thermophoresis Particle Deposition at The Levels of 1st and 4th Orders of Chemical Reaction of Buoyancy-driven Flows of Second Grade Fluid

This article presents the analytic solution to a steady, incompressible, free convective flow of an electrically conducting second grade fluid past a vertical surface with variable properties namely: variable viscosity; variable thermal conductivity and variable concentration diffusivity in the presence of thermophoresis, chemical reaction and convective boundary condition. The impact of different orders of chemical reaction on thermophoresis and the transport process of flow, heat and mass transfer in the boundary layer for assisting and opposing flow cases are properly examined and discussed. The governing equations associated with the fluid model are transformed and parameterized to a system of coupled nonlinear ordinary differential equations using similarity transformations. The resulting coupled ordinary differential equations (ODEs) were solved by adopting the Optimal Homotopy Analysis Method (OHAM). The results indicate that velocity and temperature distributions are decreasing functions of second grade parameter for both cases of assisting and opposing flows. Also, concentration distribution is a decreasing function of thermophoretic parameter for low and high orders of chemical reaction.

Thermal and solutal stratification on MHD nanofluid flow over a porous vertical plate

Nanoparticles have the highest credibility to develop the thermal properties compared to conventional particle fluid suspension. Thermal and solutal stratification on heat and mass transfer induced due to a nanofluid over a porous vertical plate is analyzed. The transport equations engaged in the study include the effect of Brownian motion and thermophoresis particle deposition. The nonlinear governing equations and their related boundary conditions are initially looked into dimensionless forms by similarity variables. The resulting equations are solved numerically utilizing the fourth-fifth order Runge–Kutta–Fehlberg method with shooting technique (MAPLE 18). It is investigated that the temperature of the nanofluid and the concentration fraction decelerate with increase in thermal and solutal stratification.

Magnetohydrodynamic and heat transfer effects on the stagnation-point flow of an electrically conducting nanofluid past a porous vertical shrinking/stretching sheet in the presence of variable stream conditions

A steady two-dimensional magnetohydrodynamic stagnation-point flow of an electrically conducting fluid and heat transfer with thermal radiation of a nanofluid past a shrinking and stretching sheet is investigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis. A similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher-order nonlinear ordinary differential equations. The result shows that the velocity, temperature, and concentration profiles are significantly influenced by the Brownian motion, heat radiation, and thermophoresis particle deposition.

Soret and Dufour effects on MHD heat and mass transfer flow of a micropolar fluid with thermophoresis particle deposition

The effect of thermophoresis on heat and mass transfer flow of a micropolar fluid in the presence of Soret and Dufour effects past a vertical porous plate have been investigated . The transformed conservation equations are solved numerically using an optimized, extensively validated, variational finite element analysis. The influence of important non-dimensional parameter, Suction parameter ( ), Soret parameter (Sr), Dufour parameter (Du) and thermophoretic parameter (?) on velocity, angular velocity (micro-rotation), temperature and concentration fields as well as shear stress, Nusselt number and Sherwood number are examined in detail and the results are shown in graphically and in tabular form to know the physical importance of the problem. It is found that the imposition of wall fluid suction (V0>0) in this present problem of flow has the effect of depreciating the velocity, micro-rotation, temperature and concentration boundary layer thicknesses at every finite value of ?.

Thermophoresis particle deposition and internal heat generation on MHD flow of an Oldroyd-B nanofluid between radiative stretching disks

This study investigates the magnetohydrodynamic steady axi-symmetric flow of Oldroyd-B nanofluid between two infinite stretching disks. The effects of internal heat generation and absorption are taken into account. The Brownian motion, thermophoresis diffusion and thermophoresis particle velocity deposition effects are investigated in the presence of radiation effects. The governing nonlinear equations are first reduced to ordinary differential equations through appropriate similarity transformations and then resulting nonlinear system has been solved successfully using homotopy analysis method (HAM). The similarity solution for velocity, temperature and nanoparticle concentration profiles are expressed graphically and examined to understand the behavior of flow between stretching disks. The values of skin friction coefficient, Sherwood and Nusselt numbers are analyzed through tabulated values for both lower and upper disks. It is observed that magnetic field and radiation effects have significant impact on fluid temperature and nanoparticle concentration. Results showed that temperature and nanoparticle concentration are enhanced due to thermophoresis diffusion parameter.

Simultaneous Effects of Convective Heat and Mass Conditions in Magnetohydrodynamic Three-Dimensional Flow of Jeffrey Fluid with Thermophoresis

AbstractMagnetohydrodynamic (MHD) mixed convection flow of an incompressible Jeffrey fluid induced by a bidirectional stretching surface was investigated. Heat and mass transfer analysis was carried out in the presence of thermophoresis particle deposition and thermal radiation. Convective heat and mass conditions at the boundaries were taken. Mathematical analysis is presented subject to boundary layer assumptions. Homotopic procedure was implemented for the computations of solutions. Impacts of various physical parameters on the dimensionless temperature and concentration fields are plotted and discussed. Physical quantities of interest, namely, the local Nusselt and Sherwood numbers are analyzed through numerical values.

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.