Thermophoresis Particle Deposition Research Articles

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 equations. 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.

Lie group analysis for the effect of temperature-dependent fluid viscosity with thermophoresis on magnetohydrodynamic free convective heat and mass transfer over a porous stretching surface

This article concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. Impact of thermophoresis particle deposition in the presence of temperature-dependent fluid viscosity plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed.

Scaling Transformation for the Effect of Temperature-Dependent Fluid Viscosity with Thermophoresis Particle Deposition on MHD-Free Convective Heat and Mass Transfer Over a Porous Stretching Surface

This article concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. The flow is permeated by a uniform transverse magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. 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 to decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases with the decreasing viscosity but the temperature increases in this case. Impact of thermophoresis particle deposition in the presence of temperature-dependent fluid viscosity plays an important role on the concentration boundary layer. The results, thus, obtained are presented graphically and discussed.

Lie group analysis for the effect of temperature-dependent fluid viscosity with thermophoresis and chemical reaction on MHD free convective heat and mass transfer over a porous stretching surface in the presence of heat source/sink

This paper concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. The flow is permeated by a uniform transverse magnetic field. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equation 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 to decrease with the increasing distance of the stretching sheet. At a particular point of the sheet the fluid velocity decreases with the decreasing viscosity but the temperature increases in this case. It is found that with the increase of magnetic field intensity the fluid velocity decreases but the temperature increases at a particular point of the heated stretching surface. Impact of thermophoresis particle deposition with chemical reaction in the presence of heat source/sink plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed.

Thermophoresis particle deposition – thermal radiation interaction on natural convection heat and mass transfer from vertical permeable surfaces

PurposeThe purpose of this paper is to study thermophoresis particle deposition and thermal radiation interaction on natural convection heat and mass transfer by steady boundary layer flow over an isothermal vertical flat plate embedded in a fluid saturated porous medium.Design/methodology/approachThe governing partial differential equations are transformed into non‐similar form by using special transformation and then the resulting partial differential equations are solved numerically by using an implicit finite difference method.FindingsDifferent results are obtained and displaced graphically to explain the effect of various physical parameters on the wall thermophoresis deposition velocity and concentration profiles. It is found that the increasing of thermal radiation parameter or dimensionless temperature ratio heats the fluid and decreases temperature gradients near permeable wall, which increases local Nusselt numbers and decreases wall thermophoresis velocities. It is also found that the effect of power indices of either temperatures or concentration enhances both local Nusselt numbers and wall thermophoresis velocities. Comparison with previously published work in the limits shows excellent agreement.Originality/valueThe paper presents useful conclusions based on graphical results obtained from studying numerical solutions for thermophoresis‐thermal radiation heat and mass transfer interaction by steady, laminar boundary layer over a vertical flat plate embedded in a porous medium.

Thermophoresis and chemical reaction effects on non-Darcy MHD mixed convective heat and mass transfer past a porous wedge in the presence of variable stream condition

An analysis is presented to investigate the effect of thermophoresis particle deposition and variable viscosity on non-Darcy MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform non-Darcian porous medium in order to allow for possible fluid wall suction or injection. The governing partial differential equations of the problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary layer analysis. Numerical calculations are carried out for different values of dimensionless parameter in the problem and an analysis of the results obtained show that the flow field is influenced appreciably by the applied magnetic field. The results are compared with those known from the literature and excellent agreement between the results is obtained.

Thermophoresis particle deposition — thermal radiation interaction on mixed convection from vertical surfaces embedded in porous medium

This work deals with thermophoresis particle deposition and thermal radiation interaction on mixed convection heat and mass transfer by steady laminar boundary-layer flow over a nonisothermal vertical flat plate embedded in a fluid-saturated porous medium. The governing partial-differential equations are transformed into nonsimilar form by using a special transformation and then solved numerically by using an implicit finite-difference method. Different results are obtained and displayed graphically to explain the effect of various physical parameters on the wall thermophoretic deposition velocity, Nusselt numbers, and temperature and concentration profiles. It was found that the increasing of radiation parameter or dimensionless temperature ratio heated the fluid and decreased the temperature gradients near the impermeable wall, which increased the local Nusselt numbers and decreased the wall thermophoresis velocities. It was also found that the effect of power indexes of either temperatures or concentration enhances both local Nusselt numbers and wall thermophoresis velocities. Comparison with previously published work in the limits of absent thermophoresis and thermal radiation effects shows excellent agreement.

Lie group analysis for the effect of viscosity and thermophoresis particle deposition on free convective heat and mass transfer in the presence of suction/injection

An analysis has been carried out to study heat and mass transfer characteristics of an incompressible and Newtonian fluid having temperature-dependent fluid viscosity and thermophoresis particle deposition over a vertical stretching surface with variable stream condition. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The vertical surface is assumed to be permeable so as to allow for possible wall suction or injection. The governing differential equations are derived and transformed using Lie group analysis. The transformed equations are solved numerically by applying Runge-Kutta Gill scheme with shooting technique. Favorable comparisons with previously published work on various special cases of the problem are obtained. Numerical results for the velocity, temperature and concentration profiles for a prescribed temperature-dependent fluid viscosity and thermophoresis particle deposition parameters are presented graphically to elucidate the influence of the various physical parameters.

Thermophoresis Particle Deposition: Natural Convection Interaction from Vertical Permeable Surfaces Embedded in a Porous Medium

Thermophoresis Particle Deposition: Natural Convection Interaction from Vertical Permeable Surfaces Embedded in a Porous Medium

Nonsimilar solutions of magnetohydrodynamic and thermophoresis particle deposition on mixed convection problem in porous media along a vertical surface with variable wall temperature

Steady-state Magnetohydrodynamic mixed convection heat and mass transfer in the presence of thermophoretic and transverse magnetic field over a vertical flat plate embedded in a conductive fluid-saturated porous medium is investigated. Variations of the wall temperature and concentration are taken into account. The non-linear governing equations of the boundary layer in non-dimensional form are discretised by the finite difference method. An excellent agreement of the results with the previously published work is observed. Representative results are displayed graphically, which show the influence of the magnetic force and boundary conditions on the governing parameters of the problem.

Variable viscosity and thermophoresis effects on Darcy mixed convective heat and mass transfer past a porous wedge in the presence of chemical reaction

An analysis is presented to investigate the effect of thermophoresis particle deposition and variable viscosity on Darcy mixed convective heat and mass transfer of a viscous, incompressible fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform Darcian porous medium in order to allow for possible fluid wall suction or injection. The viscosity of the fluid is assumed to be a inverse linear function of temperature. The results are analyzed for the effect of different physical parameters, such as variable viscosity, magnetic, chemical reaction and thermophoresis parameters, on the flow, the heat and mass transfer characteristics.

Thermophoresis Effects on Heat and Mass Transfer in MHD Flow Over a Vertical Stretching Surface with Radiation

This paper deals with the effects of thermophoresis particle deposition, radiation and magnetic field on the flow, heat and mass transfer characteristics in a combined convective boundary layer flow over a stretching vertical plate. The governing boundary layer equations are transformed to a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the shooting method. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. In addition, tabulated results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented and discussed.

Suction/injection effects on thermophoresis particle deposition in a non-Darcy porous medium under the influence of Soret, Dufour effects

The effect of suction/injection on thermophoretic particle deposition in free convection on a vertical plate embedded in a fluid saturated non-Darcy porous medium is studied using similarity solution technique. The effect of Soret and Dufour parameters on convective transport, wall thermophoretic deposition velocity, heat transfer and mass transfer is discussed in detail for different values of dispersion parameters, ( Ra γ, Ra ξ ) inertial parameter F and Lewis number Le. The result indicates that in both suction, injection the Soret effect is more influential in increasing the concentration distribution in both aiding as well as opposing buoyancies. Also, it is worth mentioning here that the combined effect of opposing buoyancy and injection will have a more significant effect on the boundary layer thickness. In both the cases, suction as well as injection, magnitude of heat transfer is observed to be more when the second order effects are considered than when they are not. But, mass transfer and the wall thermophoretic deposition velocity V tw becomes less when all effects are considered than when they are not.

Effect of thermophoresis particle deposition on mixed convection from vertical surfaces embedded in saturated porous medium

PurposeThe aim of this paper is to formulate and analyze thermophoresis effects on mixed convection heat and mass transfer from vertical surfaces embedded in a saturated porous media with variable wall temperature and concentration.Design/methodology/approachThe governing partial differential equations (continuity, momentum, energy, and mass transfer) are written for the vertical surface with variable temperature and mass concentration. Then they are transformed using a set of non‐similarity parameters into dimensionless form and solved using Keller‐box method.FindingsMany results are obtained and a representative set is displaced graphically to illustrate the influence of the various physical parameters. It is found that the increasing of thermophoresis constant or temperature differences enhances heat transfer rates from vertical surfaces and increases wall thermophoresis velocities; this is due to favorable temperature gradients or buoyancy forces. It is also found that the effect of thermophoresis phenomena is more pronounced near pure natural convection heat transfer limit, because this phenomenon is directly temperature gradient‐ or buoyancy forces‐dependent.Research limitations/implicationsThe predicted results are restricted only to porous media with small pores due to the adoption of Darcy law as a force balance.Originality/valueThe paper explains the different effect of thermophoresis on forced, natural and mixed convection heat, and mass transfer problems. It is one of the first works that formulates and describes this phenomenon in a porous media. The results of this research are important for scientific researches and design engineers.

Thermophoresis particle deposition in a non-Darcy porous medium under the influence of Soret, Dufour effects

Thermophoresis particle deposition in free convection on a vertical plate embedded in a fluid saturated non-Darcy porous medium is studied using similarity solution technique. The effect of Soret and Dufour parameters on concentration distribution, wall thermophoretic deposition velocity, heat transfer and mass transfer is discussed in detail for different values of dispersion parameters (Raγ, Raξ) inertial parameter F and Lewis number Le. The result indicates that the Soret effect is more influential in increasing the concentration distribution in both aiding as well as opposing buoyancies. Also, the non-dimensional heat transfer coefficient and non-dimensional mass transfer coefficient changes according to different values of thermophoretic coefficient k.

Influence of radiation on MHD free convection from a vertical flat plate embedded in porous media with thermophoretic deposition of particles

Magneto-hydrodynamics and thermal radiation effects on heat and mass transfer in steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate embedded in a fluid saturated porous media in the presence of the thermophoresis particle deposition effect is studied in this paper. The governing equations are transformed by special transformations. Brownian motion of particles and thermophoretic transport are considered in the flow equations. The magnetic field is considered to be applied. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting similarity equations are solved numerically by the fourth-order Runge–Kutta method with shooting technique. Many results are obtained and representative set is displayed graphically to illustrate the influence of the various parameters on the wall thermophoretic deposition velocity, concentration, temperature and velocity profiles.

Effects of thermophoresis particle deposition in free convection boundary layer from a horizontal flat plate embedded in a porous medium

The present contribution deals with the thermophoresis particle deposition effect on the free convection over a horizontal flat plate embedded in a fluid-saturated porous medium. In a certain sense, this study continues that by Chamka and Pop [A. Chamka, I. Pop, Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium, Int. Commun. Heat Mass Transfer 31 (2004) 421–430], where the vertical flat plate configuration was analyzed. The governing equations are transformed into a set of coupled differential equations, which are solved numerically using a finite difference method. For various values of the problem parameters, graphs of the profile concentration in the boundary layer and of thermophoretic deposition velocity are presented.

Combined of magnetic field and thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium

Deals with heat and mass transfer by steady laminar boundary layer flow of Newtonian, viscous fluid over a vertical flat plate embedded in a fluid-saturated porous medium in the presence of thermophoretic and magnetic field. The resulting similarity equation are solved by finite difference marching technique. The nature of variation of particle concentration profile and magnetic field with respect to buoyancy force, Fw, and Prandtl number is found to be similar. Comparisons with previous published work are performed and the results are found to be in excellent agreement. .

Effect of thermophoresis particle deposition in free convection boundary layer from a vertical flat plate embedded in a porous medium

This work deals with heat and mass transfer by steady laminar boundary layer flow of a Newtonian, viscous fluid over a vertical flat plate embedded in a fluid-saturated porous medium in the presence of the thermophoresis particle deposition effect. The governing partial differential equations are transformed into ordinary differential equations by using special transformations. The resulting similarity equations are solved numerically by an implicit finite-difference method. Comparisons with previously published work are performed

Chemical reaction on MHD flow and heat transfer of a nanofluid near the stagnation point over a permeable stretching surface with non-uniform heat source/sink

A numerical investigation has been conducted to study the laminar, boundary layer stagnation point flow of a nanofluid over a permeable, vertical stretching sheet. The model used incorporates the effects of Brownian motion with thermophoresis in the presence of uniform magnetic field and non-uniform source/sink under the influence of chemical reaction. Governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using suitable similarity transformations. The transformed equations are then solved numerically using well known Runge-Kutta-Fehlberg method of fourth-fifth order with the help of symbolic software MAPLE. The influence of governing parameters on flow field, temperature and nanoparticle volume fraction profiles are provided both in graphical and tabular form. It is observed that heat source/sink with thermophoresis particle deposition in the presence of magnetic field have a substantial effect on the flow field and thus, on the heat and mass transfer rate from the sheet to the fluid. As the strength of the chemical reaction is higher than the thermophoresis particle deposition, nanoparticle volume fraction of the fluid gradually decreases. A comparative study has been conducted and is found to be in excellent agreement.Keywords: Stagnation point flow; Chemical reaction; Heat transfer; Stretching surface; Nanofluid; Numerical solution.