Thermophoresis Parameter Nt Research Articles

Mixed convection flow of Oldroyd-B nano fluid with Cattaneo-Christov heat and mass flux model with third order slip

This study reports the three-dimensional mixed convection flow of an Oldroyd-B nanofluid past a bidirectional stretching surface. Nonlinear partial differential equations obtained from the flow problem were converted into nonlinear ordinary differential equations using similarity transformation, and then, the numerical solutions of these ODEs with corresponding boundary conditions were obtained by employing a bvp4c solver. The effect of governing parameters on nondimensional velocity along x- and y-directions, temperature, particle concentration, local Nusselt number, and Sherwood number was presented through graphs and tables. It can be seen that the increasing values of the Brownian motion parameter Nb and thermophoresis parameter Nt lead to an increase in the temperature field and thermal boundary layer thickness, while the opposite behavior is observed for concentration field and concentration boundary layer thickness. As the Deborah number β1 increases, the concentration profile as well as concentration boundary layer thickness increase. However, the effects of β2 on the concentration profile are opposite to those of β1. An increase in δt, Pr, and α results in a decrease in temperature. It is reported that the local Nusselt number increases when β and Pr increase, whereas it decreases when λ, Nb, Nt, and Sc increase. An increase in Biot number Bi results in an increase in the Nusselt number, and an increase in Nt results in an increase in the Sherwood number. The results of the present analysis were compared with the available works in particular situations, and more agreement has been noted.

Effects of homogeneous-heterogeneous reactions in flow of nanofluid between two stretchable rotating disks

The present study analyzes nanofluid flow over a two infinite rotating disk. A magnetic field addressed on momentum equation. An effect of homogeneous-heterogeneous reaction on the fluid flow is investigated. The relevant system of governing equations is transformed into ordinary differential equations by using Von Karman transformations. Homotopy approaches for different physical parameters are examined graphically on appropriate profile. For greater (S1) the radial, axial and azimuthal velocities are hiked. Energy of liquid enhances with increasing thermophoresis parameter Nt. Local Skin friction coefficient diminishes with higher Reynolds number at lower disk and opposite behavior at upper disk. Moreover concentration field elevates while increasing heterogeneous parameter.

Influence of thermophoresis and Brownian motion on mixed convection two dimensional MHD Casson fluid flow with non-linear radiation and heat generation

In this study, two dimensional mixed convective MHD stagnation point flow of Casson fluid past an infinite plate in porous medium is considered. Effects of thermophoresis, Brownian motion, non-linear thermal radiation, heat generation and chemical reaction are considered. The governing differential equations are modified using similarity transformation. System of ODE is solved using HAM. Effects of different vital parameters on velocity, temperature and concentration profiles are shown graphically. The numerical values of the velocity, temperature and concentration gradient are also obtained in tabular form. It is illustrated that, mixed convection parameter λ, buoyancy force parameter N, non-linear thermal radiation parameter Nr and heat generation parameter H tends to improve motion of the fluid throughout the flow field. It is also seen that, heat and mass transfer process improve with Brownian motion Nb and thermophoresis parameter Nt. Brownian motion and thermophoresis parameters have negative impacts on temperature gradient.

Two-phase nanofluid over rotating disk with exponential variable thickness

PurposeThe purpose of this paper is to investigate the effect of nanofluid over rotating disk with the exponential variable thickness (c > 0, b > 0) and to analyze Brownian motion and thermophoresis of Buongiorno model on the disk embedded in nanofluid-saturated porous media.Design/methodology/approachUsing the generalized von Karman transformation, the boundary layer governing equations are transformed into semi-similar forms solved by bvp4c in MATLAB.FindingsThe effects of the thickness parameter a, the shape parameter b, the Brownian motion parameter Nb and thermophoresis parameter Nt on flow, heat and mass transfer are analyzed. With the increase of thickness parameter a, the radial velocity first decreases and then increases, showing the opposite trend on the two sides of the peak value. Moreover, temperature and concentration rise as the Brownian motion parameter Nb becomes larger.Originality/valueTo the best of the authors’ knowledge, this is the first work that has been done on rotating disk with exponential variable thickness in nanofluid. The impact of the two slip effects, namely, Brownian motion and thermophoresis, on the nanofluid boundary layer flow, heat and mass transfer because of rotating disk with exponential variable thickness (c > 0, b > 0) has been addressed in this study.

Impacts of surface roughness on mixed convection nanofluid flow with liquid hydrogen/nitrogen diffusion

PurposeThe purpose of this paper is to present the surface roughness effects on mixed convection nanofluid flow with liquid hydrogen/liquid nitrogen diffusion.Design/methodology/approachThe small parameter (α) is considered along with the frequency parameter n to study the surface roughness. The non-similar transformations are used to reduce the dimensional non-linear partial differential equations into dimensionless form, and then, the resulting equations are solved with the help of Newton’s Quasilinearization technique and the finite difference scheme.FindingsThe impacts of several dimensionless parameters such as Brownian diffusion parameter (Nb), thermophoresis parameter (Nt), small parameter (α), etc., are analyzed over various profiles as well as gradients. Also, the investigation is carried out for in presence and absence of nanoparticles. The influence of surface roughness is sinusoidal in nature and is more significant near the origin in case of skin-friction coefficient. The addition of nanoparticles enhances the skin-friction coefficient and reduces the Nusselt number, while its effects are not noticeable in case of mass transfer rates. The presence of suction/blowing, respectively, enhances/decreases the Sherwood number pertaining to the liquid hydrogen.Practical implicationsThe results of the present analysis are expected to be useful for the design engineers of polymer industries in manufacturing good quality polymer sheets.Originality/valueTo the best of the author’s knowledge, no such investigation has been carried out in the literature.

Activation energy and dual stratification effects for Walter-B fluid flow in view of Cattaneo-Christov double diffusionon

The purpose of the present article is to explore the novel aspects of activation energy in nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo-Christov double diffusion model over a permeable stretched sheet. Generalized forms of Fourier's and Fick's law are utilized through Cattaneo-Christov double diffusion. Walter-B nanomaterial model is used that describes the significant slip mechanism namely Brownian and thermophoresis diffusions. Double stratification, heat generation/absorption and chemical reaction are considered. Modified Arrhenius formula for activation energy is implemented. The acquired nonlinear system is cracked through homotopic analysis method. Effects of emanating variables are examined through graphs and tables. It is evident that temperature distribution and thermal boundary layer thickness is monotonically dwindling function of thermal stratification parameter(P1), thermal relaxation time (δ2) and upsurge for the thermophoresis parameter (Nt), heat generation/absorption parameter (B₁), Brownian motion parameter (Nb). Nanoparticle concentration is directly comparable to the activation energy of reaction and impact of thermal relaxation time is qualitatively opposite to that of thermophoretic force.

Biomedical study of effects nanoparticles on unsteady blood (non-Newtonian) flow through a catheterized stenotic vessel

The purpose of this article is to theoretically discuss the unsteady hemo-dynamics of blood through a catheterized overlapping stenotic vessel with nanoparticles. The nature of the blood is characterized by the constitutive Cross model equation. This study is conducted under the assumption of mild stenotic conditions and the equations of momentum and temperature are simplified after making this assumption. Explicit finite difference method is employed to obtain the numerical results of the governing equations. Results for different values of emerging parameters, such as Weissenberg number, Lewis number, thermophoresis parameter, and Brownian motion parameter are shown at different locations of an arterial cross section. These results demonstrate a pictorial way to comprehend the theoretical biomedical problem. These results reveal that Lewis number (Le) and visco-elastic parameter Weissenberg number (We) both are decreasing functions of velocity profiles at each arterial cross section. Furthermore, it is also noted that the thermophoresis parameter (Nt) quantitatively decreases the flow of blood inside the vessel while the Brownian motion parameter (Nb) shows the opposite effects on blood flow; it increases the magnitude of velocity.

On steady two-dimensional Carreau nanofluid flow in the presence of infinite shear rate viscosity

This paper examines the steady two-dimensional Carreau nanofluid flow over a stretching surface with infinite shear rate viscosity. The effects of Brownian motion and thermophoresis under the influence of convectively heated surface are analyzed. Using suitable transformations, nonlinear partial differential equations are transformed into ordinary differential equations and solved numerically using the Runge–Kutta–Fehlberg method coupled with the shooting technique. The effects of various physical parameters like local Weissenberg number (We), thermophoresis parameter (Nt), Brownian motion parameter (Nb), Prandtl number (Pr), Lewis number (Le), viscosity ratio parameter (β*), and Biot number (γ*) on the temperature and nanoparticle concentration distributions are displayed graphically and discussed quantitatively. Generally, our results reveal that temperature and nanoparticle concentration distributions are marginally influenced by the viscosity ratio parameter. Further, it is noted that augmented values of viscosity ratio parameter thin the boundary layer thickness in shear thinning fluid and the reverse is true for shear thickening fluid.

Analytical Solution of Unsteady Boundary Layer Flow of a Nanofluid Past a Stretching Inclined Sheet With Effects of Magnetic Field

Flow of a nanofluid in a boundary layer in an inclined moving sheet at angle is considered analytically. The Mathematical formulation consists of the Magnetic parameter, thermophoresis, and Brownian motion. Previously published work considered convective boundary condition. The present study considered an inclined stretching sheet at angle in one dimension and considered thermal conditions of non convective heating and heat flux. Solutions to momentum, temperature and concentration distribution depends on seven parameters, Magnetic parameter M, Lewis number Le, Prandtl number Pr, thermophoresis parameter Nt, the Brownian motion parameter Nb, unsteady parameter c and Grashof numbers Gr and Gc. The non linear coupled Differential equations were solved using the improved Adomian decomposition method and a good agreement was established with the numerical method (Shooting technique). Analytical result is also presented graphically to illustrate the effect of the earlier listed parameters on Momentum, temperature and nanofraction boundary layers. Momentum boundary layer increases with increase in Grashof numbers, angle of inclination and unsteady parameter..Keywords— Adomian Decompostion Method (ADM), Nanofluid, Inclined sheet, magnetic field effects, Numerical Method (NM).

Viscous and Ohmic dissipation on non-Darcy MHD nanofluid mixed convection flow in porous medium with suction/injection effects

The paper presents the influence of nanofluid flow on MHD mixed convection, incompressible and electrically conducting fluid along a vertical flat plate with viscous and ohmic dissipation effects. The plate is permeable and embedded in a fluid saturated on non-Darcy (Forchheimer flow model) porous medium with suction and injection. Dissipation parameters are described in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity transformation. The non linear ordinary differential equations are linearized by using Quasi-linearization technique and then solved numerically by using implicit finite difference scheme. To compute the numerical values C programming code is used. The numerical results are analyzed for the effects of various physical parameters such as magnetic parameter Ha, Reynolds number Red, Eckert number, Ec thermophoresis parameter Nt, Brownian motion parameter Nb, suction and injection parameter fw and Lewis number Le. The results obtained are discussed with the help of graphical illustrations.

MHD three dimensional flow of Oldroyd-B nanofluid over a bidirectional stretching sheet: DTM-Padé Solution

Abstract Current article is devoted with the study of MHD 3D flow of Oldroyd B type nanofluid induced by bi-directional stretching sheet. Expertise similarity transformation is confined to reduce the governing partial differential equations into ordinary nonlinear differential equations. These dimensionless equations are then solved by the Differential Transform Method combined with the Padé approximation (DTM-Padé). Dealings of the arising physical parameters namely the Deborah numbers β1 and β2, Prandtl number Pr, Brownian motion parameter Nb and thermophoresis parameter Nt on the fluid velocity, temperature and concentration profile are depicted through graphs. Also a comparative study between DTM and numerical method are presented by graph and other semi-analytical techniques through tables. It is envisage that the velocity profile declines with rising magnetic factor, temperature profile increases with magnetic parameter, Deborah number of first kind and Brownian motion parameter while decreases with Deborah number of second kind and Prandtl number. A comparative study also visualizes comparative study in details.

Mathematical Modelling of Hydromagnetic Casson non-Newtonian Nanofluid Convection Slip Flow from an Isothermal Sphere

Abstract In this article, the combined magnetohydrodynamic heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid from an isothermal sphere surface with convective condition under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. magnetic parameter (M), Buoyancy ratio parameter (N), Casson fluid parameter (β), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr) and thermal slip (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Increasing viscoplastic (Casson) parameter decelerates the flow and also decreases thermal and nano-particle concentration. Increasing Brownian motion accelerates the flow and enhances temperatures whereas it reduces nanoparticle concentration boundary layer thickness. Increasing thermophoretic parameter increasing momentum (hydrodynamic) boundary layer thickness and nanoparticle boundary layer thickness whereas it reduces thermal boundary layer thickness. Increasing magnetohydrodynamic body force parameter decelerates the flow whereas it enhances temperature and nano-particle (species) concentrations. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

Magnetohydrodynamic (MHD) boundary layer heat and mass transfer characteristics of nanofluid over a vertical cone under convective boundary condition

This paper investigates the boundary layer flow, heat and mass transfer characteristics over a vertical cone filled with nanofluid saturated porous medium with the influence of magnetic field, thermal radiation and first order chemical reaction subject to the convective boundary condition. Similarity transformation technique is used for the purpose of converting non-linear partial differential equations into the system of complex ordinary differential equations. The computational Finite element method has been employed to solve the flow, heat and mass transfer equations together with boundary conditions. The impact of various pertinent parameters on hydrodynamic, thermal and solutal boundary layers is investigated and the results are displayed graphically. Furthermore, the values of local skin-friction coefficient, rate of temperature and rate of concentration is also calculated and the results are presented graphically. The comparisons with previously published work is made and found good agreement. The thickness of thermal boundary layer is increased with increase in the values of Brownian motion parameter (Nb) and thermophoresis parameter (Nt).

Investigation of MHD Eyring–Powell fluid flow over a rotating disk under effect of homogeneous–heterogeneous reactions

In this research, the characteristic of the Eyring–Powell Nano fluid flow due to rotating dick with various physical impacts, such as slip flow, magnetic field along with homogeneous–heterogeneous reactions is analyzed. Higher order non-linear expressions are converted to ordinary first-order differential equations and then solved using the numerical Method (4th–5th-order Runge–Kutta–Fehlberg) in Maple-18 software. The main view of this article is to investigate the impact of parameters and numbers in the problem on velocity, temperature and concentration profiles. Conclusions indicate that: the temperature profile has shown a dual behavior in terms of changes Nt and pr. T (ζ) is increased with increasing thermophoresis parameter (Nt) and is decreased with increasing Prandtl number (Pr).

Finite Difference Simulation of MHD Radiative Flow of a Nanofluid past a Stretching Sheet with Stability Analysis

In the present study, unsteady heat and mass nanofluid flow past a stretching sheet with the effect of thermal radiation and magnetic field was carried out. To obtain non-similar equation, the boundary layer governing equations including continuity, momentum, energy and concentration balance were non-dimensionalized by usual transformation. The non-similar approach was employed, which depends on the dimensionless parameters such as Magnetic parameter (M), Radiation parameter (R), Prandtl number (Pr), Eckert number (Ec) Lewis number (Le), Brownian motion parameter (Nb), Thermophoresis parameter (Nt), Local Reynolds number (Re) and velocity parameter (b/a). The temperature and concentration distributions are found affected by these dimensionless parameters. The obtained equations have been solved by explicit finite difference method (EFDM). A theoretical model of the stability and convergence to describe the aspects of the finite difference scheme was developed in this study. This analysis makes the EFDM approach more accurate and able to provide the convergence criteria of the method (Pr ≥ 0.375 and Le ≥ 0.25). The temperature and concentration profiles are discussed for the different values of the dimensionless parameters by considering different time steps. The present computational investigation finds applications in the area of magnetic nanomaterials processing.

Magnetohydrodynamic(MHD) Boundary Layer Flow of Eyring-Powell Nanofluid Past Stretching Cylinder With Cattaneo-Christov Heat Flux Model

AbstractThis study analyzed the MHD boundary layer flow of Eyring-Powell nanofluid past stretching cylinder with Cattaneo-Christov heat flux model. The governing non-linear partial differential equations corresponding to the momentum, energy and concentration have been formulated and transformed into a set of non-linear ordinary differential equations by using similarity transformations. Then the resulting non-linear high order ordinary differential equations of momentum, energy and concentration, subjected to boundary conditions were solved numerically by utilizing the second-order accurate implicit finite difference method known as Keller-Box which is programmed in the MATLABR2017b software. The results indicated that the velocity profile increases as the Eyring-Powell fluid parameterMand the curvature parameterγincrease but it decreases as the magnetic parameterHaincreases. Both the temperature and the concentration profiles have revealed an increment pattern for large values of the magnetic parameterHaand the thermophoresis parameterNtbut a decrement manner with increasing values of the Eyring-Powell fluid parameterM. The Brownian motion parameterNbhas shown an opposite influence on the temperature and the concentration profiles. The results also depicted that the local skin friction coefficient increases with increasing in Eyring-Powell fluid parameterM, magnetic parameterHa. Besides, it is found that both the local Nusselt numberNuxand the local Sherwood numberShxare higher for large vales of Eyring-Powell fluid parameterMand curvature parameterγ. Furthermore, the present results for the local skin friction coefficient, the local Nusselt number and the local Sherwood number are validated with the data of previously published literature for various limiting conditions where a very sound agreement has been attained.

Mathematical analysis of non-Newtonian nanofluid transport phenomena past a truncated cone with Newtonian heating

In the present study, we analyze the heat, momentum and mass (species) transfer in external boundary layer flow of Casson nanofluid past a truncated cone surface with Biot Number effect is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer Biot Number effect. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multi-degree non-similar partial differential equations consisting of the momentum, energy and concentration equations via. Appropriate non-similarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second order accurate finite difference method of the implicit type. The influences of the emerging parameters i.e. Casson fluid parameter (?), Brownian motion parameter (Nb) and thermophoresis parameter (Nt), Lewis number (Le), Buoyancy ratio parameter (N ), Prandtl number (Pr) and Biot number (Bi) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tri-diagonal method has been included. The study is relevant to enrobing processes for electric-conductive nano-materials of potential use in aerospace and other industries.

Stability analysis on the flow and heat transfer of nanofluid past a stretching/shrinking cylinder with suction effect

Abstract The steady boundary layer flow over a stretching/shrinking cylinder with suction effect is numerically studied. Using a similarity transformations, the governing partial differential equations are transformed into a set of nonlinear differential equations and have been solved numerically using a bvp4c code in Matlab software. The nanofluid model used is taking into account the effects of Brownian motion and thermophoresis. The influences of the governing parameters namely the curvature parameter γ, mass suction parameter S, Brownian motion parameter Nb and thermophoresis parameter Nt on the flow, heat and mass transfers characteristics are presented graphically. The numerical results obtained for the skin friction coefficient, local Nusselt number and local Sherwood number are thoroughly determined and presented graphically for several values of the governing parameters. From our investigation, it is found that the non-unique (dual) solutions exist for a certain range of mass suction parameter. It is observed that as curvature parameter increases, the skin friction coefficient and heat transfer rate decrease, meanwhile the mass transfer rates increase. Moreover, the stability analysis showed that the first solution is linearly stable, while the second solution is linearly unstable.

Computational analysis of non-Newtonian boundary layer flow of nanofluid past a semi-infinite vertical plate with partial slip

Abstract An analysis of this paper is examined, two-dimensional, laminar with heat and mass transfer of natural convective nanofluid flow past a semi-infinite vertical plate surface with velocity and thermal slip effects are studied theoretically. The coupled governing partial differential equations are transformed to ordinary differential equations by using non-similarity transformations. The obtained ordinary differential equations are solved numerically by a well-known method named as Keller Box Method (KBM). The influences of the emerging parameters i.e. Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Buoyancy ratio parameter (N), Lewis number (Le), Prandtl number (Pr), Velocity slip factor (Sf) and Thermal slip factor (ST) on velocity, temperature and nano-particle concentration distributions is illustrated graphically and interpreted at length. The major sources of nanoparticle migration in Nanofluids are Thermophoresis and Brownian motion. A suitable agreement with existing published literature is made and an excellent agreement is observed for the limiting case and also validation of solutions with a Nakamura tridiagonal method has been included. It is observed that nanoparticle concentrations on surface decreases with an increase in slip parameter. The study is relevant to enrobing processes for electric-conductive nano-materials, of potential use in aerospace and other industries.

Natural convection flow of a power-law non-Newtonian nanofluid in inclined open shallow cavities filled with porous media

A numerical study of the laminar natural convection flow of non-Newtonian nanofluids in an inclined open shallow cavity filled with a porous medium is presented. The two-phase Buongiorno's model is used to simulate the nanofluid case and the Darcy model is applied to the porous medium. The apparent viscosity and stresses are given using the non-Newtonian power-law forms. The partial differential equations governing the flow are solved using the finite volume method with approximating the boundary conditions at the opening. Streamlines and isotherms are produced and local and average Nusselt number, Bejan and total entropy generation, horizontal and velocity components are calculated for the inclination angle α from 0 to π, the power-law index n from 0.4 to 1, the Rayleigh number Ra from 105 to 109 the Darcy number from 10 − 2 to 10 − 4, the cavity aspect ratio from 0.125 to 1 and the variations of the thermophoresis parameter Nt and the Brownian motion parameter Nb from 0.1 to 1. The results indicate that the increase in the power-index n reduces the rate of heat transfer and vertical velocity while the average Bejan number is enhanced. Also, the local and average Nusselt numbers are decreasing functions of the cavity aspect ratio.