Slip Effects on the Peristaltic Motion of Nanofluid in a Channel With Wall Properties

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
M. Mustafa ◽  
S. Hina ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Brownian Motion ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Analytic Expressions ◽  
Nanoparticles Concentration ◽  
Compliant Walls ◽  
Nanoparticles Volume Fraction ◽  
Brownian Motion And Thermophoresis

This article looks at the peristaltic flow of nanofluid in a channel with compliant walls. Brownian motion and thermophoresis effects are taken into consideration. Mathematical model is formulated by using long wavelength and low Reynolds number assumptions. The analytic expressions of temperature and nanoparticles concentration are developed by homotopy analysis method (HAM). The solutions are validated through the numerical solutions obtained by employing the built in routine for solving nonlinear boundary value problem via shooting method through software mathematica. Special emphasis is given to the role of key parameters including the Brownian motion parameter (Nb), thermophoresis parameter (Nt), Prandtl number (Pr), Eckert number (Ec) on temperature, and nanoparticles concentration. It is observed that both temperature and nanoparticles volume fraction increase when the Brownian motion and thermophoresis effects intensify. Moreover, the heat transfer coefficient is increasing function of Nb and Nt.

Second-Order Slip Effects on Heat Transfer of Nanofluid with Reynolds Model of Viscosity in a Coaxial Cylinder

2015 ◽  
Vol 16 (6) ◽  
pp. 285-292
Author(s):  
Jing Zhu ◽  
Dan Yang ◽  
Liancun Zheng ◽  
Xinxin Zhang
Keyword(s):  
Volume Fraction ◽  
Nonlinear Differential Equations ◽  
Metal Oxide Nanoparticles ◽  
Velocity Slip ◽  
Coaxial Cylinder ◽  
Second Order ◽  
Effective Density ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Nanoparticles Volume Fraction

Abstract The present work makes an analysis on the effects of second-order velocity slip and temperature jump boundary conditions for third-grade nanofluid over a coaxial cylinder. In the modeling of blood-based nanofluids containing metal or metal oxide nanoparticles, the viscosity is approximated to second-order Maclaurin’s series for the first time and the effective density is handled to a combination of temperature and nanoparticles volume fraction. The governing equations are transformed into a dimensionless system of nonlinear differential equations and solved by homotopy analysis method (HAM). The accuracy and efficiency of the HAM solutions are verified by ℏ $$\hbar $$ -curves and residual error curves using package BVPh2.0. The physical interpretations are illustrated by graphs and tables. The results revealed that the Nusselt number increases with an increase of nanoparticle volume fraction. The second-order velocity slip has a significant weakened effect on the skin friction. In addition, the Brownian motion and thermophoresis movement are collaborating to increase the temperature profile.

Unsteady Boundary Layer Flow of Nanofluid Past an Impulsively Stretching Sheet

2013 ◽  
Vol 29 (3) ◽  
pp. 423-432 ◽  
Author(s):  
M. Mustafa ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Similarity Transformations ◽  
Nanoparticles Concentration ◽  
Motion Effect ◽  
Nanoparticles Volume Fraction ◽  
Layer Flow

AbstractThe unsteady laminar boundary layer flow of nanofluid caused by a linearly stretching sheet is considered. Transport equations contain the simultaneous effects of Brownian motion and thermophoretic diffusion of nanoparticles. The relevant partial differential equations are non-dimensionalized and transformed into similar forms by using appropriate similarity transformations. The uniformly valid explicit expressions of velocity, temperature and nanoparticles volume fraction are derived. Convergence of the series solutions is carefully analyzed. It is observed that an increase in the strength of Brownian motion effect rises the temperature appreciably. However rate of heat transfer and nanoparticles concentration at the sheet is reduced when Brownian motion effect intensifies. It is also found that the temperature and nanoparticles concentration are increasing functions of the unsteady parameter.

Brownian motion and thermophoresis effects on natural convection of alumina–water nanofluid

2012 ◽  
Vol 227 (1) ◽  
pp. 100-110 ◽  
Author(s):  
Habib Aminfar ◽  
Mohammad Reza Haghgoo
Keyword(s):  
Heat Transfer ◽  
Brownian Motion ◽  
Natural Convection ◽  
Volume Fraction ◽  
Effective Properties ◽  
Solid Volume Fraction ◽  
Convection Heat Transfer ◽  
Conservation Equation ◽  
Nanoparticles Volume Fraction ◽  
Brownian Motion And Thermophoresis

In this article a ‘two-component four-equation non-homogeneous equilibrium’ model has been adopted to accurately simulate the process of natural convection of Al2O3–water nanofluid inside a vertical square cavity. The aforementioned model considers conservation equation of nanoparticles which is highly coupled to other equations (mass, momentum, and energy equations for nanofluid) and includes the effects of Brownian motion and thermophoresis as the two most important mechanisms of slip velocity in laminar flow. The distribution of nanoparticles volume fraction is obtained by solving these four equations simultaneously. Renewing the effective properties of nanofluid from the nanoparticles, volume fraction distribution is another advantage of this model. Numerical results are in good agreement with published experimental data and emphasize that the use of the nanofluid for natural convection heat transfer enhancement in enclosure is impracticable for the studied range of solid volume fraction [Formula: see text]. Also, heat transfer rate decreases with an increase in nanoparticle volume fraction.

Free Convection Flow of a Nanofluid Past an Isothermal Inclined Plate

2013 ◽  
Vol 390 ◽  
pp. 129-133 ◽  
Author(s):  
Marneni Narahari ◽  
S. Akilu ◽  
A. Jaafar
Keyword(s):  
Nusselt Number ◽  
Brownian Motion ◽  
Volume Fraction ◽  
Convection Flow ◽  
Inclined Plate ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Keller Box Method ◽  
Brownian Motion And Thermophoresis ◽  
Layer Flow

In this paper, the natural convective boundary-layer flow of a nanofluid over an isothermal inclined plate is investigated numerically with the effects of Brownian motion and thermophoresis in the nanofluid model. The equations governing the flow are expressed in the form of coupled non-linear ordinary differential equations using the similarity analysis. These equations are then solved numerically by an implicit finite-difference method known as the Keller-box method. The effect of inclination angle on the dimensionless velocity, temperature, nanofluid volume fraction and Nusselt number has been analyzed through graphs. Brownian motion and thermophoresis effects on the Nusselt number at an inclined plate are also discussed.

Forced Convection of MHD Radiative Jeffrey Nanofluid Over a Moving Plate

2021 ◽  
Vol 87 (1) ◽  
pp. 12-19
Author(s):  
Syazwani Mohd Zokri ◽  
Nur Syamilah Arifin ◽  
Abdul Rahman Mohd Kasim ◽  
Norhaslinda Zullpakkal ◽  
Mohd Zuki Salleh
Keyword(s):  
Brownian Motion ◽  
Numerical Solutions ◽  
Graphical Representation ◽  
Physical Parameters ◽  
Concentration Profiles ◽  
Moving Plate ◽  
Parameter Ratio ◽  
Nanoparticles Concentration ◽  
Jeffrey Nanofluid ◽  
The Impact

Convectively heated Jeffrey nanofluid flow in the presence of magnetic field and thermal radiation is investigated from a moving plate. Parameter of Brownian motion from Boungiorno model is the imperative mechanism that contributes to the heat transfer enhancement. Governing equations, consisting of the continuity, momentum, energy and nanoparticle concentrations equations are transformed into dimensionless form by means of the appropriate similarity transformation variables. Numerical results via Runge-Kutta Fehlberg Fourth-Fifth order (RKF45) method are specifically acquired on the impact of physical parameters such as Brownian motion, magnetic parameter, ratio of relaxation to retardation and radiation parameters over the temperature and nanoparticles concentration profiles. Comparison of the present results with existing published studies has validated the accuracy of the numerical solutions. Graphical representation of different magnetic parameters has caused the increment in both temperature and nanoparticles concentration profiles. On the other hand, enhancement of Brownian motion has intensified the temperature but declined the nanoparticles concentration.

Effects of Variable Viscosity and Thermal conductivity on Natural-Convection of Nanofluids Past a Vertical Plate in Porous Media

2013 ◽  
Vol 30 (3) ◽  
pp. 265-275 ◽  
Author(s):  
A. Noghrehabadi ◽  
M. Ghalambaz ◽  
A. Ghanbarzadeh
Keyword(s):  
Thermal Conductivity ◽  
Brownian Motion ◽  
Natural Convection ◽  
Differential Equations ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Increase With Increase ◽  
Dimensional Parameters ◽  
Brownian Motion And Thermophoresis

ABSTRACTThe effects of variable viscosity and thermal conductivity on the natural convection heat transfer over a vertical plate embedded in a porous medium saturated by a nanofluid are investigated. In the nanofluid model, a gradient of nanoparticles concentration because of Brownian motion and thermophoresis forces is taken into account. The nanofluid viscosity and the thermal conductivity are assumed as a function of local nanoparticles volume fraction. The appropriate similarity variables are used to convert the governing partial differential equations into a set of highly coupled nonlinear ordinary differential equations, and then, they numerically solved using the Runge-Kutta-Fehlberg method. The practical range of non- dimensional parameters is discussed. The results show that the range of Lewis number as well as Brownian motion and thermophoresis parameters which were used in previous studies should be reconsidered. The effect of non-dimensional parameters on the boundary layer is examined. The results show that the reduced Nusselt number would increase with increase of viscosity parameter and would decrease with increase of thermal conductivity parameter.

Second Law Analysis of Heat and Mass Transfer of Nanofluids Along a Plate With Prescribed Surface Heat Flux

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Waqar A. Khan ◽  
Richard Culham ◽  
A. Aziz
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Entropy Generation Rate ◽  
Second Law ◽  
Second Law Analysis ◽  
Brownian Motion And Thermophoresis

A model based on the works of Buongiorno, which includes the effects of Brownian motion and thermophoresis, is used to develop the governing equations for convection in nanofluids. The analysis includes examples with water and ethylene glycol as the base fluids and nanoparticles of Cu and Al2O3. An assumption of zero nanoparticle flux is used at the surface of the plate to make the model more physically realistic. The model accounts for the effects of both Brownian motion and thermophoresis in the mass boundary condition. Using suitable transformations, the governing partial differential equations are converted into ordinary differential equations which are solved numerically. The dimensionless velocity, temperature, and concentration gradients are used in the second law analysis to determine heat and mass transfer rates. It is shown that the dimensionless entropy generation rate strongly depends upon the solid volume fraction of the nanoparticles, local Reynolds number, and group parameters.

Exponentially Stretching Sheet in a Powell–Eyring Fluid: Numerical and Series Solutions

2013 ◽  
Vol 68 (12) ◽  
pp. 791-798 ◽  
Author(s):  
Ammar Mushtaq ◽  
Meraj Mustafa ◽  
Tasawar Hayat ◽  
Mahmood Rahi ◽  
Ahmed Alsaedi
Keyword(s):  
Boundary Layer ◽  
Thermal Boundary Layer ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Velocity Ratio ◽  
Exponentially Stretching Sheet ◽  
Viscoelastic Effects ◽  
Homotopy Analysis ◽  
Analytic Expressions ◽  
Exponentially Stretching

This work theoretically examines the flow and heat transfer characteristics due to an exponentially stretching sheet in a Powell-Eyring fluid. Governing partial differential equations are nondimensionalized and transformed into non-similar forms. Explicit analytic expressions of velocity and temperature functions are developed by homotopy analysis method (HAM). The Numerical solutions are obtained by using shooting method with fourth-order Runge-Kutta integration technique. The fields are influence appreciably with the variation of embedding parameters. We noticed that the velocity ratio has a dual behaviour on the momentum boundary layer. On the other hand the thermal boundary layer thins when the velocity ratio is increased. The results indicate a significant increase in the velocity and a decrease in thermal boundary layer thickness with an intensification in the viscoelastic effects.

Applications of fractional derivatives to nanofluids: exact and numerical solutions

2018 ◽  
Vol 13 (1) ◽  
pp. 2 ◽  
Author(s):  
Sidra Aman ◽  
Ilyas Khan ◽  
Zulkhibri Ismail ◽  
Mohd Zuki Salleh
Keyword(s):  
Nusselt Number ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Physical Processes ◽  
Carrier Fluid ◽  
Laplace Transform Technique ◽  
Classical Models ◽  
Nanoparticles Volume Fraction ◽  
Graphene Nanoparticles

In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt heat and mass transfer of nanofluids (sodium alginate (SA) carrier fluid with graphene nanoparticles) are tackled using fractional derivative approach. Exact solutions are determined for temperature, concentration and velocity field, and Nusselt number via Laplace transform technique. The obtained solutions are then expressed in terms of wright function or its fractional derivatives. Numerical solutions for velocity, temperature, concentration and Nusselt number are obtained using finite difference scheme. It is found that these solutions are significantly controlled by the variations of parameters including thermal Grashof number, fractional parameter and nanoparticles volume fraction. It is observed that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters.

Numerical exploration of heat and mass transport for the flow of nanofluid subject to Hall and ion slip effects

2020 ◽  
Vol 16 (5) ◽  
pp. 951-965
Author(s):  
Rahila Naz ◽  
Muhammad Sohail ◽  
T. Hayat
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Content Type ◽  
Electrically Conducting ◽  
Analytical And Numerical Solutions ◽  
Heating Effects ◽  
Slip Effects ◽  
Layer Analysis ◽  
Homotopy Analysis ◽  
Ion Slip

PurposeThis paper addresses the three-dimensional flow of viscous nanofluid bounded by two plates. The lower plate stretches while the upper plate remains stationary. The fluid is electrically conducting in the presence of an applied magnetic field. In addition, the Hall, ion slip and Joule heating effects are retained. Governing equations for the considered physical happening are modeled under the phenomenon of boundary layer analysis.Design/methodology/approachBoth analytical and numerical solutions for the resulting nonlinear system are derived. Numerical solutions have been presented by using bvp4c and NDSolve techniques. The homotopy analysis method is utilized for the development of convergent analytical solutions. A comparative study for the presented solutions is made. An excellent agreement between analytical and numerical solutions is noticed.FindingsThe dimensionless velocities, temperature and concentration are examined physically by two-dimensional plots, stream plot and tabular values. It is observed that Hall and ion slip parameters reduce the velocity field and temperature profile increases for the mounting values of the Eckert number.Originality/valueThis manuscript contains the novel contents which comprise the Hall and ion slip effects for the transportation of heat and mass for the flow of viscous nanofluid.

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