Series solutions of non-Newtonian nanofluids with Reynolds’ model and Vogel’s model by means of the homotopy analysis method

Ellahi, R.; Raza, Mohsin; Vafai, Kambiz

doi:10.1016/j.mcm.2011.11.043

Cited by 221 publications

(105 citation statements)

References 21 publications

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“…It is also observed that the nanofluid can reform at rest. Ellahi et al (2012) studied analytically using a homotopy method, the fully-developed flow of an incompressible, thermodynamically-compatible non-Newtonian third-grade nanofluid in coaxial cylinders, employing the Reynolds and Vogel variable viscosity models. Akbar and Nadeem (2013) implemented the Eyring-Prandtl rheological fluid model to study peristaltic nanofluid transport in a diverging tube.…”

mentioning

confidence: 99%

Group analysis and numerical computation of magneto-convective non-Newtonian nanofluid slip flow from a permeable stretching sheet

Uddin

Ferdows

Bég³

2013

Appl Nanosci

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Two-dimensional magnetohydrodynamic boundary layer flow of non-Newtonian power-law nanofluids past a linearly stretching sheet with a linear hydrodynamic slip boundary condition is investigated numerically. The non-Newtonian nanofluid model incorporates the effects of Brownian motion and thermophoresis. Similarity transformations and corresponding similarity equations of the transport equations are derived via a linear group of transformations. The transformed equations are solved numerically using Runge-Kutta-Fehlberg fourth-fifth order numerical method available in the Maple 14 software for the influence of power-law (rheological) index, Lewis number, Prandtl number, thermophoresis parameter, Brownian motion parameter, magnetic field parameter and linear momentum slip parameter. Validation is achieved with an optimized Nakamura implicit finite difference algorithm (NANO-NAK). Representative results for the dimensionless axial velocity, temperature and concentration profiles have been presented graphically. The present results of skin friction factor and reduced heat transfer rate are also compared with the published results for several special cases of the model and found to be in close agreement. The study has applications in electromagnetic nanomaterials processing.

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mentioning

confidence: 99%

Group analysis and numerical computation of magneto-convective non-Newtonian nanofluid slip flow from a permeable stretching sheet

Uddin

Ferdows

Bég³

2013

Appl Nanosci

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“…The Reynold's model viscosity is defined as [5]                      …”

Section: Reynold's Viscosity Modelmentioning

confidence: 99%

“…Nadeem et al [4] gives the theoretical analysis of Cu-blood nanofluid in a curved channel. Ellahi et al [5] discussed series solutions of non-Newtonian nanofluids with Reynolds'model and Vogel's model by using the homotopy analysis method. A large number of papers are presented which deal with the study of nanofluid and its uses [6][7][8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Hypothetical analysis for peristaltic transport of metallic nanoparticles in an inclined annulus with variable viscosity

Nadeem¹,

Sadaf²

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The main objective of this article is to present a mathematical model for peristaltic transport in an inclined annulus. In this analysis, two-dimensional flow of a viscous nanofluid is observed in an inclined annulus with variable viscosity. Copper as nanoparticle with blood as its base fluid has been considered. The inner tube is unifom or rigid, while the outer tube takes a sinusoidal wave. Governing equations are solved under the well-known assumptions of low Reynolds number and long-wavelength. Exact solutions have been established for both velocity and nanoparticle temperature. The features of the peristaltic motion are explored by plotting graphs and discussed in detail. Nevertheless, no effort has been made yet to discuss the peristaltic motion through an inclined annulus with nano particles. The main goal of this analysis is to study the fluid motion in an inclined annulus with peristaltic walls. The problem is first modeled and then exact solution is calculated for the resultant equation. The results for velocity profile, pressure gradient, pressure rise and stream function have been depicted for several values of the parameters. Numerical results for velocity profile are also presented (see Table 1). Mathematical modelWe have considered the peristaltic motion for the two dimensional flow of an incompressible viscous nanofluid in an inclined annulus. The equations for conservation of mass and momentum can be written as

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“…In the recent years, boundary layer flow of non-Newtonian fluids over a stretching surface has received special attention from the researchers (Ellahi et al 2012;Nadeem et al, 2014;Bose et al, 2015;Akbar et al, 2016;Sahoo, 2010). This is because of their advanced industrial, engineering science and technological applications such as glass fibber, wire drawing, paper production, extrusion of plastic sheet, hot rolling, drawing of plastic films and many others.…”

Section: Introductionmentioning

confidence: 99%

Soret and Dufour Effects on MHD Radiative Heat and Mass Transfer Flow of a Jeffrey Fluid Over a Stretching Sheet

Narayana¹,

Babu²,

Venkateswarlu³

2017

Frontiers in Heat and Mass Transfer

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This paper studies the combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) on magnetohydrodynamics (MHD) boundary layer flow of a Jeffrey fluid past a stretching surface with chemical reaction and heat source. Using the similarity transformations, the governing equations are transformed into a set of non-linear ordinary differential equations (ODE's). The resulting equations are then solved numerically by using the shooting method along with Runge-Kutta fourth order integration scheme. Numerical results for the velocity, temperature and concentration distributions as well as the skin-friction coefficient, Nusselt number and Sherwood number are discussed in detail and displayed graphically for various physical parameters. The results indicate that the influence of Soret and Dufour numbers are significantly active in the study of nonNewtonian fluid flows. The accuracy of the numerical method is tested by comparing with previously published work as a limiting case (for viscous flow) and the results are found to be in excellent agreement.

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Series solutions of non-Newtonian nanofluids with Reynolds’ model and Vogel’s model by means of the homotopy analysis method

Cited by 221 publications

References 21 publications

Group analysis and numerical computation of magneto-convective non-Newtonian nanofluid slip flow from a permeable stretching sheet

Group analysis and numerical computation of magneto-convective non-Newtonian nanofluid slip flow from a permeable stretching sheet

Hypothetical analysis for peristaltic transport of metallic nanoparticles in an inclined annulus with variable viscosity

Soret and Dufour Effects on MHD Radiative Heat and Mass Transfer Flow of a Jeffrey Fluid Over a Stretching Sheet

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