Analytical solution of convective heat transfer of a quiescent fluid over a nonlinearly stretching surface using Homotopy Analysis Method

Kazemi, Mohammad; Jafari, Seyed Sajad; Musavi, Seyed Mohammad; Nejati, M.

doi:10.1016/j.rinp.2018.05.036

Cited by 13 publications

(9 citation statements)

References 26 publications

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“…In this study, we assume that the surface velocity condition is in the power-law form with an exponent of 1/3. This surface velocity condition is considered by several researchers such as Bataller (2008); Cortell (2011Cortell ( , 2014; Ferdows et al (2013); Rashidi et al (2014); Raju et al (2015) and Kazemi et al (2018).…”

Section: Hff 299mentioning

confidence: 99%

“…Here, u and v are the velocity components of the hybrid nanofluid along x-and y-axes, T is the temperature of the hybrid nanofluid, l is the constant stretching (l > 0), shrinking (l < 0) or static (l = 0) surface and q r is the radiative heat flux. Using Roselland (1931) approximation, the radiative heat flux is simply expressed as follows (Cortell, 2011;Magyari and Pantokratoras, 2011;Kazemi et al, 2018):…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The governing equations of the conservations of the hybrid nanofluid mass, momentum and energy by using the usual boundary layer approximations are written as (Tiwari and Das, 2007; Cortell, 2011; Kazemi et al , 2018): …”

Section: Mathematical Modelmentioning

confidence: 99%

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Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

Waini

Ishak

Pop

2019

HFF

158

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Purpose This paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation. Design/methodology/approach The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed. Findings Results found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches. Originality/value The problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

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Section: Hff 299mentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

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Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

Waini

Ishak

Pop

2019

HFF

158

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“…The governing equations are subject to the assumption of slender boundary layer, which holds true for the case of a high Reynolds number. Under these assumptions, the governing conservation equations of mass, momentum and energy can be expressed in Cartesian coordinates (x, y) (see Kazemi et al [19] and Devi and Devi [20]):…”

Section: Mathematical Modelmentioning

confidence: 99%

Convective Heat Transfer of a Hybrid Nanofluid over a Nonlinearly Stretching Surface with Radiation Effect

Aly

Roşca

et al. 2021

Mathematics

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The flow of the hybrid nanofluid (copper–titanium dioxide/water) over a nonlinearly stretching surface was studied with suction and radiation effect. The governing partial differential equations were then converted into non-linear ordinary differential equations by using proper similarity transformations. Therefore, these equations were solved by applying a numerical technique, namely Chebyshev pseudo spectral differentiation matrix. The results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that the rising of the mass flux parameter slows down the velocity and, hence, decreases the temperature. Further, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, it was mentioned that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases.

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“…Brownian motion and thermophoresis are accounted. Analytical and numerical solutions are constructed and compared by homotopy analysis (Sheikholeslami et al, 2018;Liao, 2003;Mustafa et al, 2014Mustafa et al, , 2017Animasaun et al, 2016;Nawaz et al, 2018;Abbasbandy et al, 2014;Awais et al, 2018;Hayat et al, 2015Hayat et al, , 2017aHayat et al, , b, 2018bKhan et al, 2018b;Kazemi et al, 2018;Kasmani et al, 2017), bvp4c and NDSolve techniques. Outcome of influential variables through graphs and tables is also examined in the current exploration.…”

Section: Introductionmentioning

confidence: 99%

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

Naz

Sohail

Hayat

2020

MMMS

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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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Analytical solution of convective heat transfer of a quiescent fluid over a nonlinearly stretching surface using Homotopy Analysis Method

Cited by 13 publications

References 26 publications

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

Convective Heat Transfer of a Hybrid Nanofluid over a Nonlinearly Stretching Surface with Radiation Effect

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

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