Simultaneous Impacts of Fe3O4 Particles and Thermal Radiation on Natural Convection of Non-Newtonian Flow Between Two Vertical Flat Plates Using ADM

Ameur Gabli; Mohamed Kezzar; Lilia Zighed; Mohamed Rafik Sari; Ismail Tabet

doi:10.1515/jnet-2019-0083

Published by De Gruyter March 24, 2020

Simultaneous Impacts of Fe3O4 Particles and Thermal Radiation on Natural Convection of Non-Newtonian Flow Between Two Vertical Flat Plates Using ADM

Ameur Gabli , Mohamed Kezzar , Lilia Zighed , Mohamed Rafik Sari and Ismail Tabet

From the journal Journal of Non-Equilibrium Thermodynamics

https://doi.org/10.1515/jnet-2019-0083

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Abstract

The main aim of this research work is to show the simultaneous effects of ferro-particles (Fe3O4) and thermal radiation on the natural convection of non-Newtonian nanofluid flow between two vertical flat plates. The studied nanofluid is created by dispersing ferro-particles (Fe3O4) in sodium alginate (SA), which is considered as a non-Newtonian base fluid. Resolution of the resulting set of coupled non-linear second order differential equations characterizing dynamic and thermal distributions (velocity/temperature) is ensured via the Adomian decomposition method (ADM). Thereafter the obtained ADM results are compared to the Runge–Kutta–Feldberg based shooting data. In this investigation, a parametric study was conducted showing the influence of varying physical parameters, such as volumic fraction of Fe3O4 nanoparticles, Eckert number (Ec) and thermal radiation parameter (N), on the velocity distribution, the skin friction coefficient, the heat transfer rate and the temperature distribution. Results obtained also show the advantages of ferro-particles over other types of standard nanoparticles. On the other hand, this investigation demonstrates the accuracy of the adopted analytical ADM technique.

Keywords: Fe3O4 particles; natural or free convection; velocity; temperature; nanofluid; thermal radiation; Adomian decomposition method (ADM)

Appendix A

In this appendix, we present the first terms of solution for velocity and temperature fields.

(A.1)Velocity:V1=−c2η2−d6η3V2=0.041A3(1−φ)2.5b2EcPrη4+0.083A3(1−φ)2.5b4EcPrδη4(1.−φ)2.5+3.(1−φ)2.5b2cδη2(1.−φ)5.+1.(1−φ)2.5b2dδη3(1.−φ)5.V3=1(1−ψ)2.5[−0.016A3bcEcPrη5−0.0027A3bdEcPrη6−0.25A3b4EcPrδη4(1.−1.ψ)2.5+0.001A3c4EcPrδη8(1.−1.ψ)2.5+……⋮⋮V=−c2η2−d6η3+0.041A3(1−φ)2.5b2EcPrη4+0.083A3(1−φ)2.5b4EcPrδη4(1.−φ)2.5+……

(A.2)Temperature:θ1=12A3b2EcPrη2(−2b2δ−1(1−φ)2.5)θ2=0.33A3(1−φ)2.5bcEcPrη3+0.083A3(1−φ)2.5bdEcPrη4+0.66A3(1−φ)2.5cNη2(1.−φ)2.5+0.22A3dNη3−0.066A3(1−φ)2.5c4EcPrδη6(1.−φ)2.5−0.095A3(1−φ)2.5c3dEcPrδη7(1.−φ)2.5−0.053A3(1−φ)2.5c2d2EcPrδη8(1.−φ)2.5−0.0138A3(1−φ)2.5cd3EcPrδη9(1.−φ)2.5−0.00138A3d4EcPrδη10θ3=1(1−ψ)17.5[0.000008A35b8Ec5Pr5δη14(1.−1.ψ)7.5−0.00006A35b10Ec5Pr5δ2η14(1.−1.ψ)10.−0.016A32b3Ec2Pr2η5(1.−1.ψ)12.5−……⋮⋮θ=12A3b2EcPrη2(−2b2δ−1(1−φ)2.5)+0.33A3(1−φ)2.5bcEcPrη3+0.083A3(1−φ)2.5bdEcPrη4+……

Nomenclature

a, b, c and d: Constants
2b: Distance between the plates [m]
A1,…,A4: Constants
F: Dimensionless velocity
θ: Dimensionless temperature
qw: Heat flux
qr: Radiative heat flux [Wm2]
Pr: Prandtl number
Ec: Eckert number
l: Distance [m]
x,y: Coordinates [m]
u,v: Velocity components [ms−1]
T: Temperature [K]
T1 and T2: Temperatures [K]
η: Similarity variable
ρf: Fluid density [kgm−3]
ρs: Nanoparticle density [kgm−3]
ρnf: Nanofluid density [kgm−3]
μnf: Dynamic viscosity of nanofluid [m2s−1]
k: Stefan Boltzmann constant
kf: Thermal conductivity of base fluid [Wm−1K−1]
ks: Thermal conductivity of nanoparticles [Wm−1K−1]
knf: Thermal conductivity of nanofluid [Wm−1K−1]
cf: Heat capacity of base fluid [Jkg−1K−1]
cs: Heat capacity of nanoparticles [Jkg−1K−1]
cnf: Heat capacity of nanofluid [Jkg−1K−1]
σ∗: Absorption coefficient [WmK−4]
δ: Dimensionless non-Newtonian viscosity
N: Thermal radiation

Subscripts

■nf: Nanofluid
■f: Base fluid
■s: Solid nanoparticles

Abbreviations

ADM: Adomian decomposition method
HAM: Homotopy analysis method
HPM: Homotopy perturbation method
DTM: Differential transform method
SA: Sodium Alginate

Correction added after online publication on 19 February 2020: Mistakenly this article was already published ahead of print with typo-mistakes in formulae (1), (2), (5) and (9). The corrected typo-mistakes do not affect simulations and results. In nomenclature the correct units of some symbols are:

Radiative heat flux [Wm−2]
Dynamic viscosity of nanofluid [Pa s]
Stefan Boltzmann constant [Wm−2K−4]
Absorption coefficient [m−1]

We thank professor Mohamed Rafik Sari for his help in finding these typo-mistakes.

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Received: 2019-10-18

Revised: 2020-01-26

Accepted: 2020-01-31

Published Online: 2020-03-24

Published in Print: 2020-04-26

Simultaneous Impacts of Fe3O4 Particles and Thermal Radiation on Natural Convection of Non-Newtonian Flow Between Two Vertical Flat Plates Using ADM

Abstract

Nomenclature

Subscripts

Abbreviations

References

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