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Research Papers

Viscous and Joule Heating in the Stagnation Point Nanofluid Flow Through a Stretching Sheet With Homogenous–Heterogeneous Reactions and Nonlinear Convection

[+] Author and Article Information
R. Nandkeolyar

School of Mathematics, Statistics,
and Computer Science,
University of KwaZulu-Natal,
Private Bag X01, Scottsville 3209,
Pietermaritzburg, South Africa
e-mail: rajnandkeolyar@gmail.com

S. S. Motsa

School of Mathematics, Statistics,
and Computer Science,
University of KwaZulu-Natal,
Private Bag X01, Scottsville 3209,
Pietermaritzburg, South Africa
e-mail: sandilemotsa@gmail.com

P. Sibanda

School of Mathematics, Statistics,
and Computer Science,
University of KwaZulu-Natal,
Private Bag X01, Scottsville 3209,
Pietermaritzburg, South Africa
e-mail: sibandap@ukzn.ac.za

1Corresponding author.

Manuscript received November 5, 2013; final manuscript received April 9, 2014; published online May 2, 2014. Assoc. Editor: Malisa Sarntinoranont.

J. Nanotechnol. Eng. Med 4(4), 041002 (May 02, 2014) (9 pages) Paper No: NANO-13-1082; doi: 10.1115/1.4027435 History: Received November 05, 2013; Revised April 09, 2014

The combined effects of viscous and Joule heating on the stagnation point flow of a nanofluid through a stretching/shrinking sheet in the presence of homogeneous–heterogeneous reactions are investigated. The nanoparticle volume fraction model is used to describe the nanofluid. In this study, the density temperature relation is nonlinear which causes a nonlinear convective heat transfer. The surface of the sheet is assumed to be convectively heated with a hot fluid. The governing nonlinear differential equations are solved using the successive linearization method (SLM), and the results are validated by comparison with numerical approximations obtained using the Matlab in-built boundary value problem solver bvp4c and with existing results in literature. The nanofluid problem finds applications in heat transfer devices where the density and temperature relations are complex and the viscosity of the fluid has significant effect on the heat transfer rate.

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Figures

Grahic Jump Location
Fig. 1

Physical model of the problem

Grahic Jump Location
Fig. 5

Effect of Eckert number Ec on (a) f′, (b) θ, and (c) g when M = 2, λ = 1, ϕ = 0.2, Bi = 5, ɛ=2, Sc = 1, K = 0.5, Ks = 0.5, and α = 0.2

Grahic Jump Location
Fig. 4

Effect of NDT parameter α on (a) f′, (b) θ, and (c) g when M = 2, λ = 1, ϕ = 0.2, Bi = 5, ɛ=2, Sc = 1, K = 0.5, Ks = 0.5, and Ec = 0.1

Grahic Jump Location
Fig. 3

Effect of nanoparticle volume fraction ϕ on (a) f′, (b) θ, and (c) g when M = 2, λ = 1, α = 0.2, Bi = 5, ɛ=2, Sc = 1, K = 0.5, Ks = 0.5, and Ec = 0.1

Grahic Jump Location
Fig. 2

Effect of magnetic parameter M on (a) f′, (b) θ, and (c) g when ϕ = 0.2, λ = 1, α = 0.2, Bi = 5, ɛ=2, Sc = 1, K = 0.5, Ks = 0.5, and Ec = 0.1

Grahic Jump Location
Fig. 6

Effect of Biot number Bi on (a) f′, (b) θ, and (c) g when M = 2, λ = 1, ϕ = 0.2, Ec = 0.1, ɛ=2, Sc = 1, K = 0.5, Ks = 0.5, and α = 0.2

Grahic Jump Location
Fig. 7

Effect of stretching parameter ɛ on (a) f′, (b) θ, and (c) g when M = 2, λ = 1, ϕ = 0.2, Ec = 0.1, Bi = 5, Sc = 1, K = 0.5, Ks = 0.5, and α = 0.2

Grahic Jump Location
Fig. 8

Effect of homogeneous reaction parameter K and heterogeneous reaction parameter Ks on (a) and (b) g and (c) g(0) when M = 2, λ = 1, ϕ = 0.2, Ec = 0.1, Bi = 5, Sc = 1, ɛ = 2, and α = 0.2

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