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Research Papers: Forced Convection

Magnetohydrodynamic Boundary Layer Flow and Heat Transfer of a Nanofluid Over Non-Isothermal Stretching Sheet

[+] Author and Article Information
Wubshet Ibrahim

Department of Mathematics,
Ambo University,
Ambo, Ethiopia
e-mail: wubshetib@yahoo.com

B. Shanker

Professor
Department of Mathematics,
Osmania University,
Hyderabad 7, India
e-mail: bandarishanker@yahoo.co.in

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 27, 2012; final manuscript received November 15, 2013; published online February 26, 2014. Assoc. Editor: He-Ping Tan.

J. Heat Transfer 136(5), 051701 (Feb 26, 2014) (9 pages) Paper No: HT-12-1599; doi: 10.1115/1.4026118 History: Received October 27, 2012; Revised November 15, 2013

The boundary-layer flow and heat transfer over a non-isothermal stretching sheet in a nanofluid with the effect of magnetic field and thermal radiation have been investigated. The transport equations used for the analysis include the effect of Brownian motion and thermophoresis. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., thermal radiation parameter R, Prandtl number Pr, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order nonlinear ordinary differential equations. These equations were numerically solved using a fourth-order Runge–Kutta method with shooting technique. The analysis has been carried out for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF) to see the effects of governing parameters for various physical conditions. Numerical results are obtained for distribution of velocity, temperature and concentration, for both cases i.e., prescribed surface temperature and prescribed heat flux, as well as local Nusselt number and Sherwood number. The results indicate that the local Nusselt number decreases with an increase in both Brownian motion parameter Nb and thermophoresis parameter Nt. However, the local Sherwood number increases with an increase in both thermophoresis parameter Nt and Lewis number Le. Besides, it is found that the surface temperature increases with an increase in the Lewis number Le for prescribed heat flux case. A comparison with the previous studies available in the literature has been done and we found an excellent agreement with it.

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Figures

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Fig. 1

Flow configuration and coordinate system

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Fig. 12

Temperature graph for different values of s when Nb = Nt = 0.2, Le = 5, s = R = M = Pr = 1, for PHF case

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Fig. 11

Temperature graph for different values of Pr when Nb = Nt = 0.2, Le = 5, s = 1, R = 0.5, M = 1, for PHF case

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Fig. 10

Concentration graph for different values of Nt when R = 1, Pr = 2, Nb = 0.5, M = 1, Le = 5, n = 1

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Fig. 9

Concentration graph for different values of Nb when Nt = 0.5, Le = 5, M = 1, Pr = 2, n = 1, and R = 1

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Fig. 8

Concentration graph for different values of Le when R = 1, n = 1, Pr = 2, Nt = Nb = 0.5, and M = 1

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Fig. 7

Temperature graph for different values of M when Nb = Nt = 0.5, Le = 5, R = 1, Pr = 2, and n = 1

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Fig. 6

Temperature graph for different values of Nb = Nt when R = M = 1, Pr = 2, Le = 5, and n = 1

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Fig. 5

Temperature graph for different values of Radiation parameter R when Nt = Nb = 0.5, M = 1, Pr = 2, Le = 5, and n = 1

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Fig. 4

Temperature graph for different values of Pr when Nb = Nt = 0.5, Le = 5, R = 1, M = 1, and n = 1

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Fig. 3

Temperature graph for different values of n when Nb = Nt = 0.5, Le = 5, Pr = 5, M = 1, and R = 1

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Fig. 13

Temperature graph for different values of M when Nb = Nt = 0.2, Le = 5, s = 0.5, R = Pr = 1 for PHF case

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Fig. 14

Temperature graph for different values of R when Nb = Nt = 0.2, Le = 5, s = 0.5, M = Pr = 1 for PHF case

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Fig. 15

Concentration graph for different values of Le when Nb = Nt = 0.2, R = 1, s = 0.5, M = 1, Pr = 1 for PHF case

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Fig. 16

Concentration graph for different values of Nt when Nb = 0.2, R = 1, s = 1, M = 1, Pr = 1, Le = 5 for PHF case

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Fig. 17

Variation of −θ′(0) with Nt for different values of Nb when Le = 10, Pr = 1

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Fig. 18

Variation of −h′(0) with Nt for different values of Nb when Le = 5, Pr = 5

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Fig. 2

Velocity graph for different values of M when Nb = Nt = 0.5, Le = 5, R = 1, and Pr = 2

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