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Fundamental Issues and Canonical Flows

Boundary-Layer Flow and Heat Transfer of Nanofluid Over a Vertical Plate With Convective Surface Boundary Condition

[+] Author and Article Information
Wubshet Ibrahim1

Department of Mathematics, Osmania University, Hyderabad 7, Indiawubshetib@yahoo.com

Bandari Shanker

Department of Mathematics, Osmania University, Hyderabad 7, Indiabandarishanker@yahoo.co.in

1

Corresponding author.

J. Fluids Eng 134(8), 081203 (Jul 27, 2012) (8 pages) doi:10.1115/1.4007075 History: Received April 18, 2012; Revised July 02, 2012; Published July 27, 2012; Online July 27, 2012

Abstract

The problem of boundary layer flow and heat transfer induced due to nanofluid over a vertical plate is investigated. The transport equations employed in the analysis include the effect of Brownian motion and thermophoresis. We used a convective heating boundary condition instead of a widely employed thermal conduction of constant temperature or constant heat flux. The solution for the temperature and nanoparticle concentration depends on six parameters, viz., convective heating parameter A, Prandtl number Pr, Lewis number Le, Brownian motion Nb, buoyancy ratio parameter Nr, and the thermophoresis parameter Nt. Similarity transformation is used to convert the governing nonlinear boundary-layer equations into coupled higher order ordinary differential equations. These equations were solved numerically using Runge-Kutta fourth order method with shooting technique. The effects of the governing parameters on flow field and heat transfer characteristics were obtained and discussed. Numerical results are obtained for velocity, temperature, and concentration distribution as well as the local Nusselt number and Sherwood number. It is found that the local Nusselt number and Sherwood number increase with an increase in convective parameter A and Lewis number Le. Likewise, the local Sherwood number increases with an increase in both A and Le. A comparison with the previous study available in literature has been done and we found an excellent agreement with them.

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Figures Figure 6

Temperature profile graph for different values of Pr when Nb=Nt=Nr=0.5, Le=10, A=1 Figure 7

Temperature profile for different values of Nb when Le=10, A=0.5, Pr=1, Nt=Nr=0.5 Figure 8

Temperature profile for different values of Nt when A=1, Pr=1, Nb=1, Nr=0.5, Le=10 Figure 9

Concentration profile graph for different values of Nb when Nr=Nt=0.5, Le=2, A=1, Pr=2 Figure 10

Concentration profile graph for different values of Le when A=1, Pr=2, Nb=Nt=Nr=0.5 Figure 11

Concentration profile graph for different values of Nt when Nb=Nt=0.5, Le=2, Pr=2, A=1 Figure 12

Concentration profile graph for different values of Nr when Nb=Nt=0.9, Le=2, Pr=2, A=1 Figure 1

Flow configuration and coordinate system Figure 2

Velocity profile graph for different values of Nr when Nb=Nt=0.5, Le=1, Pr=10, A=1 Figure 3

Velocity profile graph for different values of Pr when Nr=Nb=Nt=0.5, Le=10, A=1 Figure 4

Temperature profile graph for different values of A when Nr=Nb=Nt=0.5, Le=1, Pr=1 Figure 5

Temperature profile graph for different values of Le when A=1, Nt=Nb=Nr=0.5, Pr=1

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