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Research Papers: Forced Convection

Slip Effects on the Peristaltic Motion of Nanofluid in a Channel With Wall Properties

[+] Author and Article Information
M. Mustafa

Research Centre for Modeling and
Simulation (RCMS),
National University of Sciences and
Technology (NUST),
Sector H-12,
Islamabad 44000, Pakistan
e-mail: meraj_mm@hotmail.com

S. Hina

Department of Mathematical Sciences,
Fatima Jinnah Women University,
Rawalpindi 46000, Pakistan

T. Hayat

Department of Mathematics,
Quaid-I-Azam University 45320,
Islamabad 44000, Pakistan

A. Alsaedi

Department of Mathematics,
Faculty of Science,
King Abdulaziz University,
P.O. Box 80257,
Jeddah 21589, Saudi Arabia

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received February 28, 2012; final manuscript received July 4, 2012; published online March 20, 2013. Assoc. Editor: Darrell W. Pepper.

J. Heat Transfer 135(4), 041701 (Mar 20, 2013) (7 pages) Paper No: HT-12-1075; doi: 10.1115/1.4023038 History: Received February 28, 2012; Revised July 04, 2012

This article looks at the peristaltic flow of nanofluid in a channel with compliant walls. Brownian motion and thermophoresis effects are taken into consideration. Mathematical model is formulated by using long wavelength and low Reynolds number assumptions. The analytic expressions of temperature and nanoparticles concentration are developed by homotopy analysis method (HAM). The solutions are validated through the numerical solutions obtained by employing the built in routine for solving nonlinear boundary value problem via shooting method through software mathematica. Special emphasis is given to the role of key parameters including the Brownian motion parameter (Nb), thermophoresis parameter (Nt), Prandtl number (Pr), Eckert number (Ec) on temperature, and nanoparticles concentration. It is observed that both temperature and nanoparticles volume fraction increase when the Brownian motion and thermophoresis effects intensify. Moreover, the heat transfer coefficient is increasing function of Nb and Nt.

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Figures

Grahic Jump Location
Fig. 1

ℏ-curves for the functions θ and φ when x = ε = 0.2,t = 0.1, E1 = 0.01, E2 = 0.02, E3 = 0.01, Nb = Nt = 0.1, β1 = 0.1, β2 =β3 = 0.5 and Pr = Ec = 1

Grahic Jump Location
Fig. 5

Influence of different parameters on Z(x). (a) ε = 0.2,t = 0.1,E1 = 0.01,E2 = 0.02,E3 = 0.01,Nb = Nt = 0.1,β1 = β2 = β3 = 0.1; (b) ε = 0.2,t = 0.1,E1 = 0.01,E2 = 0.02,E3 = 0.01,β1 = β2 = β3 = 0.1,Pr = 1; (c) ε = 0.2,t = 0.1,E1 = E2 = 0.1,E3 = 0.01,Nb = Nt = 0.1,β1 = β2 = β3 = 0.1; (d) ε = 0.2,t = 0.1,E1 = E2 = 0.1,E3 = 0.01,β1 = β2 = β3 = 0.1,Pr = 1; (e) t = 0.1,E1 = E2 = 0.1,E3 = 0.01,Nb = Nt = 0.1,β1 = β2 = β3 = 0.1,Pr = 1.

Grahic Jump Location
Fig. 4

Nanoparticles' concentration profiles for different values of parameters. (a) x = ε = 0.2,t = 0.1,Nb = Nt = 0.1,β1 = β2 = β3 = 0.1,Pr = Ec = 1; (b) x = ε = 0.2,t = 0.1,E1 = 0.01,E2 = 0.02,E3 = 0.01,Nt = 0.1,β1 = β2 = β3 = 0.1,Pr = Ec = 1; (c) x = 0.2,t = 0.1,E1 = 0.01,E2 = 0.02,E3 = 0.01,Nb = Nt = 0.1,β1 = β2 = β3 = 0.1,Pr = Ec = 1; (d) x = 0.2,t = 0.1,E1 = E2 = 0.05,E3 = 0.01,Nb = Nt = 0.1,β1 = β3 = 0.1,Pr = Ec = 1.

Grahic Jump Location
Fig. 3

Temperature profiles for different values of parameters. (a) x = ε = 0.2,t = 0.1,E1 = 0.01,E2 = 0.02,E3 = 0.01,β1 = β2 = β3 = 0.1,Pr = Ec = 1; (b) x = ε = 0.2,t = 0.1,E1 = 0.01,E2 = 0.02,E3 = 0.01,Nb = Nt = 0.1,β1 = β2 = β3 = 0.1,Ec = 1; (c) x = ε = 0.2,t = 0.1,E1 = 0.01,E2 = 0.02,E3 = 0.01,Nb = Nt = 0.1,β1 = β2 = β3 = 0.1,Pr = Ec = 1; (d) x = ε = 0.2,t = 0.1,Nb = Nt = 0.1,β1 = β2 = β3 = 0.1,Pr = Ec = 1; (e) x = 0.2,t = 0.1,E1 = 0.01,E2 = 0.02,E3 = 0.01,Nb = Nt = 0.1,β1 = β2 = β3 = 0.1,Pr = Ec = 1; (f) x = 0.2,t = 0.1,E1 = E2 = 0.05,E3 = 0.01,Nb = Nt = 0.1,β1 = β3 = 0.1,Pr = Ec = 1.

Grahic Jump Location
Fig. 2

Comparison of numerical and analytic solutions when x = ε = 0.2,t = 0.1,E1 = 0.01,E2 = 0.02,E3 = 0.01,Nb = Nt = 0.1,β1 =β2 = β3 = 0.1 and Pr = Ec = 1. Points: numerical solutions; lines: homotopy solutions at tenth-order approximations with ℏθ=ℏφ=−1.

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