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Research Papers: Heat and Mass Transfer

Thermal Diffusion and Diffusion Thermo Effects on Peristaltic Flow of Sisko Fluid in Nonuniform Channel With Dissipative Heating

[+] Author and Article Information
Obaid Ullah Mehmood

e-mail: obaid.mahmood@yahoo.com

Norzieha Mustapha

Department of Mathematical Sciences,
Faculty of Science,
Universiti Teknologi Malaysia,
81310 UTM Johor,
Johor Bahru, Johor, Malaysia

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 12, 2012; final manuscript received June 6, 2013; published online October 14, 2013. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 135(12), 122004 (Oct 14, 2013) (9 pages) Paper No: HT-12-1556; doi: 10.1115/1.4024839 History: Received October 12, 2012; Revised June 06, 2013

This investigation deals with thermal diffusion and diffusion thermo effects on the peristaltic flow of a Sisko fluid in an asymmetric channel. The mode of dissipative heat transfer is taken into account with nonuniform wall temperatures. Long wavelength approximation is utilized. Solutions for the highly nonlinear coupled governing equations involving power law index as an exponent are derived by employing the perturbation technique in a Sisko fluid parameter. Closed form solutions for the stream function, the axial pressure gradient, the skin friction, the temperature, the concentration, and the Nusselt number are presented. Effects of various interesting parameters are graphically interpreted. A comparative study between Newtonian, shear thinning, and shear thickening fluids is also presented. Comparison with published results for the case of viscous fluid is observed in good agreement.

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Figures

Grahic Jump Location
Fig. 1

Sketch of the physical model

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Fig. 2

Temperature η for a = 0.7,b = 1.2,d = 2,φ = 0,θ = 1.5,x = π/2,Pr = 1,Sc = 1,Sr = 1,(a) bs = 0.2,Br = 5,Df = 1,____shearthinning fluid, _ _ _Newtonian fluid, ._._.shear thickening fluid,(b) bs = 0.01, n = 2, Df = 1,____Br = 0,_ _ _Br = 2,...Br = 4, ._._. Br = 6,(c) Br = 5, n = 0, Df = 1, ____bs = 0.0,_ _ _bs = 0.1,...bs = 0.2,._._.bs = 0.3,and (d) bs = 0.01,n = 2,Br = 5, ____Df = 0, _ _ _Df = 1, ...Df = 2,._._.Df = 3

Grahic Jump Location
Fig. 3

Concentration ϕ for a = 0.7, b = 1.2, d = 2, φ = 0, θ = 1.5, x = π/2, Br = 5, Pr = 1, Sc = 1,(a) bs = 0.3,Sr = 5,Df = 1,____shear thinning fluid, _ _ _Newtonian fluid, ._._.shear thickening fluid, (b) bs = 0.01, n = 2, Df = 1, ____Sr = 0, _ _ _Sr = 1, ...Sr = 2,._._.Sr = 3,(c) Sr = 1,n = 0,Df = 1,____bs = 0.0,_ _ _bs = 0.1,...bs = 0.2,._._.bs = 0.3, and (d) bs = 0.01,n = 2, Sr = 1, ____Df = 0, _ _ _Df = 1,...Df = 2,._._.Df = 3

Grahic Jump Location
Fig. 4

Streamlines in symmetric channel for different bs (a) 0.0, (b) 0.1, and (c) 0.2 with fixed a = 0.5,b = 0.5,d = 1,φ = 0,n = 2,θ = 1.6

Grahic Jump Location
Fig. 5

Streamlines in asymmetric channel for different bs (a) 0.0, (b) 0.1, and (c) 0.2 with fixed a = 0.5,b = 0.5,d = 1,φ = π/4,θ = 1.6,n = 2

Grahic Jump Location
Fig. 6

(a) Nusselt number Nu against bs for a = 0.6,b = 1.2,d = 2,φ = 0,x = π,Br = 5,Sc = 1,Sr = 1,Df = 1,Pr = 1,θ = 1.3, (b) Nusselt number Nu against Br for a = 0.6,b = 1.2,d = 2, φ = 0,bs = 0.3,x = π,Sr = 1,Sc = 1, Df = 1,Pr = 1,θ = 1.3, (c) Nusselt number Nu against Df for a = 0.6,b = 1.2,d = 2,φ = 0,bs = 0.3,x = π,Sr = 1,Sc = 1,Br = 7,Pr = 1,θ = 1.3, and (d) Skin friction τ against bs for a = 0.5,b = 0.5, d = 1.2, φ = 0, x = π, θ = 1.8, (____shearthinning fluid,_ _ _Newtonian fluid,._ ._.shear thickening fluid)

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Fig. 7

Comparison of pressure rise Δpλ against flow rate θ with Mishra and Rao's results [22] when d = 2,a = 0.7,b = 1.2,bs = 0, and n = 1

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