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Thermal Properties of Couple-Stress Fluid Flow in an Asymmetric Channel With Peristalsis

[+] Author and Article Information
Y. Abd elmaboud

Mathematics Department,
Faculty of Science and Arts, Khulais,
King Abdulaziz University (KAU), Saudi Arabia;
Mathematics Department,
Faculty of Science,
Al-Azhar University (Assiut Branch),
Assiut 71524, Egypt

Kh. S. Mekheimer

Faculty of Science,
Mathematics & Statistic Department,
Taif University,
Hawia (888) Taif, Saudi Arabia;
Faculty of Science (Men),
Mathematical Department,
Al-Azhar University,
11884 Nasr City, Cairo, Egypt

A. I. Abdellateef

Basic Science Department,
Higher Institute of Engineering,
Shorouk City,
Cairo, Egypt

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received October 11, 2011; final manuscript received April 29, 2012; published online March 20, 2013. Assoc. Editor: Wei Tong.

J. Heat Transfer 135(4), 044502 (Mar 20, 2013) (8 pages) Paper No: HT-11-1471; doi: 10.1115/1.4023127 History: Received October 11, 2011; Revised April 29, 2012

The heat transfer characteristics of a couple-stress fluid (CSF) in a two-dimensional asymmetric channel is analyzed. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. Mathematical modeling corresponding to the two-dimensional couple stress fluid is made. Analytical expressions for the axial velocity, stream function, heat transfer, and the axial pressure gradient are established using long wavelength assumption. Numerical computations have been carried out for the pressure rise per wavelength. The influence of various parameters of interest is seen through graphs on frictional forces, pumping and trapping phenomena, and temperature profile.

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References

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Figures

Grahic Jump Location
Fig. 1

Geometry of the problem

Grahic Jump Location
Fig. 4

Variation of pressure gradient over the length versus x for different values of Q¯ at α = 0.2, φ = π/4, d = 1.5, and a = b = 0.5

Grahic Jump Location
Fig. 5

Variation of pressure rise over the length versus Q¯ with different phase difference φ at α=0.14, d = 1.5, and a = b = 0.4

Grahic Jump Location
Fig. 2

Variation of pressure gradient over the length versus x for different values of α at Q¯ =-0.5,φ = π/2, d = 1.5, and a = b = 0.5

Grahic Jump Location
Fig. 3

Variation of pressure gradient over the length versus x for different values of φ at Q¯ = 0.2, α = 0.12, d = 1.5, and a = b = 0.4

Grahic Jump Location
Fig. 7

Variation of Fλh2 versus Q¯ for different values of α and φ at d = 2 and a = b = 0.5

Grahic Jump Location
Fig. 8

Variation of Fλh1 versus Q¯ for different values of α and φ at d = 2 and a = b = 0.5

Grahic Jump Location
Fig. 9

Effect of Prandtl number Pr and the phase difference φ on temperature distribution θ for Ec = 2, m = 2, a = b = 0.5,d = 2,α = 4, and Q¯ = 0.5 at section x = 0.1

Grahic Jump Location
Fig. 10

Effect of α couple stress parameter and the Eckert number Ec on temperature distribution θ for m = 2, φ = π/2,a = b = 0.5, d = 2,Pr = 1, and Q¯ = 0.5 at section x = 0.1

Grahic Jump Location
Fig. 11

Effect of the wall temperature ratio m on temperature distribution θ for Ec = 4,φ = π/2, a = b = 0.5, d = 2, Pr = 2, and Q¯ = 0.5 at section x = 0.1

Grahic Jump Location
Fig. 12

Streamlines for different values of α and φ with fixed values of Q¯ = 1.6 panels (a)–(c) at φ = 0 with α = 1,α = 3,α = 5, respectively, and panels (d)–(f) α = 4 with φ = 0,φ = π/2,φ = π, respectively

Grahic Jump Location
Fig. 6

Variation of pressure rise over the length versus Q¯ with different values of couple stress parameter at φ = π/4, d = 1.5, and a = b = 0.4

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