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Research Papers: Porous Media

Unsteady Flow of Magneto Thermomicropolar Fluid in a Porous Channel With Peristalsis: Unsteady Separation

[+] Author and Article Information
Y. Abd Elmaboud

Mathematics Department,
Faculty of Science and Arts,
King Abdulaziz University (KAU),
Khulais 21921,
Jeddah, Kingdom of Saudi Arabia;
Mathematics Department,
Faculty of Science,
Al-Azhar University (Assiut Branch),
Assiut, Egypt
e-mail: yass_math@yahoo.com

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received July 23, 2012; final manuscript received January 17, 2013; published online June 17, 2013. Assoc. Editor: Giulio Lorenzini.

J. Heat Transfer 135(7), 072602 (Jun 17, 2013) (11 pages) Paper No: HT-12-1397; doi: 10.1115/1.4023581 History: Received July 23, 2012; Revised January 17, 2013

The magneto thermodynamic aspects of micropolar fluid (blood model) through an isotropic porous medium in a nonuniform channel with rhythmically contracting walls have been investigated. The flow analysis has been discussed under long wavelength and low Reynolds number approximations. The closed form solutions are obtained for velocity components, microrotation, heat transfer, as well as the wall vorticity. The modified Newton–Raphson method is used to predict the unsteady flow separation points along the peristaltic wall. Numerical computations have been carried out for the pressure rise per wavelength. The study shows that peristaltic transport, fluid velocity, microrotation velocity, and wall shear stress are significantly affected by the nonuniform geometry of the blood vessels. Moreover, the amplitude ratio, the coupling number, the micropolar parameter, and the magnetic parameter are important parameters that affect the flow behavior.

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References

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Figures

Grahic Jump Location
Fig. 1

Geometry of the problem

Grahic Jump Location
Fig. 2

The velocity distribution u, across the channel with different values of Γ and M at t = 0.4m = 10, N = 0.5, Q¯ = 0.5, φ = 0.4 and x = 0.5, where y∈[ - h,h]

Grahic Jump Location
Fig. 3

The velocity distribution u, across the channel with different values of N, m, and Q¯ at t = 0.3, M = 4, Γ = 3, φ = 0.4, and x = 0.5, where y∈[-h,h]

Grahic Jump Location
Fig. 4

The velocity u, versus t for different values of x and Γ, at y = 0, Q¯ = 2, φ = 0.4, m = 3, N = 0.6, and M = 4

Grahic Jump Location
Fig. 5

The microrotation velocity w, across the channel with different values of m and N at Γ = 3, Q¯ = 1, φ = 0.4, t = 0, and x = 0.5 where y∈[-h,h]

Grahic Jump Location
Fig. 6

The microrotation velocity w, across the channel with different values of M and Γ at m = 3, N = 0.9, Q¯ = 1, φ = 0.4, t = 0.4, and x = 0.5 where y∈[-h,h]

Grahic Jump Location
Fig. 7

The microrotation velocity w, versus t for different values of φ at m = 1, N = 0.9, Q¯ = 1, M = 2, Γ = 3, and (x,y) = (0.5,0.5)

Grahic Jump Location
Fig. 8

Variation of wall vorticity ηz versus x with different values of M at Γ = 0.2, Q¯ = 1.5, φ = 0.4, t = 0, m = 5, and N = 0.4

Grahic Jump Location
Fig. 9

Variation of wall vorticity ηz versus x with different values of Γ at M = 2, Q¯ = 1.5, φ = 0.4, t = 0, m = 5, and N = 0.4

Grahic Jump Location
Fig. 10

Variation of wall vorticity ηz versus x with different values of m and N at M = 2, Q¯ = 1.5, φ = 0.4, t = 0.5, and Γ = 2

Grahic Jump Location
Fig. 11

Variation of wall vorticity ηz versus time t with different values of x and φ at M = 2, Q¯ = 1.5, N = 0.2, m = 1, and Γ = 2

Grahic Jump Location
Fig. 12

Variation of pressure rise over the length versus t with different values of M and Γ at φ = 0.6, Q¯ = 0.1, m = 2, and N = 0.1

Grahic Jump Location
Fig. 13

Variation of pressure rise over the length versus t with different values of m and N at φ = 0.6, Q¯ = -0.1, M = 4, and Γ = 4

Grahic Jump Location
Fig. 14

Wall shear stress τxy versus x with different values of M and Γ at t = 0, φ = 0.4, Q¯ = 0.1, m = 2, and N = 0.1

Grahic Jump Location
Fig. 15

Wall shear stress τxy versus t with different values of N and m at x = 0.5, φ = 0.4, Q¯ = 0.1, Γ = 1, and M = 2

Grahic Jump Location
Fig. 16

Wall shear stress τyx versus x with different values of M and Γ at t = 0, φ = 0.4, Q¯ = 0.1, m = 2, and N = 0.1

Grahic Jump Location
Fig. 17

Wall shear stress τyx versus t with different values of N and m at x = 0.5, φ = 0.4, Q¯ = 0.1, Γ = 1, and M = 2

Grahic Jump Location
Fig. 18

Temperature distribution θ versus y for different values of Γ and M at t = 0, x = 0.2, Q¯ = 0.5, φ = 0.4, m = 3, N = 0.5, Ec = 5, Q¯, and s = 2

Grahic Jump Location
Fig. 19

Temperature distribution θ versus y for different values of m and N at t = 0, x = 0.2, Q¯ = 0.5, φ = 0.4, Γ = 0.1, M = 2, Ec = 5, Pr = 3, and s = -1

Grahic Jump Location
Fig. 20

Temperature distribution θ versus Γ for different values of Ec and Pr at x = 0.2, y = 0, Q¯ = 0.5, φ = 0.4, Γ = 0.1, M = 2, m = 0.6, N = 0.4, and s = -1

Grahic Jump Location
Fig. 21

Nusselt number versus x for different values of Γ and M at t = 0, Q¯ = 0.5, φ = 0.4, m = 3, N = 0.5, Ec=5, Pr = 3, and s = 2

Grahic Jump Location
Fig. 22

Nusselt number versus x for different values of m and N at t = 0, Q¯ = 0.5, φ = 0.4, Γ = 0.1, M = 2, Ec = 5, Pr = 3, and s = -1

Grahic Jump Location
Fig. 23

Nusselt number versus x for different values of s, at t = 0, Q¯ = 0.5, φ = 0.4, Γ = 0.1, M = 2, Ec = 5, Pr = 3, m = 1, and N = 0.4

Grahic Jump Location
Fig. 24

Nusselt number versus t, for different values of Ec and Pr at x = 0.2, Q¯ = 0.5, φ = 0.4, Γ = 0.1, M = 2, s = -1, m = 0.6, and N = 0.4

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