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Research Papers: Flows in Complex Systems

Influence of Starling's Hypothesis and Joule Heating on Peristaltic Flow of an Electrically Conducting Casson Fluid in a Permeable Microvessel

[+] Author and Article Information
A. Sutradhar

Department of Mathematics,
Indian Institute of Technology,
Kharagpur 721 302, India
e-mail: asabhijitsutradhar@gmail.com

J. K. Mondal

Department of Mathematics,
Indian Institute of Technology,
Kharagpur 721 302, India
e-mail: jayantamondal874@gmail.com

P. V. S. N. Murthy

Department of Mathematics,
Indian Institute of Technology,
Kharagpur 721 302, India
e-mail: pvsnm@maths.iitkgp.ernet.in

Rama Subba Reddy Gorla

Department of Mechanical Engineering,
Cleveland State University,
Cleveland, OH 44115
e-mail: r.gorla@csuohio.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 29, 2015; final manuscript received March 15, 2016; published online July 15, 2016. Assoc. Editor: Shizhi Qian.

J. Fluids Eng 138(11), 111106 (Jul 15, 2016) (13 pages) Paper No: FE-15-1958; doi: 10.1115/1.4033367 History: Received December 29, 2015; Revised March 15, 2016

Peristaltic transport of electrically conducting blood through a permeable microvessel is investigated by considering the Casson model in the presence of an external magnetic field. The reabsorption process across the permeable microvessel wall is regarded to govern by Starling's hypothesis. Under the long wavelength approximation and low-Reynolds number assumption, the nonlinear governing equations along with the boundary conditions are solved using a perturbation technique. Starling's hypothesis at the microvessel wall provides a second-order ordinary differential equation to be solved numerically for pressure distribution which in turn gives the stream function and temperature field. Also, the location of the interface between the plug and core regions is obtained from the axial velocity. Due to an increasing reabsorption process, the axial velocity is found to increase initially but decreases near the outlet. The temperature is appreciably intensified by virtue of the Joule heating produced due to the electrical conductivity of blood.

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Figures

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Fig. 1

Physical model and coordinate system

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Fig. 2

Variation of axial velocity in the radial direction at z=0.5 for ϕ=0.09

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Fig. 3

The axial velocity for different (a) α when ξ=0.3, τy=0.02, M=0.4, ϕ=0.09; (b) ξ when τy=0.02, M=0.4, ϕ=0.09, α=0.2; (c) M when τy=0.02, ϕ=0.09, α=0.2, ξ=0.3; (d) ϕ when τy=0.02, α=0.2, ξ=0.3, M=0.4; (e) τy when α=0.2, ξ=0.3, M=0.4, ϕ=0.09

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Fig. 4

The pressure distribution for different (a) α when ξ=0.3, τy=0.02, M=0.4, ϕ=0.09; (b) ξ when τy=0.02, M=0.4, ϕ=0.09, α=0.2; (c) M when τy=0.02, ϕ=0.09, α=0.2, ξ=0.3; (d) ϕ when τy=0.02, α=0.2, ξ=0.3, M=0.4; (e) τy when α=0.2, ξ=0.3, M=0.4, ϕ=0.09

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Fig. 5

(a) Streamlines and trapping in the wave frame for (A) α=0, (B) α=0.1, (C) α=0.2 when ξ=0.3, τy=0.02, M=0.4, ϕ=0.09 and (b) streamlines and trapping in the wave frame for (A) α=0, (B) α=0.1, (C) α=0.2 with ξ=0.3, τy=0.2, M=0.4, ϕ=0.09

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Fig. 6

(a) Streamlines and trapping in the wave frame for (A) M=0, (B) M=0.2, (C) M=0.4 when τy=0.02, ϕ=0.09, α=0.2, ξ=0.3 and (b) streamlines and trapping in the wave frame for (A) M=0 (B) M=0.2 (C) M=0.4 when τy=0.2, ϕ=0.09, α=0.2, ξ=0.3

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Fig. 7

(a) Streamlines and trapping in the wave frame for (A) ϕ=0 (B) ϕ=0.05 (C) ϕ=0.09 when τy=0.02, α=0.2, ξ=0.3, M=0.4 and (b) streamlines and trapping in the wave frame for (A) ϕ=0 (B) ϕ=0.05 (C) ϕ=0.09 when  τy=0.2, α=0.2, ξ=0.3, M=0.4

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Fig. 8

Streamlines and trapping in the wave frame for (a) τy=0, (b) τy=0.02, (c) τy=0.04, (d) τy=0.1 when   α=0.2, ξ=0.3, M=0.4, ϕ=0.09

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Fig. 9

The temperature distribution for different (a) α when ξ=0.3, τy=0.02, Jh=0.032, ϕ=0.09; (b) ξ when τy=0.02, Jh=0.032, ϕ=0.09, α=0.2; (c) τy when α=0.2, ξ=0.3, Jh=0.032, ϕ=0.09; (d) Jh when τy=0.02, ϕ=0.09, α=0.2, ξ=0.3

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