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Research Papers: Flows in Complex Systems

Mixed Convective Flow of Electrically Conducting Fluid in a Vertical Cylindrical Annulus With Moving Walls Adjacent to a Radial Magnetic Field Along With Transpiration

[+] Author and Article Information
Ali Shakiba

Department of Mechanical Engineering,
Ferdowsi University of Mashhad,
Mashhad 1111, Iran

Asghar B. Rahimi

Professor
Faculty of Engineering,
Ferdowsi University of Mashhad,
P.O. Box 91775-1111,
Mashhad 1111, Iran,
e-mail: rahimiab@yahoo.com

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 11, 2018; final manuscript received January 17, 2019; published online March 4, 2019. Assoc. Editor: Nazmul Islam.

J. Fluids Eng 141(8), 081111 (Mar 04, 2019) (11 pages) Paper No: FE-18-1680; doi: 10.1115/1.4042563 History: Received October 11, 2018; Revised January 17, 2019

The steady, viscous flow and mixed convection heat transfer of an incompressible electrically conducting fluid within a vertical cylindrical annulus with moving walls are investigated. This annulus is under the influence of a radial magnetic field and the fluid is suctioned/injected through the cylinders' walls. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem where heat is transferred from the hot cylinder walls with constant temperature to the cooler moving fluid. The role of the movement of the annulus walls is studied on the flow and heat transfer of the fluid within the annulus, for the first time. The effects of other parameters, including Prandtl number, Hartman number, mixed convection parameter, suction/injection parameter and ratio of the radius, on the behavior of the flow and heat transfer of the fluid is also considered. The results indicate that if, for example, the internal cylinder wall moves in the direction of z-axis and the external cylinder is stationary, the maximum and minimum heat transfer occur on the walls of internal and external cylinders, respectively. Moreover, the augmentation of the radius ratio between the two cylinders increases the rate of heat transfer and decreases the shear stress on the wall of the internal and external cylinders, however, the results on the wall of external cylinder are exactly the reverse. Consequently, by changing the effective parameters used in this paper, the flow of the fluid can be controlled and the heat transfer of the fluid can be improved.

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Figures

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Fig. 1

Geometry and coordinate system of the annulus

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Fig. 2

Comparison of the velocity profile in an annulus with Ref. [26] for η=50, S=−0.5, Ha=0

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Fig. 3

Dimensionless temperature variations at the interval between two cylinders for different values of suction/injection parameter for upper limit of R = λ=2 and two values of Pr=2 and Pr=7

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Fig. 4

Effect of the velocity variations of annulus's internal and external cylinders on the dimensionless fully developed velocity profile for η=5, S=1, Pr=7, Ha=2, and upper limit of R=λ=2

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Fig. 5

Variations of fully developed dimensionless velocity for different Hartman numbers and various states of the cylinders' motion for η=5, S=1, Pr=7 and upper limit of R=λ=2

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Fig. 6

Variations of S parameter on the dimensionless velocity of fluid for different states of internal and external cylinders' movement for η=5,Pr=7,Ha=2 and upper limit of R=λ=2

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Fig. 7

Effects of the variations of mixed convection parameter on the fully developed dimensionless velocity for different states of internal and external cylinders' movement for S=2, Pr=7, Ha=2, and upper limit of R=λ=2

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Fig. 8

Effect of the variations of mixed convection parameter on the Nusselt number for different states of internal and external cylinders' movements for S=1, λ=2, Pr=7, Ha=2

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Fig. 9

Impact of dimensionless Prandtl number's changes and the variations of radial magnetic field intensity on the Nusselt number in A=1,B=0,R=1,η=5,S=1,λ=2

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Fig. 10

Variations of Nusselt number for different radial ratios and various suction/injection parameters in A=1,B=0,η=5,Pr=7,Ha=2

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Fig. 11

Variations of shear stress in terms of mixed convection parameter for different states of internal and external cylinders' movements in Pr=7, Ha=2

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Fig. 12

Variation of radial ratio between two cylinders (λ), Hartman number (Ha) and S parameter on the shear stress of the fluid in A=1, B=0, η=5, Pr=7

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