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Research Papers: SPECIAL SECTION PAPERS

Unsteady Flow and Heat Transfer Characteristics of Fluid Flow Over a Shrinking Permeable Infinite Long Cylinder

[+] Author and Article Information
Emad J. Elnajjar

Department of Mechanical Engineering,
UAE University,
P.O. Box 15551,
Al Ain, UAE
e-mail: eelnajjar@uaeu.ac.ae

Qasem M. Al-Mdallal

Department of Mathematical Sciences,
UAE University,
P.O. Box 15551,
Al Ain, UAE
e-mail: q.almdallal@uaeu.ac.ae

Fathi M. Allan

Department of Mathematical Sciences,
UAE University,
P.O. Box 15551,
Al Ain, UAE
e-mail: f.allan@uaeu.ac.ae

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 1, 2014; final manuscript received March 10, 2016; published online June 1, 2016. Assoc. Editor: Dennis A. Siginer.

J. Heat Transfer 138(9), 091008 (Jun 01, 2016) (8 pages) Paper No: HT-14-1575; doi: 10.1115/1.4033058 History: Received September 01, 2014; Revised March 10, 2016

The present work studies the unsteady, viscous, and incompressible laminar flow and heat transfer over a shrinking permeable cylinder. The unsteady nonlinear Navier–Stokes and energy equations are reduced, using similarity transformations, to a system of nonlinear ordinary differential equations. The boundary conditions associated with the governing equations are the time dependent surface temperature and flow conditions. The method of solution is based on a combination of the implicit Runge–Kutta method and the shooting method. The present study predicts two solutions for both the flow and heat transfer fields, and a unique solution at a specific critical unsteadiness parameter. An analysis of the results, for a specific suction parameter, suggests that the corresponding unique unsteadiness parameter does not depend on the Prandtl number. However, the unique rate of heat transfer is increasing as the Prandtl number increases. In addition, our results confirm that the unique value of heat transfer rate increases as the suction parameter increases, regardless the value of the Prandtl number.

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Figures

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Fig. 1

Schematic diagram of the physical geometry, coordinate system, with time dependent radius

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Fig. 2

The boundary condition at infinity f′(∞) versus the initial condition f″(0)=λ, for the value of S = −1: γ<γc (—), γ=γc (—), γ>γc (—)

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Fig. 3

Velocity profiles: f′(η) for the first (solid line) and second (dashed line) solutions as a function of the similarity variable; η for different values of suction parameter, γ, and constant unsteadiness parameter, S = −1

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Fig. 4

Velocity profiles: f′(η) for the first (solid line) and second (dashed line) solutions as a function of the similarity variable; η for different values of the unsteadiness parameter, S, and constant suction parameter, γ = 2

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Fig. 5

Normalized skin friction coefficient: f″(1) for the first (solid line) and second (dashed line) solutions as a function of the unsteadiness parameter, S, for different values of the suction parameter, γ

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Fig. 6

Normalize temperature profiles: θ(η) for the first (solid line) and second (dashed line) solutions as a function similarity variable; η for different values of suction parameter, γ, and constant unsteadiness parameter, S = −1. For Prandtl number, Pr=0.2,0.7,1.0, and 3.0.

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Fig. 7

Normalize temperature profiles: θ(η) for the first (solid line) and second (dashed line) solutions as a function similarity variable; η for different values of unsteadiness parameter, S, for Prandtl number, Pr=0.2,0.7,1.0, and 3.0

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Fig. 8

The heat transfer rate for the first (solid line) and second (dashed line) solutions; − θ′(1) as a function of the unsteadiness parameter, S, ranging from −4 to 0 for different values of suction parameter, γ=0.1,1,1.5, and 2

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Fig. 9

The unique heat transfer rate: −θu′(1) for both solutions as a function of unsteadiness parameter, S, for different values of suction parameter, γ, and for (the 1st bottom horizontal data set of points) Pr=0.2, (the 2nd horizontal data set of points) Pr=0.7, (the 3rd horizontal data set of points) Pr=1.0, and (the 4th horizontal data set of points) Pr=3.0

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