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Research Papers

Transient Analysis of the Interactions Between a Heat Transferring, Radial Stagnation Flow, and a Rotating Cylinder-Magnetohydrodynamic and Nonuniform Transpiration Effects

[+] Author and Article Information
Rasool Alizadeh

Department of Mechanical Engineering,
Quchan Branch,
Islamic Azad University,
Quchan, Iran

Asghar B. Rahimi

Faculty of Engineering,
Ferdowsi University of Mashhad,
P.O. Box 91775-1111,
Mashhad, Iran

Nader Karimi

School of Engineering,
University of Glasgow,
Glasgow G12 8QQ, UK
e-mail: Nader.Karimi@glasgow.ac.uk

Ahmad Alizadeh

Young Researchers Club,
Quchan Branch,
Islamic Azad University,
Quchan, Iran

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received June 22, 2017; final manuscript received April 22, 2018; published online June 14, 2018. Assoc. Editor: Sandip Mazumder.

J. Thermal Sci. Eng. Appl 10(5), 051017 (Jun 14, 2018) (13 pages) Paper No: TSEA-17-1215; doi: 10.1115/1.4040363 History: Received June 22, 2017; Revised April 22, 2018

This paper aims at providing further understanding on the fluid flow and heat transfer processes in unsteady rotating systems with mass transpiration. Such systems can be found in chemical separators, hydraulic systems, and printing devices. To this end, an unsteady viscous flow in the vicinity of an unaxisymmetric stagnation-point on a rotating cylinder is examined. The nonuniform transpiration and a transverse magnetic field are further considered. The angular speed of the cylinder and the thermal boundary conditions are expressed by time-dependent functions. A reduction of the Navier–Stokes and energy equations is obtained through using appropriate similarity transformations. The semisimilar solution of the Navier–Stokes equations and energy equation are developed numerically using an implicit finite difference scheme. Pertinent parameters including the Reynolds number and magnetic parameter and transpiration function are subsequently varied systematically. It is shown that the transpiration function can significantly affect the thermal and hydrodynamic behaviors of the system. In keeping with the findings in other areas of magnetohydrodynamics (MHD), the results show that the applied magnetic field has modest effects on the Nusselt number. However, it is demonstrated that the magnetic effects can significantly increase the imposed shear stress on the surface of the rotating cylinder.

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References

Wilson, I. D. , Adlard, E. R. , Cooke, M. , and Poole, C. F. , 2000, Encyclopaedia of Separation Science, Academic, Acedemic Press, London.
He, J. , Huang, M. , Wang, D. , Zhang, Z. , and Li, G. , 2014, “ Magnetic Separation Techniques in Sample Preparation for Biological Analysis: A Review,” J. Pharma Biomed Anal. Ens., 101(2014), pp. 84–101. [CrossRef]
Friedman, G. , and Yellen, B. , 2005, “ Magnetic Separation, Manipulation and Assembly of Solid Phase in Fluids,” Curr. Opin. Colloid Interface Sci., 10(3–4), pp. 158–166. [CrossRef]
Fetterman, A. J. , and Fisch, N. J. , 2011, “ The Magnetic Centrifugal Mass Filter,” Phys. Plasmas, 18(9), p. 094503. [CrossRef]
Zhou, Y. , Wu, W. , and Qiu, K. , 2010, “ Recovery of Materials From Waste Printed Circuit Boards by Vacuum Pyrolysis and Vacuum Centrifugal Separation,” Waste Manage., 30(11), pp. 2299–2304. [CrossRef]
Hiemenz, K. , 1911, “ Die Grenzschicht an Einem in Den Gleichförmingen Flüssigkeitsstrom Eingetauchten Geraden Kreiszylinder,” Dinglers Polytech. J., 326, pp. 321–410.
Homann, F. , 1936, “ Der Einfluss Grosser Zähigkeit Bei Der Strömung Um Den Zylinder Und Um Die Kugel,” J. Appl. Math. Mech. Z. Angew Math. Mech., 16(3), pp. 153–164. [CrossRef]
Howarth, L. , 1951, “ CXLIV. The Boundary Layer in Three Dimensional Flow—Part II. The Flow Near a Stagnation Point,” London Edinburgh Dublin Phil. Mag., 42(335), pp. 1433–1440. [CrossRef]
Davey, A. , 1961, “ Boundary-Layer Flow at a Saddle Point of Attachment,” J. Fluid. Mech., 10(4), pp. 593–610. [CrossRef]
Wang, C. Y. , 1974, “ Axisymmetric Stagnation Flow on a Cylinder,” Q. Appl. Math., 32(2), pp. 207–213. [CrossRef]
Wang, C. Y. , 1973, “ Axisymmetric Stagnation Flow Towards a Moving Plate,” AIChE. J., 19(5), pp. 1080–1081. [CrossRef]
Reddy Gorla, R. S. , 1976, “ Heat Transfer in an Axisymmetric Stagnation Flow on a Cylinder,” App. Sci. Res., 32(5), pp. 541–553. [CrossRef]
Gorla, R. S. R. , 1977, “ Unsteady Laminar Axisymmetric Stagnation Flow Over a Circular Cylinder,” Mech. Develop., 9, pp. 286–288.
Gorla, R. S. R. , 1978, “ Nonsimilar Axisymmetric Stagnation Flow on a Moving Cylinder,” Int. J. Eng. Sci., 16(6), pp. 397–400. [CrossRef]
Gorla, R. S. R. , 1978, “ Transient Response Behavior of an Axisymmetric Stagnation Flow on a Circular Cylinder Due to Time Dependent Free Stream Velocity,” Int. J. Eng. Sci., 16(7), pp. 493–502. [CrossRef]
Gorla, R. S. R. , 1979, “ Unsteady Viscous Flow in the Vicinity of an Axisymmetric Stagnation Point on a Circular Cylinder,” Int. J. Eng. Sci., 17(1), pp. 87–93. [CrossRef]
Cunning, G. M. , Davis, A. M. J. , and Weidman, P. D. , 1998, “ Radial Stagnation Flow on a Rotating Circular Cylinder With Uniform Transpiration,” J. Eng. Math., 33(2), pp. 113–128. [CrossRef]
Grosch, C. E. , and Salwen, H. , 1982, “ Oscillating Stagnation Point Flow,” Proc. R. Soc. London A: Math., Phys. Eng. Sci., 384(1786), pp. 175–190. [CrossRef]
Takhar, H. S. , Chamkha, A. J. , and Nath, G. , 1999, “ Unsteady Axisymmetric Stagnation-Point Flow of a Viscous Fluid on a Cylinder,” J. Eng. Sci., 37(15), pp. 1943–1957. [CrossRef]
Saleh, R. , and Rahimi, A. B. , 2004, “ Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time- Dependent Axial Velocity and Uniform Transpiration,” ASME J. Fluids Eng., 126(6), pp. 997–1005. [CrossRef]
Rahimi, A. B. , and Saleh, R. , 2007, “ Axisymmetric Stagnation—Point Flow and Heat Transfer of a Viscous Fluid on a Rotating Cylinder With Time-Dependent Angular Velocity and Uniform Transpiration,” ASME J. Fluids Eng., 129(1), pp. 106–115. [CrossRef]
Rahimi, A. B. , and Saleh, R. , 2009, “ Similarity Solution of Unaxisymmetric Heat Transfer in Stagnation-Point Flow on a Cylinder With Simultaneous Axial and Rotational Movements,” ASME J. Heat Transfer, 130(5), p. 054502. [CrossRef]
Abbassi, A. S. , and Rahimi, A. B. , 2009, “ Nonaxisymmetric Three-Dimensional Stagnation-Point Flow and Heat Transfer on a Flat Plate,” ASME J. Fluids Eng., 131(7), p. 074501. [CrossRef]
Rahimi, A. B. , and Abbassi, A. S. , 2009, “ Three-Dimensional Stagnation Flow and Heat Transfer on a Flat Plate With Transpiration,” J. Thermophys. Heat Transfer, 23(3), pp. 513–521. [CrossRef]
Abbassi, A. S. , Rahimi, A. B. , and Hamid Niazmand, H. , 2012, “ Exact Solution of Three-Dimensional Unsteady Stagnation Flow on a Heated Plate,” J. Thermophys. Heat Transfer, 25(1), pp. 55–58. [CrossRef]
Abbassi, A. S. , and Rahimi, A. B. , 2012, “ Investigation of Two-Dimensional Unsteady Stagnation-Point Flow and Heat Transfer Impinging on an Accelerated Flat Plate,” ASME J. Heat Transfer, 134(6), pp. 135–145.
Subhashini, S. V. , and Nath, G. , 1999, “ Unsteady Compressible Flow in the Stagnation Region of Two-Dimensional and Axi-Symmetric Bodies,” Acta Mech., 134(3–4), pp. 135–145. [CrossRef]
Kumari, M. , and Nath, G. , 1980, “ Unsteady Compressible Three-Dimensional Boundary-Layer Flow Near an Asymmetric Stagnation Point With Mass Transfer,” Int. J. Eng. Sci., 18(11), pp. 1285–1300. [CrossRef]
Kumari, M. , and Nath, G. , 1981, “ Self-Similar Solution of Unsteady Compressible Three-Dimensional Stagnation-Point Boundary Layers,” Z. Angew. Math. Phys., 32(3), pp. 267–276. [CrossRef]
Katz, A. , 1972, “ Transformations of the Compressible Boundary Layer Equations,” SIAM J. Appl. Math., 22(4), pp. 604–611. [CrossRef]
Afzal, N. , and Ahmad, S. , 1975, “ Effects of Suction and Injection on Self-Similar Solutions of Second-Order Boundary-Layer Equations,” Int. J. Heat Mass Transfer, 18(5), pp. 607–614. [CrossRef]
Libby, P. A. , 1967, “ Heat and Mass Transfer at a General Three-Dimensional Stagnation Point,” AIAA J., 5(3), pp. 507–517. [CrossRef]
Gersten, K. , Papenfuss, H. D. , and Gross, J. F. , 1978, “ Influence of the Prandtl Number on Second-Order Heat Transfer Due to Surface Curvature at a Three-Dimensional Stagnation Point,” Int. J. Heat Mass Transfer, 21(3), pp. 275–284. [CrossRef]
Ishak, A. , Nazar, R. , and Pop, I. , 2008, “ Magnetohydrodynamic (MHD) Flow and Heat Transfer Due to a Stretching Cylinder,” Energy Convers. Manage., 49(11), pp. 3265–3269. [CrossRef]
Joneidi, A. A. , Domairry, G. , Babaelahi, M. , and Mozaffari, M. , 2010, “ Analytical Treatment on Magnetohydrodynamic (MHD) Flow and Heat Transfer Due to a Stretching Hollow Cylinder,” Int. J. Numer. Meth. Fluid, 63(5), pp. 548–563.
Butt, A. S. , and Ali, A. , 2014, “ Entropy Analysis of Magnetohydrodynamic Flow and Heat Transfer Due to a Stretching Cylinder,” J. Taiwan Inst. Chem. Eng., 45(3), pp. 780–786. [CrossRef]
Chauhan, D. S. , Agrawal, R. , and Rastogi, P. , 2012, “ Magnetohydrodynamic Slip Flow and Heat Transfer in a Porous Medium Over a Stretching Cylinder: Homotopy Analysis Method,” Numer. Heat Transfer. A-Appl., 62(2), pp. 136–157.
Munawar, S. , Mehmood, A. , and Ali, A. , 2012, “ Time-Dependent Flow and Heat Transfer Over a Stretching Cylinder,” Chin. J. phys., 50(5), pp. 828–848. https://www.researchgate.net/publication/249313205_Time-dependent_flow_and_heat_transfer_over_a_stretching_cylinder
Weidman, P. D. , and Mahalingam, S. , 1997, “ Axisymmetric Stagnation-Point Flow Impinging on a Transversely Oscillating Plate With Suction,” J. Eng. Math., 31(2–3), pp. 305–318. [CrossRef]
Alizadeh, R. , Rahimi, A. B. , and Najafi, M. , 2016, “ Unaxisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Moving Cylinder With Time-Dependent Axial Velocity,” J. Braz. Soc. Mech. Sci. Eng., 38(1), pp. 85–98. [CrossRef]
Alizadeh, R. , Rahimi, A. B. , Arjmandzadeh, R. , Najafi, M. , and Alizadeh, A. , 2016, “ Unaxisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid With Variable Viscosity on a Cylinder in Constant Heat Flux,” Alexandria Eng. J., 55(2), pp. 1271–1283. [CrossRef]
Alizadeh, R. , Rahimi, A. B. , and Mohammad, N. , 2016, “ Magnetohydrodynamic Unaxisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Stationary Cylinder,” Alexandria Eng. J., 55(1), pp. 37–49. [CrossRef]
Blottner, F. G. , 1970, “ Finite Difference Methods of Solution of the Boundary Layer Equations,” AIAA. J., 8 (2), pp. 193–205. [CrossRef]
Rohsenow, W. M. , Hartnett, J. P. , and Cho, Y. I. , 1998, Handbook of Heat Transfer, McGraw-Hill, New York.
Alizadeh, R. , Rahimi, A. B. , and Najafi, M. , 2016, “ Non-Axisymmetric Stagnation-Point Flow and Heat Transfer of a Viscous Fluid on a Stationary Cylinder,” Scientia Iran., Trans. B, Mech. Eng., 23(5), p. 2238.

Figures

Grahic Jump Location
Fig. 1

Schematic diagram of a rotating cylinder under radial stagnation flow in the fixed cylindrical coordinate system (r,φ,z): (a) side view, (b) and (c) top views

Grahic Jump Location
Fig. 2

Variations of G(η,φ,τ) with changes in the magnetic parameter, M, for angular velocity function Ω(τ)=τ2 and S=cosφ: (a) M = 0, (b) M = 1, (c) M = 3, and (d) M = 4

Grahic Jump Location
Fig. 3

Temporal evolution of G(η,φ,τ) with angular velocity function, Ωτ=τ and S=cosφ,(a) τ=0, (b) τ=0.2, (c) τ=0.6, and (d) τ=1.0

Grahic Jump Location
Fig. 4

Variations of G(η,φ,τ) with changes in the external flow Reynolds number, Re, for stepwise angular velocity function, Ωτ=1 and S=cosφ, (a) Re = 0.1, (b) Re = 1, (c) Re = 10, and (d) Re = 100

Grahic Jump Location
Fig. 5

Variations of Gη,φ,τ for angular velocity function Ωτ=τ, Re = 1.0, M = 0, (a) S = 0, (b) S=cos(φ), (c) S=sin(φ), and (d) S=−sinφ

Grahic Jump Location
Fig. 6

Variations of θ(η,φ,τ) for angular velocity Ω(τ)=1, M = 0 and S=cosφ, (a) Re = 0.1, (b) Re = 1, (c) Re = 10, and (d) Re = 100

Grahic Jump Location
Fig. 7

Variations of θ(η,φ,τ) under Sφ=cosφ for different thermal boundary conditions on the wall, (a) and (b) Tw−T∞=Cexpγτ, for γ=2 and γ=−2, respectively, (c) and (d) qw=C exp γτ, for γ=2 and γ=−2, respectively

Grahic Jump Location
Fig. 8

Circumferential variation of dimensionless shear stress (σ/2kμ), for (a) Re=10, Ω(τ)=τ2 and for the selected values of magnetic parameter and (b) S(φ)=cos(φ), for step-function angular velocity and for selected values of Reynolds numbers

Grahic Jump Location
Fig. 9

Circumferential variation of Nusselt number for S(φ)=cos(φ), (a) surface temperature, varying exponentially with time and (b) surface heat flux, and for the selected values of magnetic parameter

Grahic Jump Location
Fig. 10

Profiles of dimensionless shear stress (σ/2kμ) in term of φ. For (a) Ω(τ)=τ and for selected values of magnetic parameter, (b) S(φ)=Ln(φ), for step-function angular velocity, and for selected values of Reynolds numbers.

Grahic Jump Location
Fig. 11

Nusselt number for S(φ)=Ln(φ) for (a) surface temperature, varying exponentially and for selected values of magnetic parameter and (b) surface heat flux, varying exponentially with time

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