Abstract
An unsteady three-dimensional stagnation-point flow of a nanofluid past a circular cylinder with sinusoidal radius variation is investigated numerically. By introducing new similarity transformations for the velocity, temperature, and nanoparticle volume fraction, the basic equations governing the flow and heat and mass transfer are reduced to highly nonlinear ordinary differential equations. The resulting nonlinear system is solved numerically by the fourth-order Runge–Kutta method with the shooting technique. The thermophoresis and Brownian motion effects occur in the transport equations. The velocity, temperature, and nanoparticle concentration profiles are analyzed with respect to the involved parameters of interest, namely, unsteadiness parameter, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number. Numerical values of the friction coefficient, diffusion mass flux, and heat flux are computed. It is found that the friction coefficient and heat transfer rate increase with increasing unsteadiness parameter (the highest heat transfer rate at the surface occurs if the thermophoresis and Brownian motion effects are absent) and decrease with increasing both thermophoresis and Brownian motion parameters. The present results are found to be in good agreement with previously published results.
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References
K. Hiemenz, “Die Grenzschicht an Einem in Den Gleichformigen Flussigkeitsstrom Eingetauchten Graden Kreiszylinder,” Dinglers Polytech. J. 326, 321–331 (1911).
F. Homann, “Der Einfluss Grosser Z¨ahigkeit bei der Str¨omung um den Zylinder und um die Kugel,” Z. Angew. Math. Mech. 16, 153–164 (1936).
W. K. Garg and K. R. Rajagopal, “Stagnation-Point Flow of a Non-Newtonian Fluid,” Mech. Res. Comm. 17, 415–421 (1990).
R. Seshadri, N. Sreeshylan, and G. Nat, “Unsteady Three-Dimensional Stagnation Point Flow of a Viscoelastic Fluid,” Int. J. Eng. Sci. 35, 445–454 (1997).
G. Domairry and Z. Ziabakhsh, “Solution of Boundary Layer and Heat Transfer of an Electrically Conducting Micropolar Fluid in a Non-Darcian Porous Medium,” Meccanica 47, 195–202 (2012).
L. Howarth, “The Boundary-Layer in Three Dimensional Flow. Pt 2. The Flow Near a Stagnation Point,” Philos. Mag. 42, 1433–1440 (1951).
A. Davey, “A Boundary Layer Flow at a Saddle Point of Attachment,” J. Fluid Mech., No. 10, 593–610 (1961).
S. Bhattacharyya and A. S. Gupta, “MHD Flow and Heat Transfer at a General Three-Dimensional Stagnation Point,” Int. J. Non-Linear Mech. 33, 125–134 (1998).
J. Buongiorno, “Convective Transport in Nanofluids,” Trans. ASME, J. Heat Transfer 128, 240–250 (2006).
D. A. Nield and A. V. Kuznetsov, “The Cheng–Minkowycz Problem for Natural Convective Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid,” Int. J. Heat Mass Transfer 52, 5792–5795 (2009).
A. V. Kuznetsov and D. A. Nield, “Natural Convective Boundary-Layer Flow of a Nanofluid Past a Vertical Plate,” Int. J. Thermal Sci. 49, 243–247 (2010).
N. Bachok, A. Ishak, and I. Pop, “Boundary-Layer Flow of Nanofluids over a Moving Surface in a Flowing Fluid,” Int. J. Thermal. Sci. 49, 1663–1668 (2010).
R. J. Tiwari and M. K. Das, “Heat Transfer Augmentation in a Two-Sided Lid-Driven Differentially Heated Square Cavity Utilizing Nanofluids,” Int. J. Heat Mass Transfer 50, 2002–2018 (2007).
N. Bachok, A. Ishak, R. Nazar, and I. Pop, “Flow and Heat Transfer at a General Three-Dimensional Stagnation Point in a Nanofluid,” Phys. B, No. 405, 4914–4918 (2010).
S. Dinarvand, R. Hosseini, E. Damangir, and I. Pop, “Series Solutions for Steady Three-Dimensional Stagnation Point Flow of a Nanofluid Past a Circular Cylinder with Sinusoidal Radius Variation,” Meccanica 48, 643–652 (2013).
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Original Russian Text © S. Dinarvand, R. Hosseini, H. Tamim, E. Damangir, I. Pop.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 4, pp. 72–84, July–August, 2015.
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Dinarvand, S., Hosseini, R., Tamim, H. et al. Unsteady three-dimensional stagnation-point flow and heat transfer of a nanofluid with thermophoresis and Brownian motion effects. J Appl Mech Tech Phy 56, 601–611 (2015). https://doi.org/10.1134/S0021894415040070
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DOI: https://doi.org/10.1134/S0021894415040070