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Drag reduction in a thermally modulated channel

Published online by Cambridge University Press:  15 February 2016

M. Z. Hossain*
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada
J. M. Floryan
Affiliation:
Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, N6A 5B9, Canada
*
Email address for correspondence: [email protected]

Abstract

Flow in a horizontal channel exposed to external heating which results in sinusoidal temperature variations along the upper and lower walls with a phase shift between them has been studied using a combination of analytical and numerical methods. The most intense convection is observed when the upper and lower hot spots are located above each other. It has been demonstrated that the heating results in a significant reduction of the pressure gradient required to drive the flow when compared to a similar flow in an isothermal channel. The drag reduction is associated with the formation of separation bubbles which insulate the stream from direct contact with the bounding walls. The fluid inside of the bubbles rotates due to horizontal density gradients, which further reduces the required pressure gradient. The magnitude of the drag reduction depends on the phase shift between the heating patterns and can increase by up to threefold when compared to the drag reduction which can be achieved by heating only one wall. A detailed analysis of the associated heat fluxes has been presented.

Type
Papers
Copyright
© 2016 Cambridge University Press 

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References

Bergman, T. L., Lavine, A. S., Incropera, F. P. & Dewitt, D. P. 2011 Fundamentals of Heat and Mass Transfer, 7th edn. Wiley.Google Scholar
Bewley, T. 2009 A fundamental limit on the balance of power in a transpiration-controlled channel flow. J. Fluid Mech. 632, 443446.CrossRefGoogle Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 2006 Spectral Methods: Fundamentals in Single Domains. Springer.CrossRefGoogle Scholar
Floryan, J. M. 2012 The thermo-superhydrophobic effect. Bull. Amer. Phys. Soc. 57 (1), X.50.00015.Google Scholar
Floryan, D. & Floryan, J. M. 2015 Drag reduction in heated channels. J. Fluid Mech. 765, 353395.CrossRefGoogle Scholar
Fukagata, K., Sugiyama, K. & Kasagi, N. 2009 On the lower bound of net driving power in controlled duct flows. Physica D 238, 1081086.Google Scholar
Hœpffner, J. & Fukagata, K. 2009 Pumping or drag reduction? J. Fluid Mech. 635, 171187.CrossRefGoogle Scholar
Hossain, M. Z., Floryan, D. & Floryan, J. M. 2012 Drag reduction due to spatial thermal modulations. J. Fluid Mech. 713, 398419.Google Scholar
Hossain, M. Z. & Floryan, J. M. 2013a Heat transfer due to natural convection in a periodically heated slot. Trans. ASME J. Heat Transfer 135, 022503.Google Scholar
Hossain, M. Z. & Floryan, J. M. 2013b Instabilities of natural convection in a periodically heated layer. J. Fluid Mech. 733, 3367.CrossRefGoogle Scholar
Hossain, M. Z. & Floryan, J. M. 2014 Natural convection in a fluid layer periodically heated from above. Phys. Rev. E 90, 023015.CrossRefGoogle Scholar
Hossain, M. Z. & Floryan, J. M. 2015a Mixed convection in a periodically heated channel. J. Fluid Mech. 768, 5190.Google Scholar
Hossain, M. Z. & Floryan, J. M. 2015b Natural convection in a horizontal fluid layer periodically heated from above and below. Phys. Rev. E 92, 023015.Google Scholar
Hughes, G. O. & Griffiths, R. W. 2008 Horizontal convection. Annu. Rev. Fluid Mech. 40, 185208.Google Scholar
Joseph, P., Cottin-Bizonne, C., Benoit, J. M., Ybert, C., Journet, C., Tabeling, P. & Bocquet, L. 2006 Slippage of water past superhydrophobic carbon nanotube forests in microchannels. Phys. Rev. Lett. 97, 156104.CrossRefGoogle ScholarPubMed
Martin, S. & Bhushan, B. 2014 Fluid flow analysis of a shark-inspired microstructure. J. Fluid Mech. 756, 529.Google Scholar
Maxworthy, T. 1997 Convection into domains with open boundaries. Annu. Rev. Fluid. Mech. 29, 327371.Google Scholar
Mohammadi, A. & Floryan, J. M. 2012 Mechanism of drag generation by surface corrugation. Phys. Fluids 24, 013602.Google Scholar
Mohammadi, A. & Floryan, J. M. 2013a Pressure losses in grooved channels. J. Fluid Mech. 725, 2354.Google Scholar
Mohammadi, A. & Floryan, J. M. 2013b Groove optimization for drag reduction. Phys. Fluids 25, 113601.Google Scholar
Mohammadi, A. & Floryan, J. M. 2014 Effects of longitudinal grooves on the Couette–Poiseuille flow. J. Theor. Comput. Fluid Dyn. 28, 549572.Google Scholar
Mohammadi, A. & Floryan, J. M. 2015 Numerical analysis of laminar-drag-reducing grooves. Trans. ASME J. Fluids Engng 137 (1–12), 041201.Google Scholar
Moradi, H. V. & Floryan, J. M. 2013 Flows in annuli with longitudinal grooves. J. Fluid Mech. 716, 280315.Google Scholar
Moradi, H. V. & Floryan, J. M. 2014 Stability of flow in a channel with longitudinal grooves. J. Fluid Mech. 757, 613648.Google Scholar
Ou, J., Perot, J. B. & Rothstein, J. P. 2004 Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys. Fluids 16, 46354643.Google Scholar
Ou, J. & Rothstein, J. P. 2005 Direct velocity measurements of the flow past drag-reducing ultrahydrophobic surfaces. Phys. Fluids 17, 103606.CrossRefGoogle Scholar
Quéré, D. 2008 Wetting and roughness. Annu. Rev. Mater. Res. 38, 7199.Google Scholar
Reyssat, M., Yeomans, J. M. & Quéré, D. 2008 Impalement of fakir drops. Europhys. Lett. 81, 26006.Google Scholar
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89109.Google Scholar
Samaha, M. A., Tafreshi, H. V. & Gad-el-Hak, M. 2011 Modeling drag reduction and meniscus stability of superhydrophobic surfaces comprised of random roughness. Phys. Fluids 23, 012001.Google Scholar
Siggers, J. H., Kerswell, R. R. & Balmforth, N. J. 2004 Bounds on horizontal convection. J. Fluid Mech. 517, 5570.Google Scholar
Takagi, D. & Balmforth, N. J. 2011 Peristaltic pumping of viscous fluid in an elastic tube. J. Fluid Mech. 672, 196218.CrossRefGoogle Scholar
Truesdell, R., Mammoli, P., Vorobieff, P., van Swol, P. & Brinker, C. J. 2006 Drag reduction on a patterned superhydrophobic surface. Phys. Rev. Lett. 97, 044504.CrossRefGoogle ScholarPubMed
Winters, K. B. & Young, W. R. 2009 Available potential energy and buoyancy variance in horizontal convection. J. Fluid Mech. 629, 221230.Google Scholar
Yamamoto, A., Hasegawa, Y. & Kasagi, N. 2013 Optimal control of dissimilar heat and momentum transfer in fully developed turbulent channel flow. J. Fluid Mech. 733, 189230.Google Scholar
Zhou, M., Li, J., Wu, C., Zhou, X. & Cai, L. 2011 Fluid drag reduction on superhydrophobic surfaces coated with carbon nanotube forest (CNTs). Soft Matt. 7, 43914396.Google Scholar