Research Papers: Forced Convection

Hydrodynamic and Thermal Characteristics of Laminar Slip Flow Over a Horizontal Isothermal Flat Plate

[+] Author and Article Information
Jawad Lahjomri

e-mail: Lahjomri@hotmail.com

Abdelaziz Oubarra

Laboratory of Mechanics,
Faculty of Science Ain Chock,
Hassan II University, B.P. 5366,
Maarif, Casablanca, 20100, Morocco

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received October 28, 2011; final manuscript received August 3, 2012; published online January 3, 2013. Assoc. Editor: Bruce L. Drolen.

J. Heat Transfer 135(2), 021704 (Jan 03, 2013) (9 pages) Paper No: HT-11-1490; doi: 10.1115/1.4007412 History: Received October 28, 2011; Revised August 03, 2012

In this paper, hydrodynamic and thermal characteristics of laminar incompressible slip flow over an isothermal semi-infinite flat plate at a relatively low Mach number are considered and revised. The nonsimilar and local similarity solutions of the boundary layer equations with velocity-slip and temperature-jump boundary conditions are obtained numerically for the gaseous slip flow. The numerical calculations are made by assuming no thermal jump for the liquid flow. In addition, the approximate analytical solution of the boundary layer equations for high slip parameter is presented. Results from nonsimilar solution, local similarity approach, and approximate analytical solution are compared. We show that the local similarity approach used by several authors in the last decades produces substantial errors in hydrodynamic and thermal characteristics of the flow. Furthermore, accurate correlations of these characteristics are proposed for gaseous and liquid slip flows. The results of nonsimilar solution show, unlike the previous studies, that the overall skin friction coefficient presents a very slight decrease (indistinguishable) in the interval of the slip flow regime, whereas it decreases significantly as the flow becomes more rarefied. Moreover, with increasing slip condition, the results of overall Nusselt number, for gaseous flow, show that the heat transfer at the plate decreases slightly in the interval of slip flow regime while it increases in the case of liquids flow. This study confirms that for the accurate prediction of characteristics of slip flow, the slip parameter must be treated as a variable rather than a constant in the boundary layer.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Karniadakis, G., Beskok, A., and Aluru, N., 2005, Microflows and Nanoflows: Fundamentals and Simulation, Springer, NY, p. 60, 400.
Gad-el-Hak, M., 2006, The MEMS Handbook, MEMS: Introduction and Fundamentals, 2nd ed., Taylor & Francis Group, London.
Martin, M. J., and Boyd, I. D., 2001, “Blasius Boundary Layer Solution With Slip Flow Conditions,” Rarefied Gas Dynamics: 22nd International Symposium, Sydney, Australia, July 9–14, T. J.Bartel and M. A.Gallis, eds., American Institute of Physics, AIP Conf. Proc., 585(1), pp. 518–523. [CrossRef]
Anderson, H. I., 2002, “Slip Flow Past a Stretching Surface,” Acta Mech., 158, pp. 121–125. [CrossRef]
Fang, T., and Lee, C. F., 2005, “A Moving-Wall Boundary Layer Flow of a Slightly Rarefied Gas Free Stream Over a Moving Flat Plate,” Appl. Math. Lett., 18, pp. 487–495. [CrossRef]
Vedantam, N. K., and Parthasarathy, R. N., 2006, “Effects of Slip on the Flow Characteristics of Laminar Flat Plate Boundary-Layer,” Proceedings of ASME Fluids Engineering Summer Meeting, Miami, FL, pp. 1551–1560. [CrossRef]
Martin, M. J., and Boyd, I. D., 2006, “Momentum and Heat Transfer in a Laminar Boundary Layer With Slip Flow,” J. Thermophys. Heat Transfer, 20(4), pp. 710–719. [CrossRef]
Cao, K., and Baker, J., 2009, “Slip Effects on Mixed Convective Flow and Heat Transfer From a Vertical Plate,” Int. J. Heat Mass Transfer, 52, pp. 3829–3841. [CrossRef]
Aziz, A., 2010, “Hydrodynamic and Thermal Slip Flow Boundary Layers Over a Flat Plate With Constant Heat Flux Boundary Condition,” Commun. Nonlinear Sci. Numer. Simul., 15, pp. 573–580. [CrossRef]
Bhattacharyya, K., Mukhopadhyay, S., and Layek, G. C., 2011, “MHD Boundary Layer Slip Flow and Heat Transfer Over a Flat Plate,” Chinese Phys. Lett., 28(2), p. 024701. [CrossRef]
Martin, M. J., and Boyd, I. D., 2010, “Falkner-Skan Flow Over a Wedge With Slip Boundary Conditions,” J. Thermophys. Heat Transfer, 24(2), pp. 263–270. [CrossRef]
Rahman, M. M., and Eltayeb, I. A., 2011, “Convective Slip Flow of Rarefied Fluids Over a Wedge With Thermal Jump and Variable Transport Properties,” Int. J. Therm. Sci., 50(4), pp. 468–479. [CrossRef]
Turkyilmazoglu, M., 2012, “Multiple Analytic Solutions of Heat and Mass Transfer of Magnetohydrodynamic Slip Flow for Two Types of Viscoelastic Fluids Over a Stretching Surface,” ASME J. Heat Transfer, 134, p. 071701. [CrossRef]
Izan, H., and Homayoni, H., 2008, “Analysis of Flow on a Moving Flat Plate in Slip Regime by Pseudo Spectral Method,” 2nd European Computing Conference (ECC’08), Malta, pp. 373–378.
Yazdi, M. H., Abdullah, S., Hashim, I., Zaharim, A., and Sopian, K., 2008, “Friction and Heat Transfer in Slip Flow Boundary Layer at Constant Heat Flux Boundary Conditions,” 10th WSEAS International Conference on Mathematical Methods, Computational Techniques, and Intelligent Systems, Greece.
Fazio, R., 2008, “Transformation Methods for the Blasius Problem and Its Recent Variants,” Proceedings of the World Congress on Engineering 2008 (WCE 2008), London, UK, Vol. 2.
Ajadi, S. O., Adegoke, A., and Aziz, A., 2009, “Slip Boundary Layer Flow of Non-Newtonian Fluid Over a Flat Plate With Convective Thermal Boundary Condition,” Int. J. Nonlinear Sci., 8(3), pp. 300–306. Available at http://www.world academicunion.com/journal/1749-3889-3897IJNS/IJNSVol08No3Paper06.pdf
Fazio, R., 2009, “Numerical Transformation Methods: Blasius Problem and Its Variants,” Appl. Math. Comput., 215, pp. 1513–1521. [CrossRef]
Mirels, H., 1952, “Estimate of Slip Effect on Compressible Laminar-Boundary-Layer Skin Friction,” Report No. NACA-TN-2609, pp. 1–22.
Thompson, P. A., and Troian, S. M., 1997, “A General Boundary Condition for Liquid Flow at Solid Surfaces,” Nature, 389, pp. 360–362. [CrossRef]
Tretheway, D. C., and Meinhart, C. D., 2002, “Apparent Fluid Slip at Hydrophobic Microchannel Walls,” Phys. Fluids, 14(3), pp. L9–L12. [CrossRef]
Schlichting, H., 1979, Boundary Layer Theory, 7th ed., McGraw-Hill, Inc., New York, pp. 293–295.
Schaaf, S. A., and Talbot, L., 1959, “Handbook of Supersonic Aerodynamics: Mechanics of Rarefied Gases,” Section 16, Vol. 5, Johns Hopkins University Applied Physics Laboratory, ed., Maryland, NAVORD Report No. 1488.
Schaaf, S. A., and Sherman, F. S., 1954, “Skin Friction in Slip Flow,” J. Aeronaut. Sci., 21(2), pp. 85–90. [CrossRef]
Fazio, R., 1992, “The Blasius Problem Formulated as a Free Boundary Value Problem,” Acta Mech., 95, pp. 1–7. [CrossRef]
Fazio, R., 1996, “A Novel Approach to the Numerical Solution of Boundary Value Problems on Infinite Intervals,” SIAM J. Numer. Anal., pp. 1473–1483. [CrossRef]


Grahic Jump Location
Fig. 1

Spatial variation of total local truncation error for stream function (a) and temperature field (b) for three different selected grids; grid 1 (Δη=1/4,ΔK=1/4), grid 2 (Δη=1/8,ΔK=1/8), and grid 3 (Δη=1/16, ΔK=1/32) for K = 0.74

Grahic Jump Location
Fig. 2

Dimensionless x-component of velocity profiles in the boundary layer for various values of slip parameter K

Grahic Jump Location
Fig. 3

Dimensionless y-component of velocity profiles in the boundary layer for various values of slip parameter K

Grahic Jump Location
Fig. 4

Influence of slip parameter on the local skin friction obtained by different models and comparison with the result of Martin and Boyd [7]

Grahic Jump Location
Fig. 5

Influence of slip parameter on the overall skin friction obtained by different models and comparison with correlation, Eq. (37)

Grahic Jump Location
Fig. 6

Influence of slip parameter on the local heat transfer obtained by different models for various values of Prandtl number

Grahic Jump Location
Fig. 7

Effect of Prandtl number on the variation of overall Nusselt number with the slip parameter obtained by different models and comparison with the correlations Eqs. (38)(40)

Grahic Jump Location
Fig. 8

Overall heat transfer as function of slip parameter for liquid flow with various values of Prandtl number, calculated from nonsimilar solution



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In