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.

References

1.
Karniadakis
,
G.
,
Beskok
,
A.
, and
Aluru
,
N.
,
2005
,
Microflows and Nanoflows: Fundamentals and Simulation
,
Springer
,
NY
, p.
60
, 400.
2.
Gad-el-Hak
,
M.
,
2006
,
The MEMS Handbook, MEMS: Introduction and Fundamentals
, 2nd ed.,
Taylor & Francis Group
,
London
.
3.
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
.10.1063/1.1407604
4.
Anderson
,
H. I.
,
2002
, “
Slip Flow Past a Stretching Surface
,”
Acta Mech.
,
158
, pp.
121
125
.10.1007/BF01463174
5.
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
.10.1016/j.aml.2004.08.006
6.
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
.10.1115/FEDSM2006-98151
7.
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
.10.2514/1.22968
8.
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
.10.1016/j.ijheatmasstransfer.2009.02.013
9.
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
.10.1016/j.cnsns.2009.04.026
10.
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
.10.1088/0256-307X/28/2/024701
11.
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
.10.2514/1.43316
12.
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
.10.1016/j.ijthermalsci.2010.10.020
13.
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
.10.1115/1.4006165
14.
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
.
15.
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
.
16.
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
.
17.
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
18.
Fazio
,
R.
,
2009
, “
Numerical Transformation Methods: Blasius Problem and Its Variants
,”
Appl. Math. Comput.
,
215
, pp.
1513
1521
.10.1016/j.amc.2009.07.019
19.
Mirels
,
H.
,
1952
, “
Estimate of Slip Effect on Compressible Laminar-Boundary-Layer Skin Friction
,” Report No. NACA-TN-2609, pp.
1
22
.
20.
Thompson
,
P. A.
, and
Troian
,
S. M.
,
1997
, “
A General Boundary Condition for Liquid Flow at Solid Surfaces
,”
Nature
,
389
, pp.
360
362
.10.1038/39475
21.
Tretheway
,
D. C.
, and
Meinhart
,
C. D.
,
2002
, “
Apparent Fluid Slip at Hydrophobic Microchannel Walls
,”
Phys. Fluids
,
14
(
3
), pp.
L9
L12
.10.1063/1.1432696
22.
Schlichting
,
H.
,
1979
,
Boundary Layer Theory
, 7th ed.,
McGraw-Hill, Inc.
,
New York
, pp.
293
295
.
23.
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.
24.
Schaaf
,
S. A.
, and
Sherman
,
F. S.
,
1954
, “
Skin Friction in Slip Flow
,”
J. Aeronaut. Sci.
,
21
(
2
), pp.
85
90
.10.2514/8.2936
25.
Fazio
,
R.
,
1992
, “
The Blasius Problem Formulated as a Free Boundary Value Problem
,”
Acta Mech.
,
95
, pp.
1
7
.10.1007/BF01170800
26.
Fazio
,
R.
,
1996
, “
A Novel Approach to the Numerical Solution of Boundary Value Problems on Infinite Intervals
,”
SIAM J. Numer. Anal.
, pp.
1473
1483
.10.1137/S0036142993252042
You do not currently have access to this content.