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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.

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References

Figures

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

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