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

Abstract

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.

Non-similar solution of the forced convection of laminar gaseous slip flow over a flat plate with viscous dissipation: linear stability analysis for local similar solution

“…The nonsimilar solutions have been obtained by transforming the physical coordinates (x, y) to dimensionless nonsimilar coordinates (K, g) and the resulting equations have been solved with the finite difference method by using a marching scheme. Unfortunately there seem to be some errors in their transformed equations and related results, as shown by Lahjomri and Oubarra [27]. The latter authors reconsidered and revised the problem by obtaining a correlations which give functional relations of overall skin friction coefficient and Nusselt number with the Reynolds number and the slip parameter.…”

“…Therefore, to solve in the slip flow region, as first approximation, Eqs. (15) and (16) should be solved and extended to a large region of K, including the transitional and free molecular flow regions [27].…”

“…[27,28] and in order to seek non-similar solutions, we introduce the following nonsimilar dimensionless variables:…”

“…It was shown that the hydrodynamic and thermal boundary layer in the rarefied flow regime, the conditions of slip velocity and jump temperature at the wall, leads to the loss of self-similarity of the Blasius flow. Lahjomri and Oubarra [27] have shown recently that the results given by the local similarity method are satisfactory only for small values of K (K B 0.05) and this approach presents a limitation when K becomes large than 0.05 in the interval of slip flow regime. However, the local non similar method although is more precise and powerful than the local similarity approach, it remains approximate method because the partial differential equations after some level of approximation truncation are finally reduced also to ordinary differential equations.…”

“…[27] to obtain non-similarity solution for the pure forced convection of gaseous slip flow over a flat plate due to combined effects of the velocity slip and thermal jump boundary conditions in the presence of viscous dissipation which it was neglected in [27]. The non-linear partial differential equations of momentum and energy according to these boundary conditions are solved numerically with the symbolic algebra software Maple by taking into account of the variation of the stream function and temperature field with the slip parameter.…”