Studies in laminar boundary layer theory with suction or injection

Abstract

Chapter I deals with the solution of the full Navier-Stokes equations in the neighbourhood of the leading edge in the presence of suction. We obtain exact solution further downstream on the basis of boundary layer equations without any restriction on the suction or injection velocity. Chapter II deals with the Pohlhausen method modified to deal with the problems of suction or injection. This chapter consists of three parts. In Part I, we first describe the usual modified Pohlhausen method on porous walls and point out its shortcomings. Then, following Torda, we develop a new method which is free from these restrictions. With the help of this new method we obtain general relations describing the variation of boundary layer thickness with arbitrary laws of outer velocity and suction velocity distributions using velocity profiles of degrees four and six. In Part II, we integrate these relations in the closed forms in a number of cases of interest. We have made a comparative study of the new method, using polynomials of different degrees with the modified Pohlhausen method in the presence of suction. Wherever possible, we have compared the present results with the results obtained by the previous workers in order to assess their relative accuracy. In Part III, we apply the new method to solve the problem of the compressible boundary layer flow on a flat plate with no pressure gradient and heat transfer on isothermal wall in the presence of uniform suction. Chapter III deals with the formally exact series solutions. This chapter consists of three parts. In Part I, we generalize the classical Blasius method to treat the boundary layer problem for an arbitrary law of outer velocity distribution. A number of cases treated by the previous workers follow as particular cases of this work. In Part II, we introduce an important simplification in the recent method of Görtler. With this simplification, the analysis becomes much simpler and we expect that the convergence of the series will improve. In Part III, we modify Görtler's transformation for the incompressible fluid to suit the requirements of compressible boundary layer on a body of arbitrary shape with porous wall and with suction or injection according to an arbitrary law of normal velocity distribution on the surface. The analysis holds in the case of no heat transfer when Prandtl number is unity and the viscosity-temperature relation is linear.