Numerical Investigations For The Viscous Laminar Flow Near A Semi-Porous Slider

Many problems have been studied involving the influence of a mass transfer through a porous surface upon a viscous laminar fluid flow. In a previous paper Skalak & Wang (1975) considered the two-dimensional case of a long porous slider. We continue this work, considering the influence of a positive mass transfer (suction) through either the slider or the opposite plate. Assuming a constant gap between the two surfaces, the problem admits solutions of Berman's similarity form. The velocity is expressed in the form of a unique complementary function W describing the vertical velocity. The fluid flow is described by a set of coupled non-linear differential equations with conditions on two boundaries. The solution of Berman's equation is not unique for the case of a fluid suction. In addition, the characteristics of the flow including velocity, drag and temperature are described. The temperature is non-coupled with the component U. But, for a particular Re, we find a non-physical numerical discontinuity for the horizontal velocity. The same particular value is equally found using a finite element software TRIO without any simplified hypothesis for the velocity. The purpose of this note is to show that the quasilinearization method gives rapid convergence to solutions of boundary-layer problems from uninspired initial guesses.