Solutions to Higher-Order Boundary-Layer Equations for Flow over a Semi-Infinite Plate

L.K. Chi* U.S. Naval Academy, Annapolis, Md. and Shih-liang Went Ohio University, Athens, Ohio where x and u are made dimensionless by referring to an arbitrary length L and the velocity (7, respectively, y and v are measured against \Tf/L and V77£7, respectively. The fluid density is constant throughout the entire flowfield. The dimensionless temperature T is also constant. The Reynolds number R is given by R = UL/y where y is the kinematic viscosity. We assume that R is large. First, we can eliminate P in Eqs. (2) and (3) by cross differentiation. Then, we let u = y and v= -^rx so that Eq. (1) is automatically satisfied and Eqs. (2) and (3) can be combined into a single equation in ¥. Furthermore, we assume that ^ can be expanded in a power series of R ~: