Exact Analytic Solution of a Boundary Value Problem for the Falkner–Skan Equation

Abstract

The Falkner-Skan equation, subject to appropriate physical boundary conditions arising from boundary layer theory, is exactly solved. The results obtained from this solution are compared with the numerical solution. The Blasius equation, subject to the same boundary conditions, is also solved exactly; the solution is compared with the earlier work on this equation. The analytic solution presented here agrees closely with the corresponding numerical results.

A new exact solution for boundary layer flow over a stretching plate

“…This paper devices a method that helps in obtaining a new exact analytical solution of the Falkner-Skan equations (4) and (5) for general values of b. In the following section this has been achieved using the method pioneered by Sachdev et al [14].…”

“…This unknown a 2 characterizes the coefficient of skin friction, must be obtained such that the derivative condition at 1 is satisfied (see the last boundary condition in (5)). This is equivalent to determine the value of either a 2 of the series (14) or f 00 ð0Þ of systems (4) and (5) because these are intrinsically related to each other through Eq. (10):…”

“…Liao [12] developed and implemented successfully a homotopy analysis method for the solution of the FalknerSkan equation for general value of b. Fang and Zhang [13] have given an exact solution of the Falkner-Skan equation for b ¼ À1 and explored a different branches of solutions. Recently, Sachdev et al [14] have found a new way of solving the Falkner-Skan equation for general b. In their study, exact analytical solution for b ¼ À1 is obtained in terms of error and exponential functions which is then used to give exact solution for general b. Kudenatti and Awati [15] have applied the above method, as pioneered by Sachdev et al [14] Contents lists available at SciVerse ScienceDirect for the solution of the Falkner-Skan equation for general b for a fixed plate and the plate with suction or injection.…”

“…Recently, Sachdev et al [14] have found a new way of solving the Falkner-Skan equation for general b. In their study, exact analytical solution for b ¼ À1 is obtained in terms of error and exponential functions which is then used to give exact solution for general b. Kudenatti and Awati [15] have applied the above method, as pioneered by Sachdev et al [14] Contents lists available at SciVerse ScienceDirect for the solution of the Falkner-Skan equation for general b for a fixed plate and the plate with suction or injection.…”

Solution of pressure gradient stretching plate with suction

“…He also gave closed form solution for b = À1 and asymptotic solutions for some special cases. Recently, Sachdev et al [11] have proposed a new scheme for the solution of the Falkner-Skan equation for general b and recovered all possible results of Riley and Weidman [9].…”