On the analytic solutions of the nonhomogeneous Blasius problem

In this article a totally analytic solution of the nonhomogeneous Blasius problem is obtained using the homotopy analysis method (HAM). This solution converges for 0 <= eta < infinity. Existence and nonuniqueness of solution is also discussed. An implicit relation between the velocity at the wall lambda and the shear stress alpha = f '' (0) is obtained. The results presented here indicate that two solutions exist in the range 0 <lambda <lambda c, for some critical value lambda(c) one solution exists for lambda = lambda(c), and no solution exists for lambda > lambda(c). An analytical value of the critical value of lambda(c) was also obtained for the first time. (c) 2005 Elsevier B.V. All rights reserved.