On the analytic solutions of the nonhomogeneous Blasius problem

摘要

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⩽η<∞. Existence and nonuniqueness of solution is also discussed. An implicit relation between the velocity at the wall λ and the shear stress α=f′′(0)  is obtained. The results presented here indicate that two solutions exist in the range 0<λ<λc, for some critical value λc one solution exists for λ=λc, and no solution exists for λ>λc. An analytical value of the critical value of λc was also obtained for the first time.