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 ≤ 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 < λ_c, for some critical value λ_c one solution exists for λ = λ_c, and no solution exists for λ > λ_c. An analytical value of the critical value of λ _c was also obtained for the first time.