Asymptotic analysis to free-convective boundary-layer problem by homotopy renormalization method

In this paper, the homotopy renormalization (HTR) method is applied to investigate a free-convective boundary-layer problem arising from the sheet (or fiber) manufacturing, which is modeled by a system of nonlinear ordinary differential equations. By taking the inhomogeneous variable coefficient homotopy equations, the explicit asymptotic solutions satisfying the boundary conditions are given. Moreover, the comparisons with the numerical results show that our explicit function solutions have good performances in both local and large scales.