Given the severe threat that granular flow hazards pose to human life and property, the study of granular flow models is crucial. We constructed the corresponding differential equation here to model the boundary layer problem of granular flow traveling down an inclined surface with external force. Due to the fact that the friction coefficient \(\mu (I)\) depends on the inertial number I, the equation we established here is different from traditional models. And this equation contains some famous equations as special examples, for example the Blasius equation and the Falken-Skan equation. In this paper, by using the homotopy renormalization method (HTR), we construct a simple explicit asymptotic solution to this problem with various values of \(\alpha \) , namely \(\alpha =1\) , 0.5 and 0, and other conditions could be handled very similarly. In fact, our results are not only asymptotical, but also very precise over the whole domain. This conclusion is verified by both a theoretical analysis and numerical simulations. Considering the significances of the model in fluid dynamics, the asymptotic solution we obtain can be practically applied in the real physical world.
