On implementation of a semi-analytic strategy to develop an analytical solution of a steady-state isothermal tube drawing model

In this paper, we consider an isothermal glass tube drawing model consisting of three coupled nonlinear partial differential equations. The steady-state solution of this model is required in order to investigate its stability. With the given initial and boundary conditions, it is not possible to determine an analytical solution of this model. The difficulty lies in determining the constants of integrations while solving the second order ordinary differential equation analytically appearing in the steady-state model. To overcome this difficulty, we present a numerical based approach for the first time to develop an analytical solution of the steady-state isothermal tube drawing model. We use a numerical technique called shooting method to convert the boundary value problem into a set of initial value problems. Once the model has been converted into a system of differential equations with initial values, an integrating technique is implemented to develop the analytical solution. The computed analytical solution is then compared with the numerical solution to better understand the accuracy of obtained solution with necessary discussions.

Automated summary

In this paper, an isothermal glass tube drawing model composed of three coupled nonlinear partial differential equations is studied. The steady-state solution is obtained using a numerical based approach, where the boundary value problem is converted into a set of initial value problems and an integrating technique is implemented to develop the analytical solution.