Abstract
The purpose of this paper is to provide a new analytical exact solution for the crystallization phenomena pyrolysis process of the non-isothermal nth-order instead of using numerical methods. A more considerable solution has been obtained and compared with the approximate numerical solution. The multi-order reactions of crystallization kinetics are demanded in a wide variety of short time and length scales. In addition, our solution adds an accurate result using different kinetic parameters such as pre-exponential factor and activation energy.