Exact analytical solution for the bed depth profile of solids flowing in a rotary kiln

In this communication exact analytical solution of the well known Saemanʹs model equation, which is used to find the bed depth profile of the granular material flowing in a rotary kiln, has been obtained. Mathematically this model equation is characterized by a first order nonlinear ordinary differential equation and the exact analytical solution has been obtained in terms of an implicit form of elementary transcendental function by following the methods of separation of variables and partial fraction decomposition. To the best of the authorsʹ knowledge, this is perhaps the first attempt towards obtaining the exact analytical solution for the above model equation. The results obtained by using the exact analytical solution have been successfully verified against those obtained by using the numerical method and are found to be superior to those obtained by using the existing approximate analytical solutions. Besides, the exact analytical solution has also been fruitfully employed to simulate various experimental results available in literature. Furthermore, the effects of various parameters on the bed depth profile have also been briefly analyzed.