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 Saeman's 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 authors' 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.

Exact analytical solution of the well known Saeman's equation has been obtained. This study also presents the successful simulation of various existing experimental results, comparison of the obtained analytical results with the numerical and available approximate solutions as well as the effects of parameters on results.Figure optionsDownload as PowerPoint slideHighlights
► Exact analytical solution of nonlinear Saeman's model equation has been obtained.
► The obtained results have been successfully verified against numerical results.
► Exact analytical solution effectively simulates available experimental results.
► Exact analytical solution is superior to the existing approximate solutions.
► Effects of various parameters on the bed depth profile have also been analyzed.