Implementation of Homotopy Perturbation Method to Solve a Population Balance Model in Fluidized Bed

A particle population balance formulation for a circulating fluidized bed, involving aggregation and breakage of particles, is solved using the homotopy perturbation method (HPM). The homotopy method deforms a difficult problem into a simple problem, which then can be easily solved. The HPM solution is compared with the solution obtained using a standard finite difference method. Using homotopy, a good approximation of the finite difference solution is obtained within a few iteration steps. The results reveal that the homotopy method is an effective and simple tool to solve nonlinear partial integro-differential equations and has a wide scope and applicability to solve complex engineering problems. The reliability of the algorithm is tested using three different feed inlet particle size (diameter) distributions to indicate the robustness of this method.