Application of homotopy perturbation method in inverse analysis of Jeffery–Hamel flow problem

Abstract Different authors have studied incompressible fluid flow through two inclined planes. Previous authors have used different numerical methods to find the velocity profile of fluid flow for Jeffery–Hamel problem, which is known as the forward problem. It may be interesting to study the inverse problems related to the above. In that case, the velocity profile may be known and then the angle between two inclined planes is required to be found. Accordingly, in this article, we have first used Homotopy Perturbation Method (HPM) to find the velocity profile for a fixed angle. Further, by using this velocity profile, we have found the required angle in between the inclined planes. For these, different approximations via HPM are computed and it has been shown that the identified fixed angle converges, giving the required angle. The novelty of the procedure is that if we have the velocity profile from the experiment, then we may use the same procedure to know the targeted angle. This may also be generalized to other inverse problems, and also we may similarly find other parameters.