Forward and Inverse Problems Related to Nanofluid Flow Between Nonparallel Planes in Uncertain Environment

Abstract

Fluid flow between nonparallel planes has been studied by different authors. Previously, this type of problem has been investigated by considering pure fluid or nanofluid in the constructed channel to find the velocity profile. These are generally known as forward problems. The inverse problem is to compute values of unknown parameters when velocity and remaining parameters may be known. Most of the studies related to the forward problems are reported in a crisp environment. But involved parameters may also be considered as uncertain parameters. In this regard, this article aims to study forward and inverse problems related to nanofluid flow by taking volume fraction as an uncertain parameter in terms of fuzzy number. Here, we have applied the homotopy perturbation method to handle governing differential equation for the considered problem. Firstly, the velocity profile has been computed through various order approximations. Further, the velocity profile is assumed as known, and taking fuzzy volume fraction as an unknown parameter, we have studied the inverse case. Convergence of the obtained results for both forward and inverse cases is also included. The novelty of this research is that if velocity is known to us from some experiments, then targeted unknown parameters may be calculated using the discussed procedure.