An exact solution for unsteady three-dimensional magnetohydrodynamic Casson flow of dusty nanofluid over a porous stretching sheet

Abstract

The unsteady three-dimensional (3D) Casson flow of a nanofluid containing dust particles over a porous, linearly stretching sheet in the presence of an external magnetic field is studied. It is assumed that the sheet is stretched in both directions along the xy plane. The governing equations of the two-phase model are partial differential equations that are transformed into ordinary equations using similarity transforms. The nanofluid is a suspension of water-based nanoparticles. In this study, we look at how nanoparticle size affect the properties of dusty nanofluid flow. The mathematical model contains the basic equations for the fluid and dust phases in the form of three-dimensional partial differential equations, which are transformed into dimensionless ordinary-dimensional equations using an appropriate similarity transformation. An exact analytical solution to this boundary value problem is obtained. The effects of various physical values on dust and nanofluid velocities are discussed in detail, including the Casson parameter, magnetic parameter, porosity parameter, fluid-particle interaction parameter, mass concentration of dust particles, and nanoparticle size. In a few specific instances, the current analytical solution demonstrates a good agreement with previously published numerical investigations.