Funct. Mater. 2024; 31 (1): 96-109.

doi:https://doi.org/10.15407/fm31.01.96

Three-dimensional magnetohydrodynamic Casson flow of a dust nanofluid over a stretching porous sheet: exact solutions

M.I. Kopp1, V.V. Yanovsky1,2

1Institute for Single Crystals, NAS Ukraine, Nauky Ave. 60, Kharkov 61001, Ukraine
2V.N. Karazin Kharkiv National University 4 Svobody Sq., Kharkov 61022, Ukraine

Abstract: 

In this paper, the stationary three-dimensional (3D) magnetohydrodynamic Casson flow of a nanofluid containing dust particles over a porous, linearly stretching sheet is considered. The sheet is assumed to be stretched in both directions along the xy plane. The nanofluid is presented as a suspension of water-based nanoparticles. In this study, we investigate the effects of nanoparticle size and inter-particle distance factors on the properties of the nanofluid flow. The mathematical model contains the basic equations in the form of three-dimensional partial differential equations for the fluid and dust phases, and these equations are transformed into dimensionless ordinary-dimensional equations using an appropriate similarity transformation. Exact analytical solutions to this boundary value problem are obtained. The effects of various physical values on dust and nanofluid velocities are discussed in detail, including the magnetic parameter, Casson parameter, porosity parameter, fluid-particle interaction parameter, mass concentration of dust particles, and nanoparticle size. The current analytical solutions show good agreement with previously published numerical investigations in a few particular cases.

Keywords: 
MHD Casson flow, nanofluid, dust particles, nanoparticle size, stretching sheet, analytical solutions.

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