Unsteady Carreau fluid flow in three-dimensional magnetohydrodynamics with a viscous dissipation effect

Abstract

A numerical investigation has been conducted on the 3D magnetohydrodynamic (MHD) flow of an incompressible Carreau fluid over a stretchable surface. Mathematical modeling is performed to represent the laws of conservation of mass, momentum, and heat transfer. An appropriate transformation transforms the governing partial differential equations (PDE) into the dimensionless ordinary differential equations (ODEs). To solve ODEs, we used the shooting technique with fourth order Adams-Moulton method implemented in a Fortran programming language. The validity of the computed results is established by benchmarking them against previously published findings in the literature. Key parameters influencing the flow are illustrated and discussed through graphical representations. The overall results indicate that the velocity profile diminishes with increasing magnetic parameter, while it increases in response to higher values of the Hall parameter and Weissenberg number. The fluid flow model examined in this study finds applications in nuclear reactor cooling systems, polymer extrusion processes, electromagnetic pumping, astrophysical plasma flows, and magnetohydrodynamic generators. Engineering and industrial quantities of interest, such as local skin friction and heat transfer rates, have been calculated and thoroughly discussed.