Abstract
The velocity profile and pressure gradient of an unsteady state unidirectional MHD flow of Voigt fluids moving between two parallel surfaces under magnetic field effects are solved by the Laplace transform method. The flow motion between parallel surfaces is induced by a prescribed inlet volume flow rate that varies with time. Four cases of different inlet volume flow rates are considered in this study including (1) constant acceleration piston motion, (2) suddenly started flow, (3) linear acceleration piston motion, and (4) oscillatory piston motion. The solution for each case is elaborately derived, and the results of associated velocity profile and pressure gradients are presented in analytical forms.
Highlights
Magnetohydrodynamics MHD is an academic discipline, which studies the dynamic behaviors of the interaction between magnetic fields and electrically conducting fluids
The MHD flow is encountered in a variety of applications such as MHD power generators, MHD pumps, MHD accelerators, and MHD flowmeters, and it can be expanded into various industrial uses
We investigate the flow characteristics of the MHD flow of Voigt fluids
Summary
Magnetohydrodynamics MHD is an academic discipline, which studies the dynamic behaviors of the interaction between magnetic fields and electrically conducting fluids. Hayat et al 6 solved for exact solution to some simple flows of an Oldroyd-B fluid between two parallel surfaces with and without pressure gradient. Das and Arakeri 10 gave an analytical solution for various transient volume flow rates for a Newtonian fluid, which complemented with earlier experimental work 11. Hayat et al considered the unsteady flow of an incompressible second-grade fluid in a circular duct with a given volume flow rate variation 17. We, further investigate in this paper the flow characteristics of Voigt fluids under magnetic field effects
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