Abstract
A short review of some reference solutions for the magnetohydrodynamic flow of blood is proposed in this paper. We present in details the solutions of Hartmann (1937), of Vardanyan (1973) and of Sud et al. (1974). In each case, a comparison is provided with the corresponding solution for the flow without any external magnetic field, namely Poiseuille (plane or cylindrical) and Womersley. We also present a synopsis of some other solutions for people who would like to go further in this topic. The interest in MHD flow of blood may be motivated by many reasons, such as Magnetic Resonance Imaging (MRI), Pulse Wave Velocity measurement, magnetic drug targeting, tissue engineering, mechanotransduction studies, and blood pulse energy harvesting… These fundamental solutions should also be used as particular limiting cases to validate any proposed more elaborated solutions or to validate computer codes.
Highlights
A comparison is provided with the corresponding solution for the flow without any external magnetic field, namely Poiseuille and Womersley
The motivation to study the flow of blood in the presence of an external magnetic field has changed over the years: in the years 1960; the aim was, for example, to study the influence of a magnetic field on people who worked in factories, or to try to use the Lorentz force to slow down the speed of blood in case of haemorrhage
The aim of this paper is to focus on some reference solutions for the magnetohydrodynamic flow of blood, a short synopsis of some other solutions is proposed at the end of the paper for people who would like to go further in this topic
Summary
The motivation to study the flow of blood in the presence of an external magnetic field has changed over the years: in the years 1960; the aim was, for example, to study the influence of a magnetic field on people who worked in factories, or to try to use the Lorentz force to slow down the speed of blood in case of haemorrhage.
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