TITLE:
A Review of Some Reference Analytic Solutions for the Magnetohydrodynamic Flow of Blood
AUTHORS:
Agnès Drochon, Manon Beuque, Dima Abi-Abdallah Rodriguez
KEYWORDS:
Magnetohydrodynamic Flow of Blood, Magnetic Field in Biomedical Applications, Hartmann, Womersley
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.10,
October
30,
2018
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.