On the use of Clifford algebra \(C\ell _3(\mathbb {C})\) to model solid and fluid mechanics for application to an electrodynamic sensor

For many applications, it can be useful to consider multivectorial algebra, taking benefits of multidimensional tools, especially for multiphysical applications. It can be applied for problems of fluid mechanics or solid mechanics. It can also be useful for electrodynamics, as well as the couplings between these domains. For the latters, multivectorial approaches are generally disregarded for different reasons (simplicity, ignorance...), whereas the use of such a more advanced algebra can present interesting properties for modelling of physical and mechanical systems. The aim of this article is to present applications of Clifford algebra \(C\ell _3(\mathbb {C})\) $C{\ell }_3(\mathbb{C})$ to model the motion of a chain of magnets in a fluid flow, leading to electromagnetism induction in a flat coil, that can be used as a sensor. Reversible as well as irreversible phenomena can thus be considered by use of biquaternions to describe such a case.