Eur. Phys. J. Special Topics 229, 2991–3007 (2020)
https://doi.org/10.1140/epjst/e2020-000054-1

Regular Article

Towards a theory of magnetic hyperthermia: effect of immobilized chain-like aggregates

¹ Mathematics and Computer Science Department, Faculty of Science, Menoufia University, Shebin El-Kom 32511, Egypt
² Theoretical and Mathematical Physics Department, Institute of Natural Sciences and Mathematics, Ural Federal University, Lenin Avenue 51, Ekaterinburg 620083, Russia
³ M.N. Mikheev Institute of Metal Physics of the Ural Branch of the Russian Academy of Sciences, Ekaterinburg, Russia

^a e-mail: alibakrm@yahoo.com

Received: 2 April 2020
Accepted: 9 September 2020
Published online: 19 November 2020

Abstract

We present results of theoretical approach and mathematical modeling of magnetic hyperthermia produced by aggregates of ferromagnetic nanoparticles immobilized in a non-liquid carrier medium. It is supposed that the particles, due to their magnetic either disperse interaction, can form linear chain-like clusters. The mathematical model of kinetics of the particles remagnetization is formulated and solved for the cases of the single particles as well as for two- and three-particles chains. The limiting cases of the strong and weak internal magnetic anisotropy of the nanoparticles are considered. The results show that the chain-like aggregates reduce the heat production in the case of the strong magnetic anisotropy of the particles and enhances that in the opposite case of the weak anisotropy.