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. 2021 Jan 12;11:733. doi: 10.1038/s41598-020-79871-1

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Physical model of particle interaction. A physical model of particle interaction as a function of the concentration of nanofluids during MNFH considering magnetic dipole interaction energy (E_dip), magnetic potential energy (E_p), magnetic exchange energy (E_ex), and magnetization reversal of each nanoparticle under AC magnetic field by spin rotation enabling to elucidating concentration-dependent oscillation behavior of SLP changes. (a,b) Summary of experimental results (a) and possible particle interaction models (b) at the AC magnetic field interpreted by means of interparticle distance (d_c–c).