Kelvin force in a layer of magnetic fluid

TL;DR

This paper investigates the Kelvin force in a magnetic fluid layer under uniform magnetic field and heating, demonstrating the equivalence of different formulations and analyzing the impact of approximations.

Contribution

It clarifies the relationship between the usual and new Kelvin force formulations, showing their equivalence and the effects of approximations.

Findings

The usual and new Kelvin force formulations are equivalent.

Differences between formulations arise only with approximations.

The study enhances understanding of magnetic fluid behavior under magnetic fields.

Abstract

The Kelvin force in a layer of magnetic fluid subjected to a homogeneous magnetic field and local heating is studied. The study is motivated by the question about the corresponding Kelvin force density [M. Liu, Phys. Rev. Lett., 2762 (2000)]. It is shown that the usual and the newly proposed formulation of the Kelvin force are entirely equivalent. It is only when approximations are introduced that differences arise.