Kelvin force in a layer of magnetic fluid

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.