  Ferrofluid heating by an external alternating field is studied based on the
rigid dipole model, where the magnetization of each particle in a fluid is
supposed to be firmly fixed in the crystal lattice. Equations of motion,
employing the Newton's second law for rotational motion, the condition of rigid
body rotation, and the assumption that the friction torque is proportional to
angular velocity, are used. This oversimplification permits us to expand the
model easily: to take into account the thermal noise and inter-particle
interaction that allows to estimate from unified positions the role of thermal
activation and dipole interaction in the heating process. Our studies are
conducted in three stages. The exact expressions for the average power loss of
a single particle are obtained within the dynamical approximation. Then, in the
stochastic case, the power loss of a single particle is estimated analytically
using the Fokker-Planck equation and numerically using the effective Langevin
equation. Finally, the power loss for the particle ensemble is obtained using
the molecular dynamics method. Here, the local dipole fields are calculated
approximately based on the Barnes-Hut algorithm. The revealed trends in the
behaviour of both a single particle and the particle ensemble suggest the way
of choosing the conditions for obtaining the maximum heating efficiency. The
competitiveness character of the inter-particle interaction and thermal noise
is investigated in details. Two situations, when the thermal noise rectifies
the power loss reduction caused by the interaction, are described. The first of
them is related to the complete destruction of dense clusters at high noise
intensity. The second one is originated from the rare switching of the
particles in clusters due to thermal activation, when the noise intensity is
relatively weak.
