Instantaneous acoustic heating of a viscous fluid flow in a boundary layer is the subject of investigation. The governing equation of acoustic heating is derived by means of a special linear combination of conservation equations in the differential form, which reduces all acoustic terms in the linear part of the final equation but preserves terms belonging to the thermal mode. The procedure of decomposition is valid in a weakly nonlinear flow, it yields the nonlinear terms responsible for the modes interaction. Nonlinear acoustic terms form a source of acoustic heating in the case of the dominative sound. This acoustic source reflects the thermoviscous and dispersive properties of a fluid flow. The method of deriving the governing equations does not need averaging over the sound period, and the final governing dynamic equation of the thermal mode is instantaneous. Some examples of acoustic heating are illustrated and discussed, and conclusions about efficiency of heating caused by different waveforms of sound are made.

This study is devoted to the instantaneous acoustic heating of a shear-thinning fluid. Apparent viscosity of a shear-thinning fluid depends on the shear rate. That feature distinguishes it from a viscous Newtonian fluid. The special linear combination of conservation equations in the differential form makes it possible to derive dynamic equations governing both the sound and non-wave entropy mode induced in the field of sound. These equations are valid in a weakly nonlinear flow of a shear-thinning fluid over an unbounded volume. They both are instantaneous, and do not require a periodic sound. An example of a sound waveform with a piecewise constant shear rate is considered as a source of acoustic heating.

Excitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoretically considered in this work. The dynamic equation for an excess density which specifies the entropy mode, has been obtained by means of the method of projections. It takes the form of the diffusion equation with an acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient is proportional to the thermal conduction, and the acoustic force is proportional to the total attenuation. Theoretical description of instantaneous heating allows to take into account aperiodic and impulsive sounds. Acoustic heating in a half-space and in a planar resonator is discussed. The aim of this study is to evaluate acoustic heating and determine the contribution of thermal conduction and mechanical viscosity in different boundary problems. The conclusions are drawn for the Dirichlet and Neumann boundary conditions. The instantaneous dynamic equation for variations in temperature, which specifies the entropy mode, is solved analytically for some types of acoustic exciters. The results show variation in temperature as a function of time and distance from the boundary for different boundary conditions.

Nonlinear phenomena of the planar and quasi-planar magnetoacoustic waves are considered. We focus on deriving of equations which govern nonlinear excitation of the non-wave motions by the intense sound in initially static gaseous plasma. The plasma is treated as an ideal gas with finite electrical conductivity permeated by a magnetic field orthogonal to the trajectories of gas particles. This introduces dispersion of a flow. Magnetoacoustic heating and streaming in the field of periodic and aperiodic magnetoacoustic perturbations are discussed, as well as generation of the magnetic perturbations by sound. Two cases, corresponding to magnetosound perturbations of low and high frequencies, are considered in detail.

The magnetoacoustic heating of a plasma by harmonic or periodic saw-tooth perturbations at a transducer is theoretically studied. The planar fast and slow magnetosound waves are considered. The wave vector may form an arbitrary angle θ with the equilibrium straight magnetic strength. In view of variable θ and plasma-β, the description of magnetosound perturbations and relative magnetosound heating is fairly difficult. The scenario of heating depends not only on plasma-β and θ, but also on a balance between nonlinear attenuation at the shock front and inflow of energy into a system. Under some conditions, the average over the magnetosound period force of heating may tend to a positive or negative limit, or may tend to zero, or may remain constant when the distance from a transducer tends to infinity. Dynamics of temperature specifying heating differs in thermally stable and unstable cases and occurs unusually in the isentropically unstable flows.