Efficiency of acoustic heating produced in the thermoviscous flow of a fluid with relaxation

Abstract

Abstract:Instantaneous acoustic heating of a fluid with thermodynamic relaxation is the subject of investigation. Among others, viscoelastic biological media described by the Maxwell model of the viscous stress tensor, belong to this type of fluid. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in the linear part of the final equation, but preserving terms belonging to the thermal mode responsible for heating. The procedure of decomposition is valid for weakly nonlinear flows, resulting in the nonlinear terms responsible for the modes interaction. Nonlinear acoustic terms form a source of acoustic heating in the case of dominative sound, which reflects the thermoviscous and dispersive properties of a fluid. 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, conclusions about efficiency of heating caused by different sound impulses are made. 43.25.-x PACS (2008):

Thermal self-action effects for acoustic beams containing fronts in a Maxwell relaxing fluid

“…(3) includes a linear term in its left-hand side originating from the thermal conduction. A discussion of the incorporation of the first and second viscosities and the thermal conduction of a fluid in the dynamic equation for acoustic heating, is found in [14]. In this study, we account for thermal conduction in the linear part of Eq.…”

“…With regard to the right-hand side of Eq. (3), its derivation is explained in detail in [14]. In Ref.…”

“…The system of equations describing thermal self-action in an axially symmetric flow of a relaxing fluid take the form [4,11,14]:…”

Non-Wave Variations in Temperature Caused by Sound in a Chemically Reacting Gas

“…The numerical simulations reveal that an efficiency of acoustic heating (or cooling) does not depend on waveforms associated to the entropy mode if the energy of waves is the same, independently of a sign of B * ∞ . However, in media with different relaxation process, for example the Maxwell relaxation taking place in viscoelastic biological media, efficiency of acoustic heating may depend on the sound waveform [10].…”