id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ap-364	Červenka, M.; Bednařík, M.; Koníček, P.	Temperature Effects in Acoustic Resonators	2002	5	.pdf	application/pdf	3036	81	58	The one-dimensional form of these equations with terms up to the 2nd order is presented here: Navier- -Stokes equation, see [1], � � � � � � � � � � � � � � � � 0 0 2 02 4 3 v t v t v x a a p x � � � � � � � � � � �� � � � � � � �x r x r v 1 2 2� �� � �� , (1) the continuity equation taking into account the boundary layer, see [2, 3], � � �� � � � � � � � �� � � � � � � � � � � � � �� � t r x r v r x r v v x r 0 2 2 2 2 3 0 2 1 1 Pr � � � � � � � 0 21 2 1 2 r v t x , (2) where the fractional derivative represents an integrodifferen- tial operator � � � � � � �� � � � � �� 1 2 1 2 1f t f t t t t t d (3) and the thermodynamic state equation taking into account heat conductivity and mean temperature change, see [4], � � � � � � � � � � � � � � � � � p c c c c c r p V p 2 0 0 2 0 2 1 2 1 1 1 1 � � � � � � �� � 2 2� �x r v , (4) where � �� , p v, are acoustic density, pressure and velocity, p0 0 0, ,� � are equilibrium state pressure, density and tem- perature, � is mean temperature, �� � � ��, � a a t� is the driving acceleration, x is the spatial coordinate along the reso- nant cavity, t is time, � r r x� is radius of the resonator, � � c cVp is ratio of specific heats at constant pressure and volume, is the coefficient of thermal conduction, �0 is kinematic viscosity, �, � are the coefficients of bulk and shear viscosity, Pr is the Prandtl number, c0 is the small-signal sound speed due to equilibrium temperature �0 and c is the small-signal sound speed due to changed mean temperature defined as c c c2 0 2 0 0 2 0 1� � � � �� �� � �� � � � . 1 1 2 2 2 2 r x r x c t x a t � � �� � � � � � � � � � � � � � � � � � d d , (7) where � is velocity potential, v t� �� � .	cache/ap-364.pdf	txt/ap-364.txt