A generalized theoretical formulation for the acoustic wave propagating in a narrow tube with steady gas flow is carried out considering visco-thermal effects on the boundary. The theory employs the concept of the transverse variational function of previous works and includes mean flow effect. While the simplified form of present analysis permits comparison with previous results dealing with visco-thermal effects, it includes novel features of Poiseuille-type laminar steady flow and temperature gradient. The resultant formula reduces exactly to the theory of Zwikker and Kosten, when no flow is presented. A fully-developed condition of steady flow is assumed and the propagation constant is introduced to linearize the governing differential equations. Simulations show that the flow affect the wave on phase shift and the temperature gradient on attenuation or amplification within the region of boundary layer. These two effects on acoustic wave are not independant of each other, but are coupled especially when steady flow is dominated. The theory is useful in solving the acoustic problems of the porous structures in thermoacoustic engines and monolithic catalytic converters in automotive exhaust systems, along which temperature gradient and/or gas flow exist. The averaged heat-flux and the coefficient of performance of the thermoacoustic refrigerator are calculated and a parametric study is performed. In addition, a catalytic converter is modeled as a combined system of several elements including two reactive conical diffusers and a dissipative porous structure. By using the derived 4-pole parameters for each elements, the transmission loss for the entire system is predicted and examined varying the mean flow Mach number and the temperature gradient.
