The thermoacoustic devices process various nonlinear effects in high noise levels originating from the interaction between the acoustic oscillations in the fluid and thermal and mechanical conditions on the solid walls. Many theoretical, experimental and numerical models have been proposed to interpret these complex phenomena. A numerical model is presented to describe first the acoustic field in thermoviscous fluid and second the induced phenomena such as acoustic streaming and heat transfer. The equations of the model are derived from the instantaneous mass, momentum and energy conservation equations. The formulation for heat transfer and streaming flow is presented as a standard form of weak compressible flow based on the separation of time scales, using the velocity of mass transport vector, and where exciting terms for these slow effects appear in the second member. These terms relate the average contribution of the fluctuating field, and the nonlinear effects of acoustics are considered as source terms. The unsteady streaming flow and heat transfer is presented in various acoustic devices, showing the ability of this formulation to compute numerically the slow phenomena induced by acoustics and illustrating the physics in annular or resonant thermoacoustic devices.