We develop a hydrodynamic theory of charge and heat currents induced by traveling waves, such as surface acoustic waves, in graphene devices near charge neutrality. The currents depend on the intrinsic conductivity and viscosity of the electron liquid, the disorder strength, and the geometry of the device. We obtain analytic expressions for the heat and charge currents to second order in the wave amplitude for Hall-bar devices. At charge neutrality and in the absence of DC bias, the heat content is entrained by the wave in the absence of net charge transfer. At the same time, device conductance is enhanced by the wave. Away from charge neutrality, the transport charge current induced by the wave arises in the absence of a DC bias.